TIMSS Resource Kit

&MATHEMATICS CONCEPTSMATHEMATICS ITEMS8

MATHEMATICS CONCEPTSMATHEMATICS ITEMS

The Mathematics Concepts and Mathematics Items book contains the released TIMSS mathematics assessment items. These are the released items from the 1999 and 2003 assessments (as distinct from the secure items, which are kept confidential so that they may be used in subsequent cycles to monitor trends).

Guide to Using the Mathematics Concepts and Mathematics Items Materials

The materials contained in this book can be used in a number of ways as a tool to assist teachers in making a formative assessment of student knowledge and skills. Some of these ways include the following:

Teacher-designed formative assessments. A teacher might, for example, decide to examine how well his or her class can solve routine problems. In such a case, the first step would be to review the questions in Mathematics Concepts and Mathematics Items, selecting the ones of interest. Ready-to-use versions of these items can be found in the Mathematics Items book. Teachers can print these items or present them to students on an overhead. Student responses can be scored by referring to the appropriate page in Mathematics Concepts and Mathematics Items. Teachers can also compare the overall percentage of students responding correctly to the international benchmark for that item.

Feedback on teaching. To the extent that the items coincide with concepts taught, the teacher might follow the same process to gain rapid feedback on the success of the teaching episode.

Understanding misunderstandings. Again, a teacher might decide to examine the incorrect or partially correct responses of the class for insight into any general misunderstandings, with a view to re-teaching a particular topic or skill.

Identifying individual difficulties. In the same way, the teacher might use the items to identify particular difficulties experienced by individual students, as the basis for some remedial teaching or focused practice.

18675.0206 33

Guide to the Content and Layout of This Book

This book contains the released items from both TIMSS 1999 and TIMSS 2003. Due to slight revisions in terminology and released information between cycles, the format for the items in each cycle differs slightly. Each item appears on a single page and is accompanied by a number of descriptors.

1999 Content Domains:• Fractions and number sense• Algebra• Measurement• Geometry • Data representation, analysis, and probability

2003 Content Domains:• Algebra• Data • Geometry• Measurement• Number

1999 Cognitive Domains:• Knowing• Using routine procedures• Investigating and problem solving• Mathematical reasoning• Communicating

2003 Cognitive Domains:• Knowing facts and procedures• Using concepts• Solving routine problems• Reasoning

Take a look at Calories in a portion of food from ratio, the name given to the first 1999 item in this book. As specified in boxes at the top of the page, the content domain for this item is fractions and number sense and the cognitive domain is investigating and solving problems. Looking at Value of -3x given value of x, the first item from TIMSS 2003 (page 85), the content domain (algebra) and the cognitive domain (knowing facts and procedures) are also accompanied by the Main Topic (algebraic expressions).

International item numbers identify each item. This number appears just below the item box.

Correct answers are shown beneath each item. These correct answers take two forms:

• Letter code. This form is used for the correct response on multiple-choice items. Calories in a portion of food from ratio provides an example of the letter code type—the correct answer is A.

• Scoring guide. This form is used to assist in scoring write-in responses. Division of fractions (J12) further along in the Fractions and number sense domain (page 13), provides an example of the scoring guide approach, indicating the general nature of correct and incorrect responses. In some cases, partial credit may be awarded and these items will provide guidelines for fully correct, partially correct, and incorrect responses.

Sample student responses are provided for TIMSS 2003 extended response items. An example of an actual U.S. eighth-grade student’s response is provided for each scoring category. See item M032557 on page 89.

International benchmarks are provided in a table next to each item. These consist of statistics on the percentage of students in each country who answered the question correctly. The countries are ordered in terms of this percentage. The international average is included as well, and this display also indicates which countries scored significantly higher, significantly lower, and not significantly different from this international average.

Overall Percent Correct

Country average vs.

International average:

Higher �Not different OLower �

Singapore 90 �Korea, Rep. of 86 �Hong Kong, SAR 84 �Chinese Taipei 84 �Slovak Republic 78 �Malaysia 78 �Belgium (Flemish) 78 �Czech Republic 76 �Russian Federation 76 �Thailand 75 �Slovenia 75 �Cyprus 74 �Macedonia, Rep. of 74 OItaly 74 �Moldova 73 OCanada 73 �Hungary 73 ORomania 72 OAustralia 72 ONetherlands 71 OLatvia (LSS) 70 OEngland 70 OInternational Average 69Tunisia 69 ONew Zealand 69 OBulgaria 68 OUnited States 68 OTurkey 66 OIsrael 66 OIran, Islamic Rep. 66 OFinland 65 �Japan 63 �Chile 62 �Jordan 56 �Indonesia 56 �Lithuania 54 �Morocco 53 �Philippines 42 �South Africa 37 �

TIMSS 1999 8th-Grade Mathematics Concepts and Mathematics Items

Content Domain Cognitive Domain

Fractions and Number SenseInvestigating

and Solving Problems

Correct Response: A

3

Calories in portion of food from ratio

Item Number: B08

If there are 300 calories in 100 g of a certain food, how manycalories are there in a 30 g portion of this food?

A. 90

B. 100

C. 900

D. 1000

E. 9000



Fractions and Number Sense Using Complex Procedures

Correct Response: A

4

Singapore 83 �Hong Kong, SAR 82 �Korea, Rep. of 81 �Japan 81 �Chinese Taipei 80 �Malaysia 76 �Belgium (Flemish) 74 �Canada 72 �Netherlands 69 �Slovenia 67 �Australia 65 �Finland 63 �United States 63 �Cyprus 62 ORussian Federation 62 OThailand 61 OEngland 60 OItaly 60 OIsrael 59 OPhilippines 58 OInternational Average 58New Zealand 58 OIran, Islamic Rep. 56 OMoldova 54 OHungary 53 �Bulgaria 52 OSlovak Republic 52 �Lithuania 51 �Jordan 49 �Latvia (LSS) 48 �Czech Republic 46 �Turkey 46 �Chile 46 �Indonesia 46 �Macedonia, Rep. of 45 �Romania 44 �Tunisia 33 �South Africa 29 �Morocco 23 �

Figure showing equivalent fractions

Item Number: B09


Country average vs.





Fractions and Number Sense Knowing

Correct Response: E

5

Smallest decimal fraction

Item Number: B10

Which of these is the smallest number?

A. 0.625

B. 0.25

C. 0.375

D. 0.5

E. 0.125


Country average vs.



Singapore 86 �Hong Kong, SAR 83 �Korea, Rep. of 82 �Netherlands 74 �Japan 73 �Finland 70 �Chinese Taipei 69 �Belgium (Flemish) 67 �Lithuania 61 �Canada 61 �Slovak Republic 60 �Czech Republic 59 �Malaysia 59 �Slovenia 58 �Australia 58 �Hungary 55 �Russian Federation 53 OUnited States 51 OLatvia (LSS) 49 OBulgaria 46 OInternational Average 46England 45 OThailand 45 ONew Zealand 43 OItaly 37 �Tunisia 34 �Morocco 31 �Moldova 31 �Israel 29 �Romania 28 �Cyprus 27 �Jordan 26 �Macedonia, Rep. of 25 �Chile 14 �Iran, Islamic Rep. 10 �Philippines 10 �Indonesia 9 �Turkey 9 �South Africa 6 �




Correct Response: A

6

Hong Kong, SAR 93 �Singapore 90 �Japan 89 �Netherlands 87 �Finland 85 �Chinese Taipei 85 �Canada 83 �Korea, Rep. of 83 �Belgium (Flemish) 82 �Australia 80 �United States 76 �Slovenia 75 �New Zealand 75 �Israel 75 �Cyprus 73 �England 73 �Hungary 71 �Slovak Republic 67 OCzech Republic 65 OMalaysia 65 OInternational Average 62Tunisia 61 OLatvia (LSS) 61 ORussian Federation 59 OBulgaria 59 OJordan 51 �Lithuania 50 �Romania 47 �Italy 46 �Macedonia, Rep. of 44 �Iran, Islamic Rep. 43 �Thailand 42 �Philippines 39 �Turkey 39 �Moldova 38 �Indonesia 38 �South Africa 28 �Morocco 25 �Chile 21 �

Smallest simple fraction

Item Number: D09

Which of these fractions is smallest?

A. 1––6

B. 2––3

C. 1––3

D. 1––2


Country average vs.






Correct Response: B

7

Estimate of point P on number line

Item Number: D12


Country average vs.



Japan 93 �Singapore 91 �Finland 90 �Netherlands 90 �England 88 �Hong Kong, SAR 86 �Belgium (Flemish) 84 �Canada 84 �Australia 83 �Chinese Taipei 81 �United States 81 �Korea, Rep. of 81 �Slovak Republic 80 �Hungary 80 �New Zealand 80 �Malaysia 78 �Slovenia 78 �Latvia (LSS) 78 �Russian Federation 77 �Italy 68 OInternational Average 68Czech Republic 65 OIsrael 64 OThailand 64 OBulgaria 63 OMoldova 63 �Lithuania 61 �Turkey 59 �Chile 54 �Romania 53 �Jordan 53 �Philippines 51 �Macedonia, Rep. of 49 �Indonesia 46 �Cyprus 44 �Morocco 43 �Tunisia 40 �South Africa 38 �Iran, Islamic Rep. 32 �





Correct Response: B

8

Singapore 67 �Chinese Taipei 61 �Hong Kong, SAR 60 �Japan 50 �Malaysia 47 �Russian Federation 45 �Belgium (Flemish) 44 �Korea, Rep. of 43 �Slovak Republic 42 �Bulgaria 41 OSlovenia 41 �Netherlands 40 OHungary 40 �Lithuania 34 OInternational Average 33Romania 33 OCanada 32 OCzech Republic 32 OTurkey 30 OFinland 30 OAustralia 29 OLatvia (LSS) 29 OMoldova 29 OUnited States 28 �Thailand 28 �Indonesia 27 �Israel 27 �Tunisia 26 �Macedonia, Rep. of 26 �New Zealand 25 �Italy 25 �Cyprus 23 �England 22 �Jordan 19 �Iran, Islamic Rep. 19 �Chile 17 �Morocco 16 �South Africa 16 �Philippines 15 �

Average speed from distance and time

Item Number: F07

A runner ran 3000 m in exactly 8 minutes. What was his averagespeed in meters per second?

A. 3.75

B. 6.25

C. 16.0

D. 37.5

E. 62.5


Country average vs.






Correct Response: C

9

Number between two decimal fractions

Item Number: F09

Which of these numbers is between 0.07 and 0.08?

A. 0.00075

B. 0.0075

C. 0.075

D. 0.75


Country average vs.



Singapore 87 �Netherlands 85 �Korea, Rep. of 84 �Belgium (Flemish) 84 �Japan 83 �Chinese Taipei 82 �Hong Kong, SAR 81 �Finland 80 �Canada 78 �Australia 76 �Slovenia 75 �Slovak Republic 74 �England 71 �Lithuania 71 �Czech Republic 70 �Malaysia 70 �United States 70 �Hungary 69 �Russian Federation 69 ONew Zealand 68 OBulgaria 67 OLatvia (LSS) 66 OInternational Average 63Italy 59 OIsrael 57 �Macedonia, Rep. of 56 �Moldova 56 �Thailand 54 �Cyprus 53 �Romania 52 �Tunisia 48 �Chile 42 �Indonesia 40 �Morocco 39 �Jordan 37 �Turkey 35 �Philippines 34 �South Africa 33 �Iran, Islamic Rep. 31 �




Correct Response: C

10

Netherlands 75 �Belgium (Flemish) 73 �England 72 �Hong Kong, SAR 72 �Singapore 71 �Canada 68 �Australia 68 �New Zealand 64 �United States 62 �Chinese Taipei 61 �Japan 61 �Slovenia 59 �Finland 57 �Hungary 56 �Israel 54 OBulgaria 53 OCzech Republic 51 OMalaysia 50 OCyprus 50 OInternational Average 50Korea, Rep. of 50 ORussian Federation 50 OSlovak Republic 49 OItaly 48 OLatvia (LSS) 44 OTunisia 43 �Jordan 40 �Romania 40 �Thailand 39 �Indonesia 39 �Moldova 34 �Morocco 33 �Iran, Islamic Rep. 32 �Chile 32 �Philippines 31 �Lithuania 31 �Turkey 28 �Macedonia, Rep. of 27 �South Africa 26 �

Fraction of circle shaded

Item Number: F12


Country average vs.






Correct Response: E

11

Figure showing fraction of shaded square

Item Number: H08


Country average vs.



Singapore 96 �Belgium (Flemish) 94 �Hong Kong, SAR 94 �Netherlands 92 �Canada 91 �Japan 89 �Chinese Taipei 88 �Finland 87 �Korea, Rep. of 87 �Cyprus 87 �United States 86 �Malaysia 86 �Australia 85 �England 82 �New Zealand 80 �Hungary 78 �Slovenia 78 �Iran, Islamic Rep. 76 �Israel 73 OSlovak Republic 72 OThailand 71 OInternational Average 68Latvia (LSS) 66 OCzech Republic 65 OItaly 63 ORussian Federation 61 OBulgaria 59 �Chile 57 �Jordan 54 �Turkey 53 �Macedonia, Rep. of 49 �Tunisia 48 �Philippines 46 �Lithuania 45 �Moldova 43 �Romania 41 �Indonesia 31 �South Africa 21 �Morocco 7 �




Correct Response: B

12

Singapore 97 �Belgium (Flemish) 96 �Japan 95 �Netherlands 95 �Hong Kong, SAR 93 �Canada 93 �United States 93 �Hungary 93 �Korea, Rep. of 93 �Slovenia 92 �England 92 �Czech Republic 91 �Australia 91 �Finland 91 �Slovak Republic 90 �Chinese Taipei 89 �New Zealand 88 �Malaysia 88 �Latvia (LSS) 87 �Bulgaria 86 �Cyprus 85 �Lithuania 84 ORussian Federation 83 OIsrael 83 OInternational Average 80Macedonia, Rep. of 79 OItaly 77 OThailand 77 OTurkey 74 �Romania 73 �Tunisia 67 �Jordan 66 �Moldova 66 �Chile 65 �Iran, Islamic Rep. 58 �Indonesia 54 �Philippines 53 �Morocco 43 �South Africa 37 �

Sum closest to 691 + 208

Item Number: H09

The sum 691 + 208 is closest to the sum

A. 600 + 200

B. 700 + 200

C. 700 + 300

D. 900 + 200


Country average vs.




13

Division of fractions

Item Number: J12

SCORING

Correct Response

• 10/11

• Other fractions or decimals equivalent to 10/11 (e.g., 30/33, 150/165, .909, .91, etc.)

Incorrect Response

• Any fraction with 2 as a numerator [Divides 6 by 3]

• Other incorrect (including crossed out/erased, stray marks, illegible, or off task)


Fractions and Number Sense Using Routine Procedures


Country average vs.



Singapore 84 �Chinese Taipei 83 �Hong Kong, SAR 81 �Korea, Rep. of 80 �Japan 79 �Slovenia 74 �Russian Federation 72 �Bulgaria 72 �Slovak Republic 71 �Latvia (LSS) 68 �Hungary 66 �Romania 65 �Lithuania 64 �Italy 63 �Belgium (Flemish) 58 �Moldova 57 �Czech Republic 56 OMalaysia 54 �International Average 45Turkey 41 OThailand 40 OUnited States 37 �Iran, Islamic Rep. 34 �Canada 32 �Jordan 32 �Tunisia 29 �Chile 26 �Indonesia 24 �Macedonia, Rep. of 24 �Australia 23 �Israel 22 �Cyprus 21 �Finland 17 �Netherlands 12 �Philippines 11 �New Zealand 10 �South Africa 5 �England 4 �Morocco 4 �

Divide:6 3–– ÷ –– =55 25

Answer: ______________




Correct Response: E

14

Japan 70 �Slovak Republic 69 �Russian Federation 68 �Hong Kong, SAR 66 �Lithuania 65 �Chinese Taipei 64 �Hungary 63 �Korea, Rep. of 61 �Latvia (LSS) 54 �Slovenia 54 �Moldova 53 �Bulgaria 53 �Czech Republic 52 �Belgium (Flemish) 45 OSingapore 45 ONetherlands 44 ORomania 40 OInternational Average 39United States 39 OCanada 39 OMalaysia 39 OMacedonia, Rep. of 38 OItaly 36 OJordan 30 �Finland 29 �Cyprus 26 �Indonesia 24 �Israel 24 �Thailand 23 �New Zealand 21 �Tunisia 21 �Philippines 20 �Australia 20 �South Africa 19 �Chile 18 �England 16 �Turkey 15 �Iran, Islamic Rep. 14 �Morocco 14 �

Division of decimals

Item Number: J14

Divide 0.003)15.45

A. 0.515

B. 5.15

C. 51.5

D. 515

E. 5150


Country average vs.






Correct Response: D

15

Distance between towns from map

Item Number: J18


Country average vs.



Japan 85 �Belgium (Flemish) 83 �Singapore 82 �Malaysia 77 �Lithuania 75 �Chinese Taipei 70 �Slovenia 70 �Netherlands 70 �Latvia (LSS) 68 �Russian Federation 68 �Czech Republic 67 OCanada 65 �Hungary 65 OMoldova 64 OBulgaria 64 OAustralia 64 OItaly 63 OEngland 62 OFinland 61 OCyprus 61 OSlovak Republic 61 OKorea, Rep. of 60 ONew Zealand 58 OInternational Average 57Thailand 56 OTunisia 54 ORomania 51 OJordan 46 �Indonesia 44 �Israel 44 �Macedonia, Rep. of 43 �United States 40 �Iran, Islamic Rep. 37 �Turkey 35 �Chile 30 �South Africa 26 �Morocco 25 �Philippines 24 �




Correct Response: B

16

Singapore 91 �Malaysia 90 �Czech Republic 89 �Slovak Republic 88 �Hungary 88 �Russian Federation 88 �Finland 87 �Chinese Taipei 87 �Korea, Rep. of 87 �Lithuania 87 �Latvia (LSS) 86 �Belgium (Flemish) 85 �Japan 84 �Hong Kong, SAR 83 �Australia 83 �Bulgaria 83 �Netherlands 82 �Slovenia 82 OCanada 79 ONew Zealand 78 OEngland 76 ORomania 76 OMoldova 75 OInternational Average 75Thailand 73 OItaly 73 OUnited States 72 OCyprus 71 OTunisia 70 OMacedonia, Rep. of 69 OTurkey 68 �Israel 68 �Iran, Islamic Rep. 61 �Chile 60 �Indonesia 59 �Jordan 56 �Morocco 43 �Philippines 40 �South Africa 26 �

Length of building compared to car

Item Number: L09


Country average vs.






Correct Response: B

17

Two hundred six and nine-tenths

Item Number: L10

Which number is two hundred six and nine-tenths?

A. 206.09

B. 206.9

C. 206.910

D. 2006.9


Country average vs.



Hungary 97 �Russian Federation 93 �Slovak Republic 90 �Belgium (Flemish) 87 �Iran, Islamic Rep. 83 �Moldova 81 �United States 80 �Netherlands 79 �Korea, Rep. of 78 �Canada 77 �Czech Republic 75 �Jordan 75 �Lithuania 73 OTurkey 72 �Singapore 72 OChinese Taipei 72 �Bulgaria 71 ORomania 71 OFinland 70 OHong Kong, SAR 68 OAustralia 67 OItaly 66 OInternational Average 65Israel 62 OJapan 62 OSlovenia 61 OChile 60 OMalaysia 56 �Latvia (LSS) 55 OCyprus 54 �England 53 �New Zealand 53 �Tunisia 43 �Macedonia, Rep. of 42 �Philippines 42 �Morocco 41 �Thailand 40 �South Africa 31 �Indonesia 23 �




Correct Response: B

18

Singapore 87 �Chinese Taipei 81 �Korea, Rep. of 81 �Belgium (Flemish) 78 �Hong Kong, SAR 77 �Japan 75 �Malaysia 71 �Russian Federation 64 �Slovenia 63 �Slovak Republic 62 OHungary 60 OLithuania 58 OCanada 57 OCzech Republic 55 ONetherlands 55 OUnited States 55 OInternational Average 52Indonesia 51 OFinland 51 OThailand 51 OLatvia (LSS) 50 ORomania 50 OBulgaria 48 OAustralia 48 OCyprus 47 OIsrael 44 �Turkey 44 �Moldova 43 OItaly 43 �New Zealand 41 �Jordan 40 �Macedonia, Rep. of 37 �Iran, Islamic Rep. 36 �Tunisia 36 �Philippines 35 �England 34 �Chile 32 �South Africa 23 �Morocco 16 �

Subtraction with three fractions

Item Number: L18

What is the value of 4 1 1–– – –– – –– ?5 3 15

A. 1––5

B. 2––5

C. 7––15

D. 3––4

E. 4––5


Country average vs.






Correct Response: C

19

Number of cars from rounded value

Item Number: N11

A company produced 17,175 cars in 1996. For a report, thisnumber was rounded to the nearest hundred. Which was thenumber of cars given in the report?

A. 17,000

B. 17,100

C. 17,200

D. 17,270


Country average vs.



Singapore 96 �Czech Republic 96 �Finland 94 �Slovenia 94 �Australia 94 �Belgium (Flemish) 93 �Hungary 93 �Slovak Republic 92 �Canada 92 �Netherlands 90 �United States 89 �Malaysia 89 �England 87 �New Zealand 86 �Bulgaria 86 �Hong Kong, SAR 86 �Chinese Taipei 82 �Korea, Rep. of 82 �Russian Federation 81 �Latvia (LSS) 80 OJapan 79 �Lithuania 76 OInternational Average 74Romania 72 OItaly 72 OIsrael 72 OThailand 68 OMacedonia, Rep. of 65 �Cyprus 64 �Indonesia 61 �Turkey 59 �Chile 58 �Jordan 55 �Philippines 51 �Moldova 49 �South Africa 38 �Tunisia 30 �Morocco 30 �Iran, Islamic Rep. 25 �




Correct Response: B

20

Korea, Rep. of 86 �Chinese Taipei 85 �Hong Kong, SAR 84 �Singapore 84 �Belgium (Flemish) 83 �Japan 82 �Netherlands 74 �Canada 72 �Russian Federation 71 �Hungary 70 OBulgaria 68 OMalaysia 68 OSlovak Republic 67 OLatvia (LSS) 66 OLithuania 66 OSlovenia 65 OCyprus 64 OUnited States 63 OAustralia 63 OFinland 61 OInternational Average 61Czech Republic 60 OIsrael 59 OItaly 57 OThailand 57 OJordan 55 ORomania 55 ONew Zealand 51 �England 51 �Moldova 50 �Iran, Islamic Rep. 49 �Tunisia 49 �Indonesia 48 �Turkey 45 �Macedonia, Rep. of 44 �Philippines 42 �Chile 41 �South Africa 34 �Morocco 32 �

List of equivalent fractions

Item Number: N14

In which list of fractions are all of the fractions equivalent?

A. 1 2 4–– , –– , ––2 4 6

B. 2 4 8–– , –– , ––3 6 12

C. 2 4 8–– , –– , ––5 10 50

D. 3 4 6–– , –– , ––4 6 8


Country average vs.







Correct Response: B

21

Number of marbles in bag

Item Number: N16

Penny had a bag of marbles. She gave one-third of them toRebecca, and then one-fourth of the remaining marbles to John.Penny then had 24 marbles left in the bag. How many marbleswere in the bag to start with?

A. 36

B. 48

C. 60

D. 96


Country average vs.



Singapore 81 �Japan 64 �Korea, Rep. of 64 �Chinese Taipei 60 �Hong Kong, SAR 60 �Netherlands 53 OFinland 53 OBelgium (Flemish) 52 ONew Zealand 49 OAustralia 48 OMalaysia 47 OEngland 46 OSlovak Republic 45 OThailand 45 OCanada 45 OHungary 45 OCzech Republic 44 OInternational Average 44Philippines 43 OBulgaria 43 ORussian Federation 42 OIsrael 42 OMoldova 41 OLatvia (LSS) 41 OUnited States 41 OSlovenia 39 ORomania 38 OTurkey 38 OItaly 38 OIndonesia 37 OCyprus 36 OMacedonia, Rep. of 35 �Morocco 34 �Jordan 33 �Tunisia 33 �Lithuania 32 �South Africa 31 �Iran, Islamic Rep. 31 �Chile 30 �





Correct Response: B

22

Singapore 65 �Chinese Taipei 63 �Hong Kong, SAR 56 �Malaysia 54 �Korea, Rep. of 53 �Netherlands 49 �Japan 47 �Czech Republic 43 OHungary 40 OBulgaria 39 ORussian Federation 39 OLithuania 39 OBelgium (Flemish) 39 OSlovak Republic 39 OCanada 36 OSlovenia 36 OInternational Average 35United States 35 OFinland 34 OCyprus 33 OAustralia 32 OLatvia (LSS) 31 OTurkey 29 ORomania 29 OMoldova 29 ONew Zealand 29 OMacedonia, Rep. of 28 OItaly 27 OEngland 27 OTunisia 26 �Israel 25 �Iran, Islamic Rep. 25 �Morocco 23 �Indonesia 22 �Chile 22 �Jordan 21 �Philippines 20 �South Africa 18 �

Amount of paint left

Item Number: N17

A painter had 25 L of paint. He used 2.5 L of paint every hour. Hefinished the job in 5.5 hours. How much paint did he have left?

A. 10.25 L

B. 11.25 L

C. 12.75 L

D. 13.75 L


Country average vs.




23

Shade in 3/8 of squares in grid

Item Number: N19

SCORING

Correct Response

• 9 squares are shaded (regardless of which squares)

• Other correct (e.g., 6 full squares and 6 half squares shaded or other equivalent of nine squares)

Incorrect Response

• 3 squares shaded

• 8 squares shaded

• 11 or 13 squares shaded

• 3 squares shaded and 8 more squares shaded (areas are shaded separately)





Country average vs.



Singapore 89 �Hong Kong, SAR 87 �Belgium (Flemish) 87 �Korea, Rep. of 81 �Chinese Taipei 80 �Japan 78 �Malaysia 73 �Canada 68 �Finland 65 �Hungary 63 �Netherlands 61 OAustralia 60 �Slovenia 55 OBulgaria 54 OCyprus 54 OEngland 52 OSlovak Republic 52 ORussian Federation 52 OUnited States 49 OInternational Average 49Thailand 49 ONew Zealand 46 OItaly 46 OLatvia (LSS) 46 OMoldova 44 OCzech Republic 42 OIsrael 40 �Romania 39 �Macedonia, Rep. of 32 �Jordan 31 �Iran, Islamic Rep. 31 �Tunisia 28 �Turkey 26 �Lithuania 26 �Indonesia 21 �Chile 13 �Philippines 11 �Morocco 8 �South Africa 7 �




Correct Response: C

24

Singapore 94 �Hong Kong, SAR 85 �Belgium (Flemish) 83 �Japan 82 �Korea, Rep. of 82 �Chinese Taipei 81 �Netherlands 81 �Finland 79 �United States 79 �Slovak Republic 78 �Hungary 78 �Canada 78 �Czech Republic 78 �Malaysia 78 �Australia 77 �Slovenia 76 �England 74 �New Zealand 67 ORussian Federation 65 OInternational Average 65Israel 63 OLatvia (LSS) 62 OCyprus 60 OBulgaria 60 OThailand 58 OJordan 58 OLithuania 57 ORomania 55 OMacedonia, Rep. of 53 �Italy 52 �Moldova 52 �Turkey 50 �Chile 48 �Tunisia 48 �Iran, Islamic Rep. 48 �Indonesia 44 �Philippines 42 �South Africa 30 �Morocco 17 �

Estimate of total cars in parking lot

Item Number: P13

There are 68 rows of cars in a parking lot. Each row has 92cars. Which of these would give the closest estimate of the totalnumber of cars in the parking lot?

A. 60 x 90 = 5400

B. 60 x 100 = 6000

C. 70 x 90 = 6300

D. 70 x 100 = 7000


Country average vs.







Correct Response: B

25

Estimate of distance from explosion

Item Number: P14

Sound travels at approximately 330 meters per second. Thesound of an explosion took 28 seconds to reach a person. Which ofthese is the closest estimate of how far away the person was fromthe explosion?

A. 12,000 m

B. 9,000 m

C. 8,000 m

D. 6,000 m


Country average vs.



Singapore 83 �Japan 81 �Korea, Rep. of 78 �Hong Kong, SAR 78 �Chinese Taipei 77 �Slovak Republic 76 �Slovenia 71 �Czech Republic 71 �Malaysia 70 �Belgium (Flemish) 69 �Canada 64 �Netherlands 63 OFinland 63 OUnited States 63 �Australia 62 OLithuania 62 OHungary 61 ORussian Federation 59 OThailand 59 OInternational Average 56Bulgaria 55 OItaly 52 OLatvia (LSS) 52 OIsrael 51 OTurkey 50 OCyprus 50 ONew Zealand 50 OEngland 50 OMacedonia, Rep. of 47 �Moldova 45 �Philippines 43 �Jordan 42 �Tunisia 42 �Indonesia 41 �Romania 40 �Iran, Islamic Rep. 38 �Chile 37 �South Africa 21 �Morocco 13 �





Correct Response: A

26

Singapore 85 �Hong Kong, SAR 75 �Chinese Taipei 68 �Belgium (Flemish) 62 �Japan 62 �Netherlands 61 �Cyprus 56 �Malaysia 55 �Korea, Rep. of 55 �Hungary 55 �Canada 53 �United States 52 ORussian Federation 51 OAustralia 51 OSlovenia 51 OLatvia (LSS) 49 OFinland 48 OSlovak Republic 48 ORomania 47 OLithuania 46 OInternational Average 45Moldova 44 OCzech Republic 43 OIsrael 43 ONew Zealand 43 OBulgaria 43 OEngland 42 OMacedonia, Rep. of 38 OJordan 34 �Indonesia 34 �Italy 32 �Iran, Islamic Rep. 32 �Turkey 32 �Tunisia 31 �Thailand 29 �Philippines 22 �Chile 22 �South Africa 18 �Morocco 14 �

Fraction of cherries in basket

Item Number: P15


Country average vs.



Robin and Jim took cherries from a basket. Robin took –– of

the cherries and Jim took –– of the cherries. What fraction of

the cherries remained in the basket?

A. 1––2

B. 1––3

C. 1––6

D. 1––18

13

16


27

Write decimal as fraction

Item Number: P17

Write 0.48 as a fraction reduced to its lowest terms.

Answer: ______________

SCORING

Correct Response

• 12/25

Incorrect Response

• 48/100 OR 24/50

• Any fraction other than 48/100 with 48 as numerator

• Any fraction with 48 as denominator

• 4/8 OR 2/4 OR 1/2





Country average vs.



Singapore 87 �Korea, Rep. of 78 �Hong Kong, SAR 74 �Chinese Taipei 71 �Japan 65 �Belgium (Flemish) 56 �Moldova 55 �Canada 50 �Slovenia 48 �United States 46 �Iran, Islamic Rep. 43 �Bulgaria 42 OAustralia 42 OSlovak Republic 42 ORussian Federation 42 ORomania 41 OMalaysia 40 OHungary 40 OInternational Average 36Tunisia 34 ONetherlands 31 OCzech Republic 30 OLatvia (LSS) 28 OItaly 25 �Israel 24 �Turkey 24 �Thailand 24 �Lithuania 24 �New Zealand 23 �Cyprus 22 �Jordan 22 �Indonesia 22 �Finland 19 �England 18 �Macedonia, Rep. of 13 �Philippines 12 �Chile 11 �South Africa 4 �Morocco 3 �




Correct Response: A

28

Malaysia 92 �Singapore 90 �Hungary 90 �Slovenia 90 �Korea, Rep. of 88 �Russian Federation 88 �Slovak Republic 87 �Japan 86 �Lithuania 86 �Czech Republic 85 OChinese Taipei 84 �Hong Kong, SAR 83 �Thailand 83 �Tunisia 82 OBulgaria 81 OMoldova 80 OCanada 80 OLatvia (LSS) 79 OIndonesia 78 ORomania 77 OUnited States 77 OItaly 77 OInternational Average 77Chile 75 OAustralia 74 OBelgium (Flemish) 73 OFinland 72 OCyprus 71 OMacedonia, Rep. of 71 OIran, Islamic Rep. 71 OTurkey 71 ONetherlands 69 OPhilippines 69 �Jordan 65 �Israel 63 �Morocco 62 �New Zealand 61 �England 59 �South Africa 42 �

Subtraction of decimals to 0.001

Item Number: R07

Subtract: 4.722 – 1.935 =

A. 2.787

B. 2.797

C. 2.887

D. 2.897


Country average vs.






Correct Response: B

29

Item Number: R08

The total weight of a pile of 500 salt crystals is 6.5 g. What isthe average weight of a salt crystal?

A. 0.0078 g

B. 0.013 g

C. 0.0325 g

D. 0.078 g


Country average vs.



Hong Kong, SAR 75 �Chinese Taipei 75 �Singapore 74 �Japan 73 �Korea, Rep. of 72 �Hungary 67 �Slovak Republic 66 �Russian Federation 65 �Malaysia 64 �Belgium (Flemish) 63 �Lithuania 57 OSlovenia 57 ONetherlands 57 OBulgaria 55 OMoldova 54 OFinland 54 OInternational Average 52Romania 52 OCzech Republic 50 OChile 49 OCanada 49 OTunisia 48 OTurkey 48 OLatvia (LSS) 47 OMacedonia, Rep. of 47 OAustralia 47 OIndonesia 46 OItaly 45 OThailand 44 �United States 44 �New Zealand 43 �Jordan 41 �England 40 �Israel 40 �Iran, Islamic Rep. 36 �Morocco 35 �South Africa 35 �Cyprus 31 �Philippines 29 �

Average weight of salt crystals




Correct Response: B

30

Malaysia 94 �Singapore 92 �Chinese Taipei 90 �Hong Kong, SAR 90 �Korea, Rep. of 88 �Hungary 87 �Slovak Republic 86 �Japan 86 �Belgium (Flemish) 85 �Slovenia 83 �Canada 83 �Czech Republic 82 OUnited States 81 �Lithuania 80 OTunisia 80 �Russian Federation 79 OMoldova 79 ONetherlands 79 OAustralia 77 OThailand 77 OFinland 76 OBulgaria 76 OInternational Average 74Latvia (LSS) 74 OIran, Islamic Rep. 73 OCyprus 70 OTurkey 69 OJordan 69 ORomania 68 OIsrael 67 OItaly 67 OMacedonia, Rep. of 65 �Chile 59 �Philippines 58 �New Zealand 58 �Indonesia 55 �Morocco 54 �England 51 �South Africa 37 �

Subtraction of 4-digit whole numbers

Item Number: R13

Subtract: 7003– 4078–––––

A. 2035

B. 2925

C. 3005

D. 3925


Country average vs.




31

How much money left if spent 5/8

Item Number: R14

SCORING

Note: There is no distinction made between responses with and without units.

Correct Response

• 90

Incorrect Response

• 150 [money spent]






Country average vs.



Singapore 78 �Hong Kong, SAR 66 �Malaysia 59 �Japan 50 �Korea, Rep. of 50 �Chinese Taipei 49 �Finland 48 �Netherlands 47 �Belgium (Flemish) 45 �Hungary 40 �Moldova 38 OAustralia 37 OSlovenia 35 OSlovak Republic 33 OCyprus 33 OCanada 30 OCzech Republic 30 OInternational Average 30Bulgaria 27 ORussian Federation 27 OUnited States 25 �Italy 24 ONew Zealand 24 OEngland 24 OLatvia (LSS) 24 OIsrael 23 OTunisia 22 �Romania 21 �Thailand 21 �Iran, Islamic Rep. 20 �Lithuania 19 �Turkey 17 �Macedonia, Rep. of 14 �Jordan 14 �Indonesia 11 �Chile 6 �Philippines 4 �South Africa 3 �Morocco 1 �

Laura had $240. She spent –– of it. How much money didshe have left?

Answer: ______________

58


32

Money from total magazine sales

Item Number: R15

John sold 60 magazines and Mark sold 80 magazines. Themagazines were all sold for the same price. The total amountof money received for the magazines was $700. How muchmoney did Mark receive?

Answer: ______________

SCORING

Note: There is no distinction made between responses with and without units.

Correct Response

• 400

Incorrect Response

• 500 [price per magazine x 100]

• 350 [700 ÷ 2]

• 300 [money John received]






Country average vs.



Singapore 84 �Chinese Taipei 75 �Hong Kong, SAR 72 �Korea, Rep. of 69 �Japan 67 �Malaysia 65 �Slovenia 60 �Belgium (Flemish) 60 �Hungary 58 �Moldova 54 �Czech Republic 54 OSlovak Republic 54 OLithuania 54 �Netherlands 53 ORussian Federation 52 OBulgaria 50 OLatvia (LSS) 48 OFinland 47 OCanada 46 OInternational Average 44Australia 44 ORomania 43 OUnited States 41 OCyprus 40 OTunisia 39 OThailand 38 OItaly 36 ONew Zealand 33 �England 31 �Israel 30 �Macedonia, Rep. of 30 �Iran, Islamic Rep. 28 �Indonesia 27 �Turkey 26 �Jordan 23 �Chile 22 �Philippines 12 �South Africa 9 �Morocco 3 �

A book publisher sent 140 copies of a certain book to a book-store. The publisher packed the books in two types of boxes.One type of box held 8 copies of the book, and the other typeof box held 12 copies of the book. The boxes were all full, andthere were equal numbers of both types of boxes.

a) How many boxes holding 12 books were sent to the book-store?

Answer: ________________

b) What fraction of the books sent to the bookstore werepacked in the smaller boxes?

Answer: ________________


33

Number/fraction of 2 types of boxes

Item Number: T02A

SCORING

A: Scoring for Total Number of Boxes

Correct Response

• 7

Incorrect Response

• Incorrect (including crossed out/erased, stray marks, illegible, or off task)





Country average vs.



Singapore 62 �Chinese Taipei 60 �Korea, Rep. of 59 �Japan 58 �Hong Kong, SAR 58 �Belgium (Flemish) 43 �Bulgaria 33 OMalaysia 33 �Finland 32 OAustralia 32 �Netherlands 32 OHungary 31 �Canada 31 �Slovenia 31 OLatvia (LSS) 29 ORussian Federation 29 OUnited States 26 OInternational Average 26Slovak Republic 25 OEngland 24 OMoldova 24 ONew Zealand 24 ORomania 22 OCzech Republic 22 OLithuania 22 OThailand 19 �Israel 18 �Italy 18 �Cyprus 15 �Jordan 12 �Indonesia 10 �Turkey 9 �Tunisia 8 �Macedonia, Rep. of 8 �Iran, Islamic Rep. 7 �Chile 4 �Philippines 2 �South Africa 2 �Morocco 1 �


34

Number/fraction of 2 types of boxes

Item Number: T02B

A book publisher sent 140 copies of a certain book to a book-store. The publisher packed the books in two types of boxes.One type of box held 8 copies of the book, and the other typeof box held 12 copies of the book. The boxes were all full, andthere were equal numbers of both types of boxes.

a) How many boxes holding 12 books were sent to the book-store?

Answer: ________________

b) What fraction of the books sent to the bookstore werepacked in the smaller boxes?

Answer: ________________

SCORING

B: Scoring for Fraction of Books in Smaller Boxes

Note: The term “equivalent” in the scoring guide below includes decimal fractions and percentages.

Correct Response

• 2/5

• Another fraction or percent equivalent to 2/5 (e.g., 8/20, 14/35, 28/70, etc.)• Other correct

Incorrect Response

• 1/2

• 2/3 OR 8/12 OR 56/84 [fraction of boxes]

• Any integer






Country average vs.



Singapore 48 �Hong Kong, SAR 43 �Chinese Taipei 43 �Japan 32 �Korea, Rep. of 30 �Bulgaria 18 OMalaysia 16 ORussian Federation 15 OCanada 14 ONetherlands 13 OHungary 13 OAustralia 12 OInternational Average 12Slovenia 11 OUnited States 11 OSlovak Republic 11 ORomania 10 OBelgium (Flemish) 10 OThailand 10 ONew Zealand 10 OMoldova 10 OEngland 9 OFinland 8 �Czech Republic 8 �Latvia (LSS) 8 �Cyprus 7 �Italy 6 �Israel 5 �Lithuania 4 �Jordan 3 �Iran, Islamic Rep. 2 �Indonesia 2 �Macedonia, Rep. of 2 �Chile 2 �Turkey 2 �Tunisia 1 �Philippines 1 �South Africa 1 �Morocco 0 �





Correct Response: C

35

Height of stack from paper thickness

Item Number: T04

A sheet of paper is 0.012 cm thick. Of the following, whichwould be the height of a stack of 400 sheets of this paper?

A. 0.048 cm

B. 0.48 cm

C. 4.8 cm

D. 48 cm


Country average vs.



Japan 83 �Singapore 80 �Hong Kong, SAR 78 �Chinese Taipei 75 �Korea, Rep. of 75 �Belgium (Flemish) 75 �Netherlands 72 �Finland 72 �Czech Republic 70 �Slovak Republic 69 �Malaysia 67 �Canada 67 �Hungary 65 �Slovenia 62 �United States 62 �Australia 59 �Latvia (LSS) 59 ORussian Federation 59 OLithuania 54 OBulgaria 54 ONew Zealand 54 OInternational Average 54England 53 OMoldova 49 OItaly 48 OIsrael 47 �Romania 46 OThailand 45 �Cyprus 44 �Jordan 36 �Turkey 36 �Iran, Islamic Rep. 33 �Macedonia, Rep. of 33 �Indonesia 33 �Tunisia 31 �Chile 23 �Philippines 22 �Morocco 22 �South Africa 20 �


36

Two possibilities for actual height

Item Number: V01

The height of a boy was reported as 140 cm. The height hadbeen rounded to the nearest 10 cm. What are two possibilitiesfor the boy’s actual height?

Answer: ______________ cm and ______________ cm

SCORING

Correct Response

• One answer 140 and the other answer is in an acceptable range, 135 ≤ x < 140 or 140 < x < 145.

• Neither answer is 140 cm but both are in the acceptable range 135 ≤ x < 140 and/or 140 < x < 145.

Incorrect Response

• Both answers within the intervals 145 ≤ x ≤ 150 and/or 130 ≤ x < 135

• 130 AND 150





Country average vs.



Finland 85 �Czech Republic 82 �Slovak Republic 79 �Singapore 78 �Canada 72 �Australia 69 �Russian Federation 69 �Japan 69 �Korea, Rep. of 66 �Hungary 66 �Hong Kong, SAR 66 �Chinese Taipei 65 �Netherlands 64 �Belgium (Flemish) 61 �England 61 �Thailand 61 �New Zealand 58 �Lithuania 57 �United States 56 �International Average 44Israel 44 OMoldova 43 OSlovenia 41 OBulgaria 40 OLatvia (LSS) 39 OMalaysia 33 �Jordan 29 �Italy 25 �Indonesia 24 �Cyprus 21 �Romania 15 �Macedonia, Rep. of 13 �Philippines 9 �Chile 8 �Tunisia 7 �South Africa 6 �Iran, Islamic Rep. 5 �Turkey 4 �Morocco 3 �





Correct Response: D

37

Ratio of nitrate to total fertilizer

Item Number: V03

In making a garden fertilizer, a gardener mixes 2 kg of anitrate, 3 kg of a phosphate, and 6 kg of potash. What is theratio of nitrate to the total amount of fertilizer?

A. 11––9

B. 2––3

C. 2––9

D. 2––11


Country average vs.



Singapore 87 �Korea, Rep. of 84 �Chinese Taipei 74 �Netherlands 74 �Hong Kong, SAR 74 �Finland 65 �Malaysia 62 �Japan 61 �Canada 55 �United States 55 �Belgium (Flemish) 54 �Slovenia 53 �Hungary 50 OAustralia 48 OItaly 47 ORussian Federation 46 OInternational Average 45New Zealand 44 OThailand 44 OIndonesia 43 OEngland 42 ORomania 40 OBulgaria 40 OCyprus 40 OIsrael 40 OSlovak Republic 37 OJordan 36 �Latvia (LSS) 35 �Turkey 35 �Iran, Islamic Rep. 35 �Moldova 34 �Czech Republic 30 �Tunisia 29 �Macedonia, Rep. of 26 �Lithuania 23 �Chile 22 �Philippines 21 �Morocco 15 �South Africa 15 �



Algebra Knowing

Correct Response: A

38

Hong Kong, SAR 93 �Singapore 89 �Japan 86 �Korea, Rep. of 85 �Chinese Taipei 84 �Slovenia 83 �Canada 82 �Russian Federation 82 �Slovak Republic 81 �Belgium (Flemish) 81 �Netherlands 80 �Hungary 80 �United States 77 �Bulgaria 76 �Australia 72 �Czech Republic 72 �Latvia (LSS) 71 �Lithuania 71 OFinland 68 OIsrael 68 OThailand 67 ORomania 67 OCyprus 66 OInternational Average 65Moldova 65 OMacedonia, Rep. of 63 OEngland 62 OItaly 58 �New Zealand 58 �Tunisia 58 �Malaysia 57 �Jordan 46 �Iran, Islamic Rep. 46 �Turkey 41 �Chile 38 �Indonesia 37 �Morocco 35 �South Africa 21 �Philippines 19 �

Equation representing relationship

Item Number: B12

n is a number. When n is multiplied by 7, and 6 is then added, theresult is 41. Which of these equations represents this relation?

A. 7n + 6 = 41

B. 7n ± 6 = 41

C. 7n x 6 = 41

D. 7(n + 6) = 41


Country average vs.





Algebra Using Routine Procedures

Correct Response: C

39

Value of x from equivalent ratios

Item Number: D08

If the ratio 7 to 13 is the same as the ratio x to 52, what is thevalue of x?

A. 7

B. 13

C. 28

D. 364


Country average vs.



Singapore 96 �Korea, Rep. of 93 �Chinese Taipei 90 �Hong Kong, SAR 88 �Malaysia 84 �Canada 84 �Japan 82 �Australia 80 �United States 78 �Slovenia 77 �Russian Federation 76 �Hungary 75 �Belgium (Flemish) 75 �Italy 74 ONew Zealand 73 OEngland 73 OThailand 72 ONetherlands 70 OCyprus 70 OCzech Republic 70 OInternational Average 69Slovak Republic 68 OBulgaria 68 OLatvia (LSS) 66 OMacedonia, Rep. of 66 ORomania 64 OFinland 63 �Jordan 61 �Israel 61 �Moldova 60 �Tunisia 60 �Indonesia 59 �Turkey 59 �Iran, Islamic Rep. 58 �Lithuania 58 �Chile 49 �Philippines 47 �South Africa 38 �Morocco 35 �



Algebra Knowing

Correct Response: A

40

Chinese Taipei 78 �Japan 75 �Hong Kong, SAR 74 �Korea, Rep. of 74 �Netherlands 74 �Thailand 69 �Singapore 64 �Bulgaria 62 �Belgium (Flemish) 60 �Canada 56 �Slovenia 55 OAustralia 55 OUnited States 55 �Russian Federation 54 OEngland 53 OIndonesia 53 ONew Zealand 52 OMacedonia, Rep. of 51 OPhilippines 51 OCzech Republic 51 OInternational Average 50Hungary 48 OFinland 48 OSlovak Republic 47 OCyprus 46 OJordan 46 ORomania 45 OItaly 42 �Israel 42 �Malaysia 42 �Lithuania 42 �Turkey 41 �Chile 37 �Moldova 33 �Iran, Islamic Rep. 30 �Latvia (LSS) 29 �South Africa 27 �Morocco 24 �Tunisia 21 �

Equation to determine cost of cards

Item Number: D10

The cost, C, of printing greeting cards consists of a fixed chargeof 100 cents and a charge of 6 cents for each card printed.Which of these equations can be used to determine the cost ofprinting n cards?

A. C = (100 + 6n) cents

B. C = (106 + n) cents

C. C = (6 + 100n) cents

D. C = (106n) cents

E. C = (600n) cents


Country average vs.





AlgebraInvestigating


Correct Response: A

41

Find 1/3 of number from relationship

Item Number: F11

If 4 times a number is 48, what is 1 of the number?––3

A. 4

B. 8

C. 12

D. 16


Country average vs.



Hong Kong, SAR 89 �Korea, Rep. of 85 �Chinese Taipei 83 �Singapore 82 �Japan 73 �Belgium (Flemish) 72 �Finland 68 �Bulgaria 66 �Hungary 63 �Russian Federation 63 �Australia 54 �Slovenia 54 �Malaysia 54 �Canada 53 �United States 50 OCyprus 49 OInternational Average 47Latvia (LSS) 46 OIsrael 44 OTurkey 44 ONew Zealand 43 ORomania 41 ONetherlands 41 OMoldova 41 OCzech Republic 40 OEngland 40 �Slovak Republic 38 �Jordan 36 �Iran, Islamic Rep. 36 �Macedonia, Rep. of 34 �Thailand 31 �Italy 29 �South Africa 27 �Chile 23 �Indonesia 20 �Lithuania 19 �Philippines 19 �Morocco 15 �Tunisia 10 �



Algebra Knowing

Correct Response: D

42

Equation from x/y table

Item Number: H10


Country average vs.



Korea, Rep. of 84 �Hungary 80 �Japan 76 �Chinese Taipei 72 �Singapore 71 �Netherlands 71 �Australia 68 �Hong Kong, SAR 68 �Russian Federation 65 �Slovenia 60 �Belgium (Flemish) 60 �United States 57 �England 57 �Slovak Republic 57 OCanada 55 �Czech Republic 53 ONew Zealand 52 OMacedonia, Rep. of 51 OMalaysia 51 OJordan 50 OLatvia (LSS) 50 OInternational Average 49Bulgaria 47 OTunisia 41 �Israel 41 �Italy 40 �Finland 39 �Indonesia 37 �Lithuania 36 �Romania 36 �Cyprus 36 �Thailand 33 �Turkey 32 �Iran, Islamic Rep. 31 �Moldova 31 �Philippines 22 �Chile 21 �Morocco 20 �South Africa 19 �



Algebra Knowing

Correct Response: B

43

Symbolic linear equation of magazines

Item Number: H12


Country average vs.



Singapore 95 �Belgium (Flemish) 88 �Chinese Taipei 87 �Netherlands 87 �Canada 86 �United States 86 �Malaysia 86 �Japan 85 �Australia 83 �Finland 82 �Hungary 81 �Slovenia 81 �Korea, Rep. of 81 �Czech Republic 80 �England 79 �Slovak Republic 79 �New Zealand 77 �Latvia (LSS) 77 �Russian Federation 77 OIsrael 77 �Cyprus 75 OTunisia 75 OBulgaria 73 OItaly 72 OInternational Average 72Romania 71 OLithuania 66 OHong Kong, SAR 64 �Jordan 64 �Thailand 63 �Moldova 63 �Indonesia 54 �Chile 54 �Iran, Islamic Rep. 51 �Turkey 51 �Macedonia, Rep. of 47 �Philippines 45 �Morocco 44 �South Africa 36 �




Correct Response: A

44

Missing number in table

Item Number: J17


Country average vs.



Netherlands 81 �Chinese Taipei 79 �Japan 78 �Korea, Rep. of 78 �Hong Kong, SAR 77 �Hungary 74 �Slovenia 73 �New Zealand 72 �Canada 71 OAustralia 70 OMoldova 69 OIsrael 69 OSlovak Republic 68 OThailand 68 OBelgium (Flemish) 67 OFinland 67 OSingapore 67 ORussian Federation 66 OItaly 65 OTunisia 65 OLithuania 65 OInternational Average 65Latvia (LSS) 65 OBulgaria 64 OCyprus 64 ORomania 63 OUnited States 63 OCzech Republic 63 OMacedonia, Rep. of 63 OEngland 62 OJordan 61 OMalaysia 58 OTurkey 58 �Indonesia 57 �Iran, Islamic Rep. 53 �Philippines 48 �Chile 47 �South Africa 43 �Morocco 40 �





Correct Response: C

45

Distance traveled by elevator

Item Number: L12

In a sequence of starts and stops, an elevator travels from thefirst floor to the fifth floor and then to the second floor. Fromthere, the elevator travels to the fourth floor and then to thethird floor. If the floors are 3 m apart, how far has the elevatortraveled?

A. 18 m

B. 27 m

C. 30 m

D. 45 m


Country average vs.



Korea, Rep. of 77 �Japan 74 �Chinese Taipei 72 �Hong Kong, SAR 72 �Finland 72 �Belgium (Flemish) 70 �Australia 69 �Singapore 69 �Czech Republic 66 �Malaysia 63 �Slovak Republic 62 OHungary 61 �Canada 60 �Lithuania 60 ONew Zealand 59 ORussian Federation 59 OSlovenia 58 ONetherlands 58 OEngland 57 OLatvia (LSS) 55 OUnited States 55 OInternational Average 53Cyprus 52 OItaly 51 OMoldova 49 OMacedonia, Rep. of 45 OTunisia 44 �Turkey 43 �Romania 42 �Jordan 39 �Chile 39 �Israel 39 �Iran, Islamic Rep. 38 �Thailand 38 �Indonesia 37 �South Africa 33 �Morocco 32 �Philippines 26 �Bulgaria 21 �



AlgebraCommunicating

and Reasoning

Correct Response: E

46

Korea, Rep. of 80 �Hungary 75 �Chinese Taipei 75 �Singapore 74 �Hong Kong, SAR 74 �Japan 69 �Belgium (Flemish) 67 �Australia 64 �Netherlands 64 �Russian Federation 61 �Slovak Republic 56 �Slovenia 54 OCanada 53 OEngland 51 OCzech Republic 50 OUnited States 49 ONew Zealand 49 OMacedonia, Rep. of 48 OJordan 48 OLatvia (LSS) 45 OInternational Average 45Bulgaria 44 OIsrael 41 OMalaysia 41 OItaly 39 OLithuania 36 ORomania 35 OTunisia 33 �Moldova 33 �Finland 32 �Indonesia 27 �Thailand 24 �Cyprus 24 �Iran, Islamic Rep. 22 �Turkey 21 �South Africa 14 �Morocco 14 �Philippines 13 �Chile 12 �

Correct equation based on x/y table

Item Number: L14


Country average vs.






Correct Response: E

47

Values in proportionality table

Item Number: L15


Country average vs.



Chinese Taipei 69 �Japan 62 �Singapore 57 �Korea, Rep. of 54 �Hong Kong, SAR 51 �Belgium (Flemish) 49 �Netherlands 49 �Russian Federation 43 �Malaysia 43 �Slovak Republic 38 OCanada 38 OHungary 38 OJordan 37 OSlovenia 34 OUnited States 34 ORomania 34 OInternational Average 33Australia 33 OBulgaria 32 OThailand 30 OIndonesia 29 OItaly 28 OCzech Republic 28 OEngland 28 OLithuania 26 OMoldova 26 OCyprus 26 ONew Zealand 24 �Turkey 24 �Iran, Islamic Rep. 24 �Latvia (LSS) 23 �Macedonia, Rep. of 23 �South Africa 21 �Finland 21 �Philippines 21 �Israel 20 �Morocco 17 �Chile 15 �Tunisia 15 �


48

Value of x in mathematical equation

Item Number: L17

Find the value of x if 12x – 10 = 6x + 32

Answer: ______________

SCORING

Correct Response

• 7

Incorrect Response

• 3 23

OR 2 13

OR 1 29

[uses incorrect operation: 32 – 10 = 22, 12x + 6x = 18x, or both]

• Any expression or equation, other than x = 7, containing x• Other incorrect (including crossed out/erased, stray marks, illegible, or off task)




Country average vs.



Japan 85 �Hong Kong, SAR 80 �Korea, Rep. of 80 �Slovak Republic 78 �Russian Federation 77 �Slovenia 76 �Singapore 75 �Hungary 74 �Chinese Taipei 73 �Romania 70 �Czech Republic 66 �Lithuania 62 �Latvia (LSS) 58 �Belgium (Flemish) 58 �Moldova 56 �Macedonia, Rep. of 54 OCyprus 51 OIsrael 51 OItaly 46 OInternational Average 44Malaysia 43 OBulgaria 34 �United States 34 �Canada 33 �Turkey 32 �Australia 31 �Thailand 29 �England 26 �Finland 24 �Iran, Islamic Rep. 23 �Netherlands 19 �New Zealand 19 �Jordan 18 �Indonesia 18 �Chile 12 �Morocco 7 �Philippines 6 �Tunisia 6 �South Africa 5 �


49

Value of expression substituting x=3

Item Number: N13

If x = 3, what is the value of 5x + 3–––––– ?4x – 3

Answer: ______________

SCORING

Correct Response

• 2

• 18/9, 2/1 or other fraction equivalent to 2

• Other correct

Incorrect Response

• Indicates the correct substitution of x = 3 in numerator and/or denominator but student did not

correctly complete the solution.

• Indicates a wrong substitution such as 5x = 53 or 5x = 5 + 3 in the numerator; for example,

any fractions with 56 or 11 as numerators, or 40 or 4 as denominators.

• A response containing the variable x• Cancels or ignores x’s (e.g., 8/1, 8, 7, etc.)• Other incorrect (including crossed out/erased, stray marks, illegible, or off task)




Country average vs.



Singapore 83 �Chinese Taipei 81 �Hong Kong, SAR 81 �Hungary 80 �Russian Federation 79 �Slovenia 75 �Korea, Rep. of 75 �Slovak Republic 72 �Japan 69 �Lithuania 67 �Belgium (Flemish) 67 �Canada 67 �Bulgaria 65 �Latvia (LSS) 64 �Czech Republic 62 OUnited States 61 �Australia 61 ORomania 59 OMoldova 57 OInternational Average 53Macedonia, Rep. of 53 OIsrael 53 ONetherlands 50 OMalaysia 48 OCyprus 47 OThailand 47 OTunisia 47 �Italy 47 OEngland 46 OFinland 44 �New Zealand 42 �Jordan 40 �Turkey 35 �Indonesia 28 �Iran, Islamic Rep. 28 �Philippines 15 �Chile 14 �Morocco 12 �South Africa 9 �



Algebra Knowing

Correct Response: D

50

Singapore 90 �Korea, Rep. of 86 �Hong Kong, SAR 85 �United States 85 �Japan 85 �Tunisia 84 �Chinese Taipei 83 �Czech Republic 81 �Belgium (Flemish) 80 OSlovak Republic 80 �Indonesia 80 �Slovenia 80 �Thailand 80 �Hungary 79 �Latvia (LSS) 77 OAustralia 77 ORussian Federation 76 OCanada 75 OCyprus 74 OMalaysia 74 OItaly 72 OLithuania 71 OInternational Average 71Iran, Islamic Rep. 71 OBulgaria 69 OIsrael 67 OChile 67 ORomania 66 ONew Zealand 66 OEngland 61 �Jordan 61 �Netherlands 55 �South Africa 55 �Moldova 53 �Finland 53 �Philippines 49 �Turkey 47 �Morocco 34 �

Expression equivalent to n x n x n

Item Number: P09

Which of these expressions is equivalent to n x n x n for allvalues of n?

A. n3

B. n + 3

C. 3n

D. n3


Country average vs.





Algebra Knowing

Correct Response: B

51

Equivalent expression: k+k+k+k+k

Item Number: P11

For all numbers k,k + k + k + k + k can be written as

A. k + 5

B. 5k

C. k 5

D. 5(k + 1)


Country average vs.



Slovak Republic 80 �Hong Kong, SAR 80 �Singapore 76 �Chinese Taipei 76 �Hungary 75 �Slovenia 72 �Czech Republic 70 �Korea, Rep. of 69 �Belgium (Flemish) 69 �Russian Federation 68 �Malaysia 67 �Latvia (LSS) 67 �Cyprus 65 OBulgaria 65 ORomania 65 OMacedonia, Rep. of 62 OJapan 61 OTurkey 59 OIsrael 58 OInternational Average 57Netherlands 57 OItaly 57 OFinland 57 OCanada 56 OMoldova 55 OAustralia 54 ONew Zealand 54 OTunisia 53 OLithuania 52 OJordan 48 �England 48 �United States 46 �Indonesia 41 �South Africa 38 �Philippines 37 �Iran, Islamic Rep. 36 �Chile 35 �Thailand 33 �Morocco 19 �



Algebra Knowing

Correct Response: D

52

Russian Federation 72 �Korea, Rep. of 69 �Hong Kong, SAR 67 �Chinese Taipei 64 �Hungary 58 �Belgium (Flemish) 56 �Singapore 53 �Czech Republic 50 OJapan 49 �Slovak Republic 48 �Bulgaria 47 �Canada 43 OLatvia (LSS) 42 ORomania 42 OAustralia 41 OSlovenia 41 OUnited States 40 ONetherlands 40 OInternational Average 37Tunisia 37 OMoldova 36 OIsrael 35 OJordan 31 OMacedonia, Rep. of 30 ONew Zealand 30 OEngland 30 OLithuania 30 OThailand 29 �Cyprus 28 �Malaysia 26 �Italy 23 �Morocco 21 �Turkey 20 �Finland 19 �South Africa 19 �Iran, Islamic Rep. 18 �Indonesia 14 �Chile 11 �Philippines 8 �

Expression when a, b, c are real

Item Number: R10

Which of the following is true when a, b, and c are differentreal numbers?

A. a – b = b – a

B. a(b – c) = b(c – a)

C. b – c = c – b

D. ab = ba

E. ab – c = ab – b


Country average vs.





Algebra Knowing

Correct Response: A

53

Operations on negative number

Item Number: R12

If k represents a negative number, which of these is a positive number?

A. k 2

B. k 3

C. 2k

D. k2


Country average vs.



Chinese Taipei 84 �Russian Federation 81 �Hong Kong, SAR 79 �Korea, Rep. of 69 �Japan 69 �Slovenia 67 �Latvia (LSS) 67 �Hungary 67 �Slovak Republic 66 �Bulgaria 66 �Lithuania 64 �Belgium (Flemish) 63 �Singapore 63 �Romania 59 �Czech Republic 55 OMoldova 49 OItaly 49 OIsrael 48 OInternational Average 47United States 46 ONetherlands 42 OMalaysia 42 OTunisia 41 OMacedonia, Rep. of 40 OCanada 39 OAustralia 34 �Turkey 33 �Thailand 32 �Indonesia 30 �Iran, Islamic Rep. 30 �Cyprus 29 �Morocco 29 �Jordan 28 �Chile 27 �England 27 �Finland 25 �Philippines 25 �New Zealand 20 �South Africa 16 �


54

Total club members: boys and girls

Item Number: T01

A club has 86 members, and there are 14 more girls than boys.How many boys and how many girls are members of the club?

Show your work.

SCORING

Correct Response

• 36 boys and 50 girls [Numerical method: e.g., 86 ÷ 2 = 43; 43 – 7 = 36 boys; 43 + 7 = 50 girls]

• 36 boys and 50 girls [Algebraic method: e.g., b + (b + 14) = 86; 2b = 72; b = 36; g = 36 + 14 = 50]

• Other fully satisfactory method including “guess and check” with justification that 36 + 50 = 86

Partial Response

• Either 36 boys or 50 girls, with or without another (incorrect) number

• 36 and 50 are given [Makes correct computations but reverses labels or does not include any

mention of which is boys or girls]

• 36 boys and 50 girls, no method shown

• Gives an algebraic equation or system of equations that can lead to the correct solution

• Other partially correct

Incorrect Response

• 29 boys and 57 girls [Computes 86 ÷ 2 = 43; 43 – 14 = 29 and 43 + 14 = 57]

• One of the numbers is 72 [Computes 86 – 14]

• 29 boys and 43 girls [Computes 43 – 14 = 29]

• Gives an algebraic equation or system of equations that cannot lead to a correct solution






Country average vs.



Singapore 72 �Chinese Taipei 66 �Hong Kong, SAR 62 �Belgium (Flemish) 62 �Korea, Rep. of 61 �Slovak Republic 53 �Japan 53 �Hungary 46 �Czech Republic 46 �Canada 42 �Bulgaria 41 ORussian Federation 40 ONetherlands 38 ORomania 38 OAustralia 37 OSlovenia 37 OEngland 34 OCyprus 34 OInternational Average 33Finland 32 OLatvia (LSS) 32 ONew Zealand 32 OMalaysia 32 OIsrael 30 OUnited States 29 �Moldova 26 �Italy 24 �Lithuania 23 �Turkey 20 �Thailand 20 �Macedonia, Rep. of 16 �Iran, Islamic Rep. 14 �Indonesia 14 �Jordan 13 �Tunisia 10 �Philippines 9 �Chile 8 �Morocco 5 �South Africa 4 �


55

Sequence of figures with circles

Item Number: V04A

SCORING

A. Scoring for Number of Circles in Figures 4 and 5

Correct Response

• 10 AND 15

Incorrect Response

• 10 and any number other than 15

• 10 and no numerical response for 5th figure






Country average vs.



Korea, Rep. of 91 �Japan 91 �Singapore 89 �Chinese Taipei 87 �Hong Kong, SAR 87 �Netherlands 83 �England 81 �Belgium (Flemish) 81 �Canada 81 �Australia 81 �New Zealand 81 �Finland 80 �Czech Republic 79 �Hungary 77 �Slovenia 77 �Slovak Republic 77 �Malaysia 73 �United States 73 �Bulgaria 68 ORussian Federation 67 OItaly 66 OInternational Average 65Lithuania 64 OCyprus 64 OMoldova 64 OLatvia (LSS) 63 OIsrael 63 ORomania 57 OThailand 54 �Macedonia, Rep. of 51 �Indonesia 47 �Turkey 43 �Jordan 41 �Tunisia 39 �Iran, Islamic Rep. 36 �Chile 35 �Philippines 27 �Morocco 20 �South Africa 14 �


56


Item Number: V04B

SCORING

B. Scoring for Number of Circles in Figure 7

Correct Response

• 28

Incorrect Response

• 21

• 22






Country average vs.



Korea, Rep. of 86 �Japan 83 �Hong Kong, SAR 83 �Singapore 82 �Chinese Taipei 81 �Canada 72 �Australia 71 �Belgium (Flemish) 70 �England 68 �Netherlands 67 �Slovak Republic 67 �Hungary 66 �Slovenia 66 �Czech Republic 64 �New Zealand 64 �Malaysia 64 �Finland 62 �United States 62 �Russian Federation 54 OInternational Average 54Bulgaria 54 OCyprus 53 OMoldova 52 OItaly 52 OIsrael 52 OLatvia (LSS) 50 OLithuania 47 ORomania 47 �Thailand 46 �Macedonia, Rep. of 41 �Indonesia 38 �Turkey 33 �Jordan 30 �Tunisia 29 �Iran, Islamic Rep. 24 �Chile 24 �Philippines 21 �Morocco 12 �South Africa 9 �

SCORINGC. Scoring for Explanation and Answer for 51st Figure

Correct Response

• 1326. Correct general expression n (n + 1), 51(52),

or equivalent2 2

• 1326 [Adds 1275 + 51]

• Other fully correct, including [( figure number)2 – number of circles in previous figure]

Partial Response

• 1326 without showing how obtained

• Correct method but does not write 1326 as answer

• Other partially correct

Incorrect Response



57


Item Number: V04C


AlgebraCommunicating

and Reasoning


Country average vs.



Korea, Rep. of 70 �Chinese Taipei 68 �Japan 66 �Singapore 65 �Hong Kong, SAR 57 �Netherlands 48 �Belgium (Flemish) 44 �Canada 43 �Australia 39 �Hungary 38 �Malaysia 37 �Slovenia 37 OEngland 35 OUnited States 34 �Czech Republic 34 OSlovak Republic 31 ONew Zealand 31 OInternational Average 30Finland 30 OIsrael 27 ORussian Federation 27 OMoldova 26 OBulgaria 26 OThailand 25 OItaly 24 �Indonesia 24 �Latvia (LSS) 22 �Romania 19 �Lithuania 19 �Cyprus 15 �Macedonia, Rep. of 13 �Jordan 13 �Turkey 11 �Philippines 9 �Chile 8 �Tunisia 8 �Iran, Islamic Rep. 8 �South Africa 3 �Morocco 3 �



Measurement Knowing

Correct Response: C

58

Units to measure mass of egg

Item Number: D11

What units would be best to use to measure the weight (mass)of an egg?

A. centimeters

B. milliliters

C. grams

D. kilograms


Country average vs.



Japan 98 �Slovak Republic 96 �Hungary 96 �Czech Republic 95 �Korea, Rep. of 93 �Bulgaria 93 �Slovenia 93 �Singapore 93 �Belgium (Flemish) 92 �Russian Federation 92 �Australia 91 �Italy 90 �Netherlands 89 �Latvia (LSS) 89 �Malaysia 88 �Lithuania 88 �Finland 87 �Macedonia, Rep. of 87 �New Zealand 87 �Tunisia 86 �England 86 �Canada 85 �Romania 85 OMoldova 82 OHong Kong, SAR 82 OInternational Average 81Cyprus 79 OTurkey 78 OIsrael 75 �Chinese Taipei 73 �Jordan 73 �Thailand 69 �Chile 69 �Iran, Islamic Rep. 68 �United States 68 �Morocco 55 �South Africa 48 �Philippines 47 �Indonesia 34 �



Measurement Knowing

Correct Response: D

59

Measurement accuracy of ruler

Item Number: F10


Country average vs.



Finland 81 �Belgium (Flemish) 80 �Slovenia 75 �Latvia (LSS) 75 �Russian Federation 74 �Czech Republic 74 �Netherlands 72 �Hungary 71 �Bulgaria 65 �Australia 63 �Korea, Rep. of 61 �Italy 61 �Slovak Republic 60 �Lithuania 59 �Hong Kong, SAR 57 �New Zealand 56 �Singapore 52 OCanada 52 OEngland 51 OInternational Average 49Israel 48 OChinese Taipei 47 ORomania 45 OMacedonia, Rep. of 43 �United States 42 �Moldova 41 �Thailand 37 �Indonesia 35 �Japan 35 �Chile 33 �Malaysia 29 �Tunisia 29 �South Africa 27 �Cyprus 24 �Iran, Islamic Rep. 23 �Jordan 23 �Morocco 20 �Philippines 18 �Turkey 18 �



MeasurementInvestigating


Correct Response: B

60

Hong Kong, SAR 79 �Singapore 78 �Japan 74 �Chinese Taipei 73 �Korea, Rep. of 67 �Netherlands 57 �Australia 52 �Malaysia 52 �Slovak Republic 51 OCanada 51 OBelgium (Flemish) 51 �Finland 46 OHungary 46 OSlovenia 46 OCyprus 45 OItaly 45 OBulgaria 42 OInternational Average 42Czech Republic 40 OEngland 40 ONew Zealand 40 OTunisia 38 ORussian Federation 38 OThailand 35 OMoldova 34 OUnited States 33 �Morocco 31 �Lithuania 31 �Macedonia, Rep. of 30 �Romania 29 �Jordan 29 �Israel 28 �Latvia (LSS) 28 �Iran, Islamic Rep. 26 �Indonesia 25 �Turkey 22 �Chile 18 �Philippines 15 �South Africa 15 �

Area of path around garden

Item Number: J10


Country average vs.







Correct Response: D

61

Most paces to walk to end of hallway

Item Number: L13


Country average vs.



Belgium (Flemish) 94 �Hungary 91 �Finland 90 �Netherlands 90 �Japan 86 �Lithuania 84 �Latvia (LSS) 81 �Chinese Taipei 81 �Czech Republic 81 �Slovak Republic 81 �Chile 81 �Australia 79 �Slovenia 79 �Russian Federation 77 �Canada 76 �Italy 75 �Jordan 75 �Hong Kong, SAR 75 �England 74 OKorea, Rep. of 72 OCyprus 70 ORomania 68 ONew Zealand 68 OInternational Average 67Tunisia 67 OIsrael 67 OMoldova 66 OBulgaria 65 OSingapore 62 OUnited States 57 �Macedonia, Rep. of 56 �Thailand 54 �Malaysia 50 �Iran, Islamic Rep. 48 �Turkey 45 �Indonesia 27 �South Africa 23 �Morocco 20 �Philippines 20 �



Measurement Knowing

Correct Response: D

62

Angle closest to 45 degrees

Item Number: N15


Country average vs.



Japan 81 �Korea, Rep. of 81 �Chinese Taipei 79 �Slovak Republic 76 �Canada 73 �Finland 73 �Russian Federation 73 �Hong Kong, SAR 73 �Singapore 72 �Hungary 72 �Belgium (Flemish) 70 �Latvia (LSS) 70 �Australia 68 OThailand 64 OMalaysia 63 ORomania 62 OIran, Islamic Rep. 61 OCzech Republic 61 OBulgaria 61 OEngland 61 OSlovenia 61 OInternational Average 60Macedonia, Rep. of 60 OMoldova 58 OLithuania 58 OCyprus 56 ONew Zealand 56 OTunisia 53 ONetherlands 52 OIndonesia 51 �Israel 51 �United States 51 �Italy 51 �Chile 48 �Turkey 45 �Jordan 45 �Morocco 39 �Philippines 32 �South Africa 32 �





Correct Response: D

63

Ratio of width/perimeter in rectangle

Item Number: P08


Country average vs.



Singapore 56 �Chinese Taipei 53 �Hong Kong, SAR 45 �Japan 44 �Italy 32 �Korea, Rep. of 30 �Belgium (Flemish) 29 �Romania 28 ORussian Federation 26 OBulgaria 25 OInternational Average 22Slovak Republic 21 OMalaysia 21 OSlovenia 21 OMoldova 21 OJordan 20 OCzech Republic 20 OLatvia (LSS) 20 OLithuania 19 OAustralia 18 OTurkey 18 OSouth Africa 18 OTunisia 17 OIndonesia 17 OCyprus 17 OHungary 16 ONew Zealand 16 OCanada 16 �Israel 15 �Netherlands 15 OIran, Islamic Rep. 15 �Chile 14 �England 13 �Macedonia, Rep. of 13 �Morocco 12 �United States 11 �Finland 11 �Thailand 9 �Philippines 8 �



Measurement Using Complex Procedures

Correct Response: C

64

Length of string pulled straight

Item Number: P12


Country average vs.



Hungary 59 �Japan 57 �Slovak Republic 57 �Netherlands 56 �Belgium (Flemish) 54 �Hong Kong, SAR 53 �Czech Republic 53 �Chinese Taipei 53 �Latvia (LSS) 53 �Singapore 52 �Australia 52 �Slovenia 52 �Finland 50 OKorea, Rep. of 50 �Russian Federation 48 OMalaysia 46 OCanada 46 ONew Zealand 45 OLithuania 44 OEngland 43 OInternational Average 41Thailand 41 OMoldova 40 OBulgaria 39 OUnited States 39 OTunisia 38 OCyprus 36 ORomania 36 OIsrael 34 OIran, Islamic Rep. 33 �Italy 32 �Macedonia, Rep. of 32 �Turkey 30 �Jordan 26 �Chile 25 �Indonesia 23 �Philippines 15 �South Africa 15 �Morocco 11 �

Note: There is no distinction made between responses with or without units.

Correct Response

• 20

Incorrect Response

• 32 [4 x 8]

• 18 [perimeter]



65

Area of rectangle inside parallelogram

Item Number: T03

SCORING





Country average vs.



Singapore 83 �Japan 80 �Hong Kong, SAR 78 �Korea, Rep. of 78 �Chinese Taipei 75 �Belgium (Flemish) 65 �Canada 58 �Slovak Republic 57 �Finland 57 �Malaysia 56 �Netherlands 55 OAustralia 55 �Bulgaria 52 OSlovenia 49 ORussian Federation 49 OItaly 48 OEngland 48 OCzech Republic 46 OHungary 45 OLatvia (LSS) 44 OInternational Average 43Romania 43 ONew Zealand 41 OCyprus 41 OMoldova 38 OTunisia 38 �Lithuania 35 �United States 34 �Thailand 33 �Israel 28 �Jordan 26 �Iran, Islamic Rep. 25 �Macedonia, Rep. of 25 �Turkey 20 �Indonesia 20 �Morocco 8 �Chile 7 �Philippines 6 �South Africa 3 �



Geometry Using Complex Procedures

Correct Response: C

66

Cube from folded 2-dimensional net

Item Number: B11


Country average vs.



Japan 89 �Korea, Rep. of 85 �Hong Kong, SAR 84 �Singapore 83 �Chinese Taipei 83 �Netherlands 82 �Belgium (Flemish) 82 �Czech Republic 78 �Finland 77 �Australia 75 �Slovak Republic 74 �Canada 74 �Malaysia 71 �Latvia (LSS) 71 �New Zealand 70 �Slovenia 68 �Hungary 68 �United States 65 �England 64 OBulgaria 64 OLithuania 60 ORussian Federation 60 OInternational Average 59Italy 55 OThailand 53 OChile 48 �Israel 48 �Moldova 47 �Cyprus 45 �Romania 42 �Macedonia, Rep. of 39 �Indonesia 38 �Tunisia 37 �Turkey 34 �Jordan 34 �Iran, Islamic Rep. 28 �Philippines 24 �Morocco 21 �South Africa 15 �



GeometryInvestigating


Correct Response: C

67

Angles in symmetric polygon

Item Number: D07


Country average vs.



Hong Kong, SAR 82 �Korea, Rep. of 82 �Singapore 82 �Japan 80 �Bulgaria 80 �Latvia (LSS) 79 �Russian Federation 79 �Tunisia 77 �Slovak Republic 77 �Chinese Taipei 74 �Czech Republic 73 �Canada 72 �Lithuania 71 �Moldova 71 �Cyprus 69 �Finland 69 �Slovenia 66 ORomania 66 OItaly 65 OMacedonia, Rep. of 65 OBelgium (Flemish) 65 ONetherlands 64 OAustralia 62 OInternational Average 62Malaysia 59 OIsrael 58 OThailand 58 OHungary 56 �New Zealand 54 �United States 52 �Iran, Islamic Rep. 50 �England 46 �Jordan 44 �Indonesia 43 �Morocco 36 �Chile 35 �Turkey 35 �Philippines 23 �South Africa 19 �



Geometry Knowing

Correct Response: E

68

NOT true for all rectangles

Item Number: J11

Of the following, which is NOT true for all rectangles?

A. The opposite sides are parallel.

B. The opposite sides are equal.

C. All angles are right angles.

D. The diagonals are equal.

E. The diagonals are perpendicular.


Country average vs.



Japan 76 �Tunisia 75 �Belgium (Flemish) 74 �Korea, Rep. of 73 �Chinese Taipei 71 �Russian Federation 71 �Hungary 69 �Bulgaria 68 �Thailand 67 �Latvia (LSS) 64 �Slovak Republic 64 �Slovenia 62 OSingapore 61 OAustralia 61 ORomania 59 OEngland 58 OItaly 56 OLithuania 55 OCanada 55 OCyprus 54 OMacedonia, Rep. of 54 OInternational Average 54New Zealand 53 OHong Kong, SAR 53 OMoldova 53 OMalaysia 52 OJordan 50 OUnited States 46 �Iran, Islamic Rep. 46 ONetherlands 42 OTurkey 42 �Israel 39 �Finland 38 �Chile 36 �Indonesia 34 �Philippines 29 �Czech Republic 28 �Morocco 27 �South Africa 24 �



Geometry Knowing

Correct Response: C

69

Two similar triangles

Item Number: J15


Country average vs.



Japan 84 �Korea, Rep. of 82 �Singapore 76 �Malaysia 74 �Chinese Taipei 74 �Bulgaria 74 �Russian Federation 71 �Slovak Republic 70 OLithuania 69 OThailand 69 �Macedonia, Rep. of 68 OMoldova 68 OLatvia (LSS) 68 OHungary 67 OBelgium (Flemish) 66 OAustralia 66 OSlovenia 66 ORomania 66 OCzech Republic 66 OCanada 65 OItaly 65 OHong Kong, SAR 65 OFinland 63 ONetherlands 62 OUnited States 62 OInternational Average 62Iran, Islamic Rep. 61 OEngland 60 ONew Zealand 57 OCyprus 55 OJordan 53 �Turkey 52 �Tunisia 48 �Morocco 46 �Chile 46 �Indonesia 44 �Israel 42 �Philippines 41 �South Africa 29 �



Geometry Using Routine Procedures

Correct Response: D

70

Point on graph from coordinates

Item Number: J16


Country average vs.



Japan 84 �Korea, Rep. of 84 �Chinese Taipei 83 �Hong Kong, SAR 81 �Singapore 80 �Netherlands 78 �Malaysia 78 �Slovenia 76 �Slovak Republic 76 �England 75 �Australia 74 �Finland 72 �New Zealand 72 �Hungary 71 �Russian Federation 71 �Belgium (Flemish) 71 �Canada 67 �United States 67 �Lithuania 63 OItaly 62 OCzech Republic 58 OInternational Average 58Jordan 57 OIran, Islamic Rep. 55 OBulgaria 53 OIsrael 51 OIndonesia 50 �Moldova 48 �Romania 47 �Latvia (LSS) 46 �Macedonia, Rep. of 44 �Thailand 37 �Turkey 32 �Morocco 26 �Cyprus 24 �Philippines 23 �Chile 23 �South Africa 20 �Tunisia 10 �



GeometryInvestigating


Correct Response: A

71

Measure of angle in quadrilateral

Item Number: L16

In a quadrilateral, each of two angles has a measure of 115°. Ifthe measure of a third angle is 70°, what is the measure of theremaining angle?

A. 60°

B. 70°

C. 130°

D. 140°

E. None of the above


Country average vs.



Japan 73 �Belgium (Flemish) 70 �Singapore 67 �Chinese Taipei 61 �Hong Kong, SAR 60 �Korea, Rep. of 56 �Finland 53 �Slovenia 53 �Bulgaria 49 OMalaysia 49 �Russian Federation 49 OSlovak Republic 49 ORomania 48 OEngland 43 OItaly 41 OMoldova 40 OCzech Republic 40 OInternational Average 40Hungary 39 ONetherlands 39 OLatvia (LSS) 39 OTunisia 38 OAustralia 36 OMacedonia, Rep. of 36 OCanada 36 OLithuania 35 OJordan 35 OIsrael 35 OCyprus 30 OTurkey 29 �New Zealand 27 �Morocco 26 �Iran, Islamic Rep. 23 �Chile 23 �Thailand 22 �Indonesia 22 �United States 19 �South Africa 15 �Philippines 13 �




Correct Response: A

72

Position of point on number line

Item Number: N12


Country average vs.



Korea, Rep. of 67 �Netherlands 67 �Japan 66 �Belgium (Flemish) 65 �Hong Kong, SAR 63 �Russian Federation 60 �Chinese Taipei 56 �Hungary 51 �Finland 51 OCanada 50 �Australia 50 OSingapore 50 OSlovak Republic 48 ONew Zealand 47 OSlovenia 46 OThailand 46 OCzech Republic 46 OTunisia 44 OInternational Average 42United States 42 OMalaysia 42 OBulgaria 40 OLithuania 39 OMoldova 39 OCyprus 38 OEngland 36 OItaly 34 �Indonesia 34 �Latvia (LSS) 32 �Israel 32 �Macedonia, Rep. of 31 �Chile 31 �Romania 30 �Iran, Islamic Rep. 27 �Turkey 27 �Philippines 26 �South Africa 23 �Jordan 20 �Morocco 15 �




Correct Response: B

73

Length of side from similar triangle

Item Number: P10


Country average vs.



Korea, Rep. of 70 �Japan 68 �Singapore 64 �Hong Kong, SAR 56 �Chinese Taipei 52 �Belgium (Flemish) 50 �Netherlands 44 OHungary 43 ORussian Federation 41 OFinland 39 OAustralia 39 ORomania 38 OSlovak Republic 38 OInternational Average 37United States 36 OMoldova 36 OCanada 35 ONew Zealand 34 OSlovenia 34 OEngland 34 OBulgaria 33 OCzech Republic 32 OMalaysia 32 OJordan 32 OLithuania 31 OCyprus 31 OLatvia (LSS) 30 OThailand 30 �Italy 29 �Israel 29 OMacedonia, Rep. of 27 �Philippines 27 �Indonesia 26 �Iran, Islamic Rep. 26 �Tunisia 24 �Chile 23 �South Africa 23 �Turkey 22 �



Geometry Using Complex Procedures

Correct Response: C

74

Right triangles to cover rectangle

Item Number: R11


Country average vs.



Japan 80 �Korea, Rep. of 76 �Hong Kong, SAR 75 �Singapore 72 �Belgium (Flemish) 68 �Netherlands 66 �Malaysia 60 �Chinese Taipei 60 �Hungary 59 �Slovenia 57 �Slovak Republic 57 �Australia 56 �Czech Republic 55 ONew Zealand 55 �Canada 50 OFinland 49 OItaly 49 OEngland 48 OLatvia (LSS) 48 OUnited States 47 OInternational Average 46Russian Federation 44 OLithuania 43 OIran, Islamic Rep. 42 OIsrael 41 OThailand 40 OCyprus 37 OMoldova 37 �Romania 35 �Bulgaria 34 �Tunisia 33 �Turkey 30 �Macedonia, Rep. of 30 �Indonesia 29 �Chile 27 �Jordan 26 �Morocco 21 �Philippines 15 �South Africa 12 �



Data Representation,

Analysis and ProbabilityUsing Complex Procedures

Correct Response: D

75

Graph showing greatest increase

Item Number: B07


Country average vs.



Japan 92 �Korea, Rep. of 90 �Singapore 85 �Hong Kong, SAR 83 �Netherlands 82 �Finland 81 �Chinese Taipei 79 �Slovenia 77 �Australia 76 �Canada 75 �England 74 �United States 73 �New Zealand 72 �Hungary 72 �Belgium (Flemish) 71 �Russian Federation 70 �Malaysia 68 �Slovak Republic 65 OLithuania 62 OLatvia (LSS) 62 OIsrael 62 OItaly 61 OInternational Average 60Czech Republic 58 OBulgaria 55 OThailand 55 �Macedonia, Rep. of 52 �Turkey 42 �Indonesia 42 �Cyprus 40 �Chile 39 �Jordan 38 �Romania 36 �Philippines 36 �Tunisia 35 �Moldova 30 �South Africa 23 �Morocco 22 �




Analysis and ProbabilityKnowing

Correct Response: C

76

Likely result of fifth coin toss

Item Number: F08

If a fair coin is tossed, the probability that it will land heads up is12 . In four successive tosses, a fair coin lands heads up each time.What is likely to happen when the coin is tossed a fifth time?

A. It is more likely to land tails up than heads up.

B. It is more likely to land heads up than tails up.

C. It is equally likely to land heads up or tails up.

D. More information is needed to answer the question.


Country average vs.



Hungary 86 �England 81 �Netherlands 79 �Czech Republic 77 �Chinese Taipei 77 �Australia 76 �Latvia (LSS) 75 �Canada 75 �Belgium (Flemish) 74 �Finland 71 �New Zealand 71 �Bulgaria 70 �Slovenia 70 �Lithuania 70 �Italy 70 �Slovak Republic 70 �Korea, Rep. of 65 �Russian Federation 63 OUnited States 62 �Cyprus 60 OJapan 58 OInternational Average 57Jordan 57 OChile 56 OHong Kong, SAR 55 OIsrael 55 ORomania 53 OTurkey 52 OMacedonia, Rep. of 50 �Singapore 48 �Moldova 36 �South Africa 34 �Iran, Islamic Rep. 33 �Philippines 29 �Indonesia 28 �Tunisia 27 �Morocco 24 �Malaysia 24 �Thailand 20 �





Correct Response: C

77

Barchart histogram of travel time

Item Number: H07


Country average vs.



Korea, Rep. of 93 �Hong Kong, SAR 91 �Singapore 91 �Japan 84 �England 83 �Chinese Taipei 82 �Netherlands 82 �Belgium (Flemish) 82 �Australia 79 �New Zealand 79 �Finland 78 �Canada 78 �Slovenia 77 �United States 77 �Thailand 72 �Czech Republic 70 OHungary 69 OSlovak Republic 65 OInternational Average 64Latvia (LSS) 61 OMoldova 60 OItaly 59 OIsrael 59 �Russian Federation 59 OCyprus 58 �Lithuania 58 OIndonesia 52 �Tunisia 51 �Philippines 51 �Jordan 50 �Turkey 49 �Romania 47 �Chile 46 �Malaysia 46 �Macedonia, Rep. of 45 �Iran, Islamic Rep. 38 �Morocco 36 �South Africa 21 �




Analysis and Probability

Investigating


Correct Response: C

78

Defective bulbs from random sample

Item Number: H11

From a batch of 3,000 light bulbs, 100 were selected at randomand tested. If 5 of the light bulbs in the sample were found tobe defective, about how many defective light bulbs would beexpected in the entire batch?

A. 15

B. 60

C. 150

D. 300

E. 600


Country average vs.



Netherlands 86 �Hong Kong, SAR 85 �Chinese Taipei 83 �Singapore 83 �Korea, Rep. of 83 �Belgium (Flemish) 79 �Hungary 75 �Czech Republic 75 �Japan 73 �Slovenia 71 �Malaysia 71 �Slovak Republic 70 �Latvia (LSS) 70 �Finland 68 OCanada 67 ORussian Federation 65 OBulgaria 65 OCyprus 64 OAustralia 64 OThailand 64 OInternational Average 62England 59 OTunisia 59 OUnited States 58 ORomania 56 OItaly 56 ONew Zealand 56 OLithuania 56 OTurkey 54 �Macedonia, Rep. of 54 �Moldova 53 �Israel 52 �Indonesia 49 �Iran, Islamic Rep. 47 �Chile 46 �Jordan 44 �Philippines 36 �Morocco 32 �South Africa 30 �


79

Interpretation of pictograph of houses

Item Number: J13

SCORING

Correct Response

• 6 houses

Incorrect Response

• One house

• 5 houses






Country average vs.



Singapore 95 �Japan 93 �Hong Kong, SAR 93 �Korea, Rep. of 89 �Netherlands 88 �Chinese Taipei 88 �Canada 88 �Australia 86 �Finland 86 �Malaysia 85 �England 82 �United States 82 �New Zealand 82 �Slovenia 81 �Belgium (Flemish) 80 �Slovak Republic 79 �Latvia (LSS) 79 �Lithuania 78 OThailand 77 �Czech Republic 76 OItaly 74 ORussian Federation 73 OInternational Average 69Cyprus 67 ORomania 63 OTurkey 62 �Hungary 61 OIsrael 61 OBulgaria 58 �Iran, Islamic Rep. 57 �Tunisia 55 �Macedonia, Rep. of 54 �Chile 53 �Moldova 52 �Jordan 42 �Philippines 36 �Indonesia 31 �Morocco 23 �South Africa 14 �





Correct Response: C

80

Finland 79 �Japan 76 �Netherlands 76 �Chinese Taipei 73 �Australia 72 �Belgium (Flemish) 72 �Hungary 69 �Korea, Rep. of 68 �Singapore 68 �Canada 68 �England 68 �Hong Kong, SAR 68 �Slovak Republic 66 �Latvia (LSS) 65 OBulgaria 64 OLithuania 64 OUnited States 63 �Czech Republic 63 ORussian Federation 63 ONew Zealand 62 OMalaysia 61 OIsrael 60 OTunisia 58 OInternational Average 58Cyprus 57 OIran, Islamic Rep. 51 �Turkey 49 �Slovenia 47 �Chile 46 �Thailand 44 �Jordan 43 �Macedonia, Rep. of 43 �Romania 41 �Moldova 39 �Philippines 34 �Morocco 31 �Indonesia 30 �South Africa 29 �

Graph of humidity in room

Item Number: L11


Country average vs.







Investigating


Correct Response: C

81

Probability of drawing chip

Item Number: N18


Country average vs.



Korea, Rep. of 92 �Belgium (Flemish) 82 �Japan 77 �United States 77 �Canada 74 �England 73 �Australia 73 �Chinese Taipei 71 �Finland 66 �Hong Kong, SAR 65 �Netherlands 64 �Singapore 64 �Italy 61 �New Zealand 60 �Hungary 53 OSlovenia 51 OCyprus 51 OCzech Republic 49 OIsrael 49 OInternational Average 48Slovak Republic 48 OBulgaria 46 OTurkey 43 OMalaysia 42 OIndonesia 39 �Jordan 38 �Russian Federation 35 �Iran, Islamic Rep. 33 �Romania 32 �Chile 31 �Thailand 27 �Latvia (LSS) 27 �Macedonia, Rep. of 25 �South Africa 23 �Philippines 23 �Morocco 22 �Moldova 22 �Tunisia 21 �Lithuania 11 �





Correct Response: A

82

Japan 96 �Singapore 95 �Belgium (Flemish) 95 �Finland 93 �Korea, Rep. of 92 �England 92 �Chinese Taipei 91 �Slovenia 91 �Czech Republic 91 �Australia 91 �Slovak Republic 91 �Hong Kong, SAR 90 �Netherlands 90 �Canada 89 �United States 89 �New Zealand 88 �Hungary 87 �Cyprus 86 �Russian Federation 85 OMalaysia 85 �Lithuania 84 OLatvia (LSS) 83 OItaly 81 OInternational Average 79Israel 74 OBulgaria 72 OChile 67 �Moldova 66 �Romania 65 �Jordan 65 �Macedonia, Rep. of 65 �Iran, Islamic Rep. 59 �Philippines 54 �Indonesia 50 �South Africa 43 �Turkey 38 �

Day/time in table at shown temperature

Item Number: P16


Country average vs.







Correct Response: B

83

Time for pendulum to swing 20 times

Item Number: R09


Country average vs.



Korea, Rep. of 78 �Japan 78 �Hong Kong, SAR 71 �Singapore 71 �Netherlands 70 �Chinese Taipei 70 �England 68 �Belgium (Flemish) 68 �Finland 67 �Australia 67 �Canada 66 �Thailand 65 �Slovenia 63 �Malaysia 62 �Hungary 62 �Slovak Republic 59 OUnited States 59 ORussian Federation 58 ONew Zealand 58 OLithuania 57 OLatvia (LSS) 55 OIsrael 55 OInternational Average 54Czech Republic 53 OBulgaria 51 OItaly 48 OCyprus 46 OTunisia 43 �Romania 41 �Indonesia 40 �Jordan 40 �Philippines 37 �Chile 36 �Moldova 36 �Macedonia, Rep. of 35 �Morocco 35 �Turkey 32 �Iran, Islamic Rep. 31 �South Africa 18 �


84

Cheaper magazine subscription

Item Number: V02

SCORING

Note: There is no distinction made between responses with or without units.

Correct Response

• Teen Life. Calculations of both magazines are correct (60 ceds for Teen Life and 63 ceds for

Teen News) and correct savings of 3 ceds

• Other correct (e.g., Teen Life. Calculation of one magazine correct, the other not shown, andcorrect savings of 3 ceds).

Partial Response

• Correct calculations (60 and 63 ceds), but incorrect or no magazine identified and/or no differ-

ence given

• Correct calculation for Teen News (63 ceds), but incorrect calculation for Teen Life

• Incorrect calculation for Teen News but correct calculation for Teen Life (60 ceds)

• Teen Life, 3 ceds. No work shown

• Other partially correct response (e.g., correct calculations but incorrect difference)

Incorrect Response





Communicating

and Reasoning


Country average vs.



Singapore 57 �Korea, Rep. of 52 �Chinese Taipei 50 �Belgium (Flemish) 42 �Japan 39 �Slovak Republic 36 �Slovenia 36 �Hungary 35 �Latvia (LSS) 35 �Hong Kong, SAR 34 �Czech Republic 34 �Canada 32 �Russian Federation 30 OAustralia 29 OFinland 28 OItaly 27 OUnited States 26 ONetherlands 25 OLithuania 25 OInternational Average 24Bulgaria 22 OThailand 21 OCyprus 21 ORomania 20 OMalaysia 19 �Israel 19 �New Zealand 18 �Macedonia, Rep. of 17 �England 17 �Moldova 16 �Jordan 12 �Turkey 10 �Tunisia 9 �Iran, Islamic Rep. 9 �Chile 5 �Indonesia 5 �Philippines 3 �Morocco 2 �South Africa 1 �

Main TopicContent Domain

Correct Response: A

Cognitive Domain

85



Country average vs. International average:

Higher pNotdifferent OLower q

AlgebRA AlgebraicExpressionsKnowingFactsandProcedures

Valueof-3xgivenvalueofx

Item Number: M012042

e

M012042

If x = −3, what is the value of −3x ?

a −9

b −6

c −1

d 1

e 9

Hong Kong, SAR 84 pKorea, Republic of 84 pChinese Taipei 83 pSingapore 80 pEstonia 77 pJapan 74 pRussian Federation 73 pHungary 69 pIsrael 67 pSerbia and Montenegro 65 pUnited States 65 pBelgium (Flemish) 63 pArmenia 62 pLatvia 61 pLithuania 60 pSlovak Republic 58 pBulgaria 57 pMoldova, Republic of 54 pNetherlands 54 pRomania 51 OSlovenia 51 OLebanon 49 OInternational average 48 OMalaysia 48 OMacedonia, Republic of 47 OIran, Islamic Republic of 44 OPhilippines 44 qIndonesia 43 qJordan 41 qBahrain 40 qCyprus 38 qAustralia 37 qEgypt 37 qEngland 37 qItaly 37 qNew Zealand 35 qBotswana 30 qSweden 28 qTunisia 26 qPalestinian Nat’l Auth. 25 qMorocco 24 qScotland 24 qSouth Africa 16 qChile 15 qSaudi Arabia 11 qNorway 9 q

Correct Response:

86

Main TopicContent Domain Cognitive Domain






e


Subtractfractionsinvolvingx

M022185

Subtract:

3

7 7

x x− =

a

2

7

b 3

c 2x

d

x

7

e

2

7

x

Korea, Republic of 86 pHong Kong, SAR 83 pSingapore 81 pJapan 76 pLatvia 76 pChinese Taipei 76 pHungary 74 pRussian Federation 67 pLebanon 67 pRomania 65 pIsrael 65 pEstonia 65 pSerbia and Montenegro 64 pSlovak Republic 63 pBulgaria 63 pMalaysia 61 pArmenia 60 pBelgium (Flemish) 60 pCyprus 58 pMoldova, Republic of 58 pLithuania 57 OInternational average 54 OJordan 54 OBahrain 49 qPhilippines 49 qUnited States 49 qItaly 48 qEgypt 48 qSlovenia 47 qTunisia 47 qBotswana 46 qIran, Islamic Republic of 46 qPalestinian Nat’l Auth. 44 qAustralia 44 qIndonesia 43 qMorocco 43 qNew Zealand 42 qScotland 41 qNorway 40 qSweden 39 qNetherlands 39 qSaudi Arabia 37 qMacedonia, Republic of 37 qEngland 36 qChile 27 qSouth Africa 27 q


Correct Response:

Cognitive Domain

87






Whichequals2xminus3yplus7xplus5y


C

M03

2036

Which of these is equal to 2x − 3y + 7x + 5y?

a 5x + 2y

b 5x + 8y

c 9x + 2y

d 9x + 8y

Korea, Republic of 82 pJapan 82 pChinese Taipei 79 pSingapore 79 pSlovak Republic 76 pHong Kong, SAR 74 pHungary 74 pEstonia 72 pBelgium (Flemish) 67 pLatvia 66 pIsrael 65 pSerbia and Montenegro 62 pRussian Federation 62 pBulgaria 58 pRomania 58 pLebanon 55 OSlovenia 55 ONetherlands 54 OLithuania 53 OItaly 53 OIran, Islamic Republic of 52 OMalaysia 51 OInternational average 49 OScotland 48 OUnited States 47 OMoldova, Republic of 46 OSweden 45 OEgypt 45 OAustralia 45 OMacedonia, Republic of 41 qNorway 41 qArmenia 41 qJordan 38 qPhilippines 36 qCyprus 35 qPalestinian Nat’l Auth. 33 qEngland 33 qNew Zealand 33 qMorocco 32 qBahrain 27 qChile 25 qBotswana 25 qTunisia 24 qSouth Africa 23 qSaudi Arabia 23 qIndonesia 22 q

88






AlgebRA AlgebraicExpressions Reasoning

Thevalueofa+2times(bplusc)


SCORINgCorrect Response

• 11

Incorrect Response

• 8

• Otherincorrect(includingcrossedout/erased,straymarks,illegibleorofftask).

M032557

If a + 2b = 5 and c = 3, what is the value of a + 2(b + c)?

Answer: _______________

Korea, Republic of 64 pSingapore 58 pChinese Taipei 57 pHong Kong, SAR 56 pRussian Federation 53 pRomania 40 pHungary 38 pIsrael 38 pJapan 37 pEstonia 35 pLatvia 34 pSerbia and Montenegro 34 pArmenia 33 pMoldova, Republic of 31 pBulgaria 30 pSlovak Republic 28 pBelgium (Flemish) 28 pLithuania 26 pLebanon 25 OInternational average 22 OMalaysia 20 OAustralia 20 OUnited States 20 OCyprus 20 OMacedonia, Republic of 18 qScotland 18 OItaly 16 qNetherlands 16 qEngland 15 qNew Zealand 14 qSlovenia 13 qSweden 10 qEgypt 10 qJordan 9 qIndonesia 8 qTunisia 5 qPalestinian Nat’l Auth. 5 qPhilippines 5 qMorocco 4 qIran, Islamic Republic of 3 qChile 3 qNorway 3 qSouth Africa 3 qBotswana 2 qBahrain 2 qSaudi Arabia 0 q

89

Student Responses


Thevalueofa+2times(bplusc)(continued)Item Number: M032557

Correct Response:

Incorrect Response:

Correct Response: A

90







Threeconsecutiveevennumbers

AlgebRA AlgebraicExpressions SolvingRoutineProblems

M022002

Sam wanted to find three consecutive even numbers that add up to 84.He wrote the equation k + (k + 2) + (k + 4) = 84.What does the letter k represent?

a The least of the three even numbers

b The middle even number

c The greatest of the three even numbers

d The average of the three even numbers

Hong Kong, SAR 57 pChinese Taipei 50 pSingapore 48 pKorea, Republic of 46 pRomania 42 pEstonia 37 pRussian Federation 36 pMoldova, Republic of 34 pJapan 34 pBulgaria 34 pSerbia and Montenegro 33 pLatvia 33 pHungary 31 pIsrael 31 pArmenia 30 pBelgium (Flemish) 30 pSlovak Republic 27 ONetherlands 27 OPhilippines 25 OBahrain 25 OInternational average 24 OUnited States 23 OMacedonia, Republic of 22 OItaly 21 OAustralia 20 OBotswana 20 qSouth Africa 19 qSaudi Arabia 19 qLithuania 19 qCyprus 19 qEgypt 18 qJordan 18 qIndonesia 16 qEngland 16 qPalestinian Nat’l Auth. 16 qNew Zealand 16 qIran, Islamic Republic of 15 qSweden 15 qMorocco 15 qSlovenia 12 qLebanon 12 qChile 11 qScotland 11 qNorway 11 qMalaysia 11 qTunisia 6 q


Correct Response:

Cognitive Domain

91





AlgebRA AlgebraicExpressions UsingConcepts

Totalnumberofbooksthreeboyshave


C

M022251

Graham has twice as many books as Bob. Chan has six more books thanBob. If Bob has x books, which of the following represents the total numberof books the three boys have?

a 3x + 6

b 3x + 8

c 4x + 6

d 5x + 6

e 8x + 2

Singapore 66 pChinese Taipei 59 pKorea, Republic of 55 pHong Kong, SAR 53 pIsrael 41 pHungary 41 pSlovak Republic 38 pRussian Federation 36 pJapan 35 pRomania 35 pNetherlands 35 pEstonia 34 pCyprus 34 pBelgium (Flemish) 33 pItaly 33 OLatvia 32 OLithuania 32 ONew Zealand 31 OSerbia and Montenegro 31 OSlovenia 31 OInternational average 29 OMoldova, Republic of 29 OAustralia 28 OBulgaria 28 OSweden 28 OArmenia 26 OUnited States 26 qEngland 25 qMalaysia 25 qScotland 25 qTunisia 24 qNorway 23 qIran, Islamic Republic of 23 qMorocco 22 qMacedonia, Republic of 22 qEgypt 21 qJordan 20 qLebanon 20 qPalestinian Nat’l Auth. 20 qPhilippines 19 qBahrain 18 qChile 18 qIndonesia 18 qSaudi Arabia 15 qBotswana 13 qSouth Africa 12 q

Correct Response:

92






AlgebRA AlgebraicExpressions UsingConcepts

Carlapaidxzedsfor3cartonsofjuice


A

M032044

Carla paid x zeds for 3 cartons of juice. What is the price in zeds of1 carton of juice?

a 3x

b x

3

c 3 + x

d 3x

Singapore 85 pHong Kong, SAR 81 pChinese Taipei 74 pBelgium (Flemish) 67 pNetherlands 62 pMalaysia 59 pRussian Federation 58 pEngland 55 pHungary 55 pKorea, Republic of 53 pEstonia 53 pIsrael 53 pSlovak Republic 52 pSweden 52 pJapan 51 pLithuania 51 pScotland 49 pAustralia 49 OUnited States 48 pArmenia 48 OLebanon 48 OLatvia 46 OItaly 45 OInternational average 45 ONew Zealand 43 OSerbia and Montenegro 42 ORomania 42 OBulgaria 42 OMoldova, Republic of 41 OPhilippines 40 qNorway 40 qSlovenia 40 qMacedonia, Republic of 39 qIndonesia 39 qTunisia 36 qCyprus 36 qEgypt 35 qJordan 34 qChile 31 qBahrain 30 qPalestinian Nat’l Auth. 30 qBotswana 29 qMorocco 28 qGhana 28 qSouth Africa 23 qSaudi Arabia 22 qIran, Islamic Republic of 21 q


Correct Response:

Cognitive Domain

93






b

Findnfromproportionalityequation

AlgebRA EquationsandFormulasKnowingFactsandProcedures

M012040

If

12n

=

3621

, then n equals

a 3

b 7

c 36

d 63

Singapore 93 pKorea, Republic of 89 pHong Kong, SAR 88 pBelgium (Flemish) 86 pNetherlands 85 pChinese Taipei 83 pMalaysia 83 pUnited States 80 pHungary 79 pJapan 79 pScotland 79 pAustralia 76 pEngland 74 pSlovak Republic 74 pIsrael 72 pSlovenia 72 pEstonia 71 pLebanon 71 pRussian Federation 71 pLatvia 70 pNew Zealand 68 OIran, Islamic Republic of 66 OSweden 66 OCyprus 65 OItaly 65 OInternational average 64 OLithuania 64 OTunisia 64 OSerbia and Montenegro 63 OMoldova, Republic of 61 ORomania 61 OBulgaria 59 qNorway 59 qEgypt 58 qIndonesia 58 qArmenia 54 qMorocco 54 qJordan 53 qPalestinian Nat’l Auth. 52 qPhilippines 52 qMacedonia, Republic of 50 qBahrain 44 qChile 44 qBotswana 41 qSaudi Arabia 30 qGhana 28 qSouth Africa 26 q

Correct Response: A

94







TrueexpressionforvaluesofL,K,M


M022196

If L = 4 when K = 6 and M = 24, which of the following is true?

a L =

M

K

b L =

K

M

c L = KM

d L = K + M

e L = M − K

Singapore 88 pKorea, Republic of 86 pHong Kong, SAR 84 pChinese Taipei 82 pEstonia 81 pRussian Federation 79 pHungary 79 pJapan 77 pBelgium (Flemish) 76 pSlovak Republic 75 pLatvia 75 pSerbia and Montenegro 73 pLithuania 73 pSweden 70 pLebanon 69 pRomania 67 pArmenia 66 pSlovenia 66 pIsrael 64 pMoldova, Republic of 63 pBulgaria 63 OTunisia 63 pUnited States 62 pMacedonia, Republic of 60 ONetherlands 59 OInternational average 58 OMorocco 57 OItaly 57 OEngland 54 OMalaysia 54 OIndonesia 54 OCyprus 52 qAustralia 49 qScotland 49 qNew Zealand 49 qJordan 44 qNorway 40 qEgypt 38 qIran, Islamic Republic of 38 qPalestinian Nat’l Auth. 35 qBahrain 35 qBotswana 28 qPhilippines 25 qSaudi Arabia 22 qChile 21 qSouth Africa 14 q

95







• 15

Incorrect Response

• 25[100÷4]

• 60[80–(4x5)]

• 71[80–4–5]

• Anyexpressionorequation,otherthanx=15,containingx.

• Otherincorrect(includingcrossedout/erased,straymarks,illegible,orofftask).


Solveequationforx


M022253

If 4(x + 5) = 80, then x =

Answer: _______________

Hong Kong, SAR 90 pSingapore 82 pKorea, Republic of 82 pJapan 80 pChinese Taipei 80 pEstonia 72 pHungary 70 pRussian Federation 66 pSlovak Republic 65 pBelgium (Flemish) 64 pLatvia 64 pSlovenia 64 pArmenia 61 pSerbia and Montenegro 61 pRomania 60 pBulgaria 59 pUnited States 57 pIsrael 57 pCyprus 54 pMoldova, Republic of 53 pLithuania 51 pAustralia 50 pMalaysia 46 ONetherlands 44 OInternational average 44 OEngland 44 ONew Zealand 44 OMacedonia, Republic of 37 qItaly 37 qScotland 37 qLebanon 31 qSweden 28 qTunisia 26 qJordan 25 qIndonesia 25 qEgypt 23 qPhilippines 22 qBahrain 19 qIran, Islamic Republic of 18 qPalestinian Nat’l Auth. 17 qMorocco 16 qNorway 11 qChile 9 qSaudi Arabia 6 qSouth Africa 5 qBotswana 5 q

96

Student Responses


Solveequationforx(continued)Item Number: M022253

Correct Response:

Incorrect Response:


Correct Response: A

Cognitive Domain

97






Ifxplus3yequals11and2xplus3yequals13


M032728

If x + 3y = 11 and 2x + 3y = 13, then y =

a 3

b 2

c −2

d −3

Korea, Republic of 76 pSingapore 70 pChinese Taipei 69 pJapan 61 pHong Kong, SAR 59 pScotland 55 pBelgium (Flemish) 53 pLatvia 51 pEstonia 50 pUnited States 49 pSerbia and Montenegro 49 pEngland 49 ORomania 48 OHungary 47 OSlovak Republic 46 ONew Zealand 45 OMoldova, Republic of 45 OBulgaria 45 ORussian Federation 44 OAustralia 44 OIsrael 44 ONetherlands 43 OMalaysia 43 OInternational average 42 OLebanon 40 OBotswana 38 OLithuania 37 OJordan 37 qTunisia 36 qSlovenia 36 OMacedonia, Republic of 36 qSweden 35 qPhilippines 35 qCyprus 34 qEgypt 34 qIran, Islamic Republic of 34 qIndonesia 33 qChile 31 qPalestinian Nat’l Auth. 31 qSouth Africa 31 qNorway 30 qSaudi Arabia 29 qArmenia 29 qItaly 28 qBahrain 27 qMorocco 23 q

Correct Response:

98






AlgebRA EquationsandFormulas SolvingRoutineProblems

Ifxminusyequals5andx/2equals3


b

M032208

If x − y = 5 and

x

2 = 3, what is the value of y?

a 6

b 1

c −1

d −7

Singapore 82 pKorea, Republic of 79 pHong Kong, SAR 78 pChinese Taipei 77 pAustralia 69 pBelgium (Flemish) 69 pNew Zealand 67 pHungary 67 pEngland 66 pUnited States 63 pScotland 61 pJapan 61 pMalaysia 58 pIsrael 58 pEstonia 58 pSerbia and Montenegro 58 pRomania 57 pLatvia 56 pSlovenia 55 OCyprus 55 pNorway 55 OSweden 53 ONetherlands 53 OLithuania 53 ORussian Federation 52 OInternational average 51 OLebanon 48 OSlovak Republic 47 OMoldova, Republic of 47 OItaly 46 qMacedonia, Republic of 45 qBulgaria 44 qPalestinian Nat’l Auth. 43 qArmenia 43 qBotswana 39 qIndonesia 38 qBahrain 38 qJordan 38 qChile 37 qEgypt 36 qPhilippines 33 qTunisia 31 qMorocco 31 qSouth Africa 30 qIran, Islamic Republic of 26 qSaudi Arabia 24 q


Correct Response: A

Cognitive Domain

99





Ifa/bequals70



M032210

If

a

b = 70, then

a

b2 =

a 35

b 68

c 72

d 140

Chinese Taipei 70 pSingapore 69 pKorea, Republic of 69 pHong Kong, SAR 68 pEstonia 61 pRussian Federation 60 pHungary 58 pSerbia and Montenegro 57 pJapan 55 pRomania 53 pLatvia 53 pBelgium (Flemish) 52 pLithuania 51 pSlovak Republic 47 pBulgaria 46 pIsrael 44 pItaly 44 OMacedonia, Republic of 42 OMoldova, Republic of 41 OIndonesia 41 OArmenia 41 OInternational average 40 ONetherlands 40 OSweden 38 OUnited States 38 OEngland 38 OLebanon 37 OSlovenia 37 OAustralia 37 OMalaysia 36 ONew Zealand 32 qScotland 30 qCyprus 30 qTunisia 30 qPhilippines 27 qIran, Islamic Republic of 27 qEgypt 26 qBotswana 25 qMorocco 24 qJordan 23 qNorway 22 qChile 22 qPalestinian Nat’l Auth. 21 qSouth Africa 17 qSaudi Arabia 15 qBahrain 15 q

100







7orangesand4lemonscost43zeds



• 7x+4y=43(orequivalent)and11x+12y=79(orequivalent).

Incorrect Response

• Oneequationcorrectandoneincorrect/missing.


M032545

At a market, 7 oranges and 4 lemons cost 43 zeds, and 11 oranges and12 lemons cost 79 zeds. Using x to represent the cost of an orange and y torepresent the cost of a lemon, write two equations that could be used to findthe values of x and y.

Equation 1:__________________________________________________________

Equation 2:__________________________________________________________

Hong Kong, SAR 72 pJapan 67 pChinese Taipei 62 pArmenia 61 pSingapore 60 pKorea, Republic of 57 pEstonia 46 pSerbia and Montenegro 43 pIsrael 41 pRussian Federation 39 pRomania 38 pJordan 37 pHungary 34 pBulgaria 33 pMoldova, Republic of 27 OEgypt 27 OSlovak Republic 25 OMacedonia, Republic of 24 OInternational average 24 OBelgium (Flemish) 22 OIran, Islamic Republic of 20 OUnited States 20 qLatvia 20 qScotland 20 qLithuania 19 qEngland 18 qBahrain 16 qIndonesia 16 qMalaysia 15 qSweden 15 qAustralia 15 qItaly 14 qNew Zealand 12 qCyprus 11 qSlovenia 9 qMorocco 9 qNetherlands 9 qPhilippines 7 qPalestinian Nat’l Auth. 6 qLebanon 6 qBotswana 5 qSaudi Arabia 4 qNorway 3 qChile 3 qGhana 2 qSouth Africa 2 qTunisia 1 q

101

Student Responses


Correct Response:

Incorrect Response:

7orangesand4lemonscost43zeds(continued)Item Number: M032545

Correct Response:

102






C


Objectsbalancedonscale

AlgebRA EquationsandFormulas UsingConcepts

M012002

The objects on the scale make it balance exactly. On the left pan there is a1 kg weight (mass) and half a brick. On the right pan there is one brick.

What is the weight (mass) of one brick?

a 0.5 kg

b 1 kg

c 2 kg

d 3 kg

1 kg

Estonia 86 pRussian Federation 85 pNetherlands 83 pJapan 82 pSingapore 82 pHong Kong, SAR 81 pItaly 79 pBelgium (Flemish) 78 pKorea, Republic of 78 pSlovak Republic 78 pSweden 78 pLatvia 77 pAustralia 76 pChinese Taipei 76 pEngland 76 pLithuania 76 pHungary 75 pNew Zealand 75 pMalaysia 74 pScotland 74 pUnited States 74 pBulgaria 73 pSlovenia 73 pMoldova, Republic of 68 pIsrael 67 pNorway 66 ORomania 66 OSerbia and Montenegro 65 OCyprus 64 OInternational average 63 OIran, Islamic Republic of 63 OMacedonia, Republic of 63 OJordan 52 qArmenia 51 qTunisia 51 qChile 50 qMorocco 49 qPalestinian Nat’l Auth. 45 qBahrain 42 qEgypt 42 qIndonesia 41 qLebanon 41 qBotswana 36 qPhilippines 34 qSaudi Arabia 31 qSouth Africa 28 qGhana 26 q


Correct Response: A

Cognitive Domain

103





M032046

If 23 += xy , which of these expresses x in terms of y?

a 32−

=y

x

b 32+

=y

x

c x =

y

3 − 2

d x =

y

3 + 2

AlgebRA EquationsandFormulas UsingConcepts

Ifyequals3xplus2


Singapore 61 pHong Kong, SAR 60 pKorea, Republic of 52 pChinese Taipei 48 pJapan 46 pArmenia 45 pRussian Federation 44 pRomania 44 pSerbia and Montenegro 43 pMoldova, Republic of 34 pBulgaria 34 pMalaysia 31 pBelgium (Flemish) 31 pIndonesia 30 pMacedonia, Republic of 30 pEstonia 27 OUnited States 26 OInternational average 25 OLebanon 24 OIsrael 24 OJordan 23 OPhilippines 22 qEgypt 21 qLithuania 21 qHungary 21 qLatvia 21 qCyprus 20 qItaly 20 qEngland 20 qSlovak Republic 19 qAustralia 18 qNetherlands 17 qTunisia 17 qIran, Islamic Republic of 16 qPalestinian Nat’l Auth. 15 qBahrain 15 qSlovenia 15 qNew Zealand 14 qScotland 12 qMorocco 12 qSaudi Arabia 12 qSweden 11 qBotswana 10 qSouth Africa 10 qChile 9 qNorway 6 q

Correct Response:

104






AlgebRA Patterns Reasoning

Numberofmatchstickscontinuingpattern


b

M012017

Matchsticks are arranged as shown in the figures.

If the pattern is continued, how many matchsticks would be used to makeFigure 10?

a 30

b 33

c 36

d 39

e 42

Figure 1 Figure 3Figure 2

Korea, Republic of 78 pSingapore 73 pChinese Taipei 71 pJapan 67 pHong Kong, SAR 66 pBelgium (Flemish) 64 pNew Zealand 63 pAustralia 62 pScotland 61 pHungary 61 pSlovak Republic 60 pNetherlands 59 pRussian Federation 59 pSweden 59 pEstonia 58 pIsrael 58 pMalaysia 57 pUnited States 56 pSlovenia 56 pLithuania 56 pMoldova, Republic of 55 pItaly 54 pBulgaria 53 OEngland 52 ORomania 51 OSerbia and Montenegro 51 OMacedonia, Republic of 50 OLatvia 49 OCyprus 49 OInternational average 48 OArmenia 47 ONorway 46 OChile 43 qPhilippines 41 qBahrain 37 qIran, Islamic Republic of 34 qJordan 33 qLebanon 32 qEgypt 30 qTunisia 29 qIndonesia 29 qPalestinian Nat’l Auth. 29 qBotswana 27 qMorocco 26 qSouth Africa 24 qSaudi Arabia 16 qGhana 16 q

105






SCORINgCorrect

• 55

Incorrect Response

• 27AND46[23+4and37+9]

• Either27OR46



Numbersinsequenceincreasingby4

AlgebRA Patterns Reasoning

M022008

The numbers in the sequence 7, 11, 15, 19, 23, … increase by four. Thenumbers in the sequence 1, 10, 19, 28, 37, … increase by nine. The number19 is in both sequences. If the two sequences are continued, what is the nextnumber that is in BOTH the first and the second sequences?

Answer: _______________

Armenia 63 pKorea, Republic of 51 pSingapore 50 pHungary 49 pJapan 46 pUnited States 45 pItaly 45 pBelgium (Flemish) 43 pSlovenia 41 pAustralia 39 pHong Kong, SAR 39 pSlovak Republic 39 pChinese Taipei 39 pBulgaria 38 pEstonia 38 pNetherlands 38 pScotland 37 pSweden 35 pMalaysia 35 pEngland 34 OTunisia 34 ONew Zealand 33 OLithuania 33 ORussian Federation 32 ORomania 32 OIsrael 31 OCyprus 31 OLatvia 31 OInternational average 31 OMoldova, Republic of 30 OIran, Islamic Republic of 25 qMacedonia, Republic of 24 qChile 24 qIndonesia 23 qSerbia and Montenegro 23 qBahrain 22 qMorocco 20 qNorway 20 qPalestinian Nat’l Auth. 19 qBotswana 18 qLebanon 17 qJordan 16 qEgypt 14 qPhilippines 14 qSaudi Arabia 8 qSouth Africa 6 qGhana 4 q

106

Student Responses


Numbersinsequenceincreasingby4(continued)Item Number: M022008

Correct Response:

Incorrect Response:

107


Item Number: M022261A


• 18AND32

Incorrect Response

• 18andanynumberotherthan32.

• 18andnonumericalresponseforthe4thfigure.


Sequenceoffigureswithtriangles:filltable

M022261

The three figures below are divided into small congruent triangles.

A. Complete the table below. First, fill in how many small triangles makeup Figure 3. Then, find the number of small triangles that would beneeded for the 4th figure if the sequence of figures is extended.

Number ofFigure Small Triangles

1 2

2 8

3

4

B. The sequence of figures is extended to the 7th figure. How many smalltriangles would be needed for Figure 7?

Answer: _______________

C. The sequence of figures is extended to the 50th figure. Explain a way tofind the number of small triangles in the 50th figure that does notinvolve drawing it and counting the number of triangles.

Figure 1 Figure 2 Figure 3

1

2

12

34

5

6

7

8




Korea, Republic of 78 p

Singapore 74 p

Japan 74 p

Hong Kong, SAR 72 p

Chinese Taipei 69 p

Netherlands 59 p

Australia 57 p

England 57 p

New Zealand 55 p

Armenia 53 p

Scotland 53 p

Belgium (Flemish) 51 p

Hungary 50 p

United States 50 p

Estonia 50 p

Sweden 49 p

Slovenia 42 p

Malaysia 42 p

Israel 42 p

Russian Federation 41 p

Slovak Republic 40 O

Latvia 38 O

Lithuania 38 O

International average 36 O

Italy 35 O

Norway 34 O

Romania 31 O

Moldova, Republic of 31 q

Serbia and Montenegro 31 q

Cyprus 30 q

Bulgaria 30 q

Macedonia, Republic of 25 q

Chile 23 q

Jordan 21 q

Indonesia 20 q

Palestinian Nat’l Auth. 17 q

Philippines 17 q

Morocco 16 q

Bahrain 16 q

Iran, Islamic Republic of 15 q

Egypt 15 q

Lebanon 12 q

Botswana 11 q

South Africa 6 q

Tunisia 5 q

Saudi Arabia 4 q

Ghana 3 q

Main Topic

A. AlgebRAB.ALgEBRAC.ALgEBRA

PatternsPatternsPatterns

Solving Routine ProblemsSolvingRoutineProblems

Reasoning


108

Student Responses


Sequenceoffigureswithtriangles:filltable(continued)Item Number: M022261A

Correct Response:

Incorrect Response:

109

Item Number: M022261B


• 98

Incorrect Response

• 49[Multiplies7x7]

• 58[Seriesis2,8,18,28,38…7thtermis58]


Sequenceoffigureswithtriangles:7thfigure

M022261




1 2

2 8

3

4


Answer: _______________



1

2

12

34

5

6

7

8





Singapore 56 p

Chinese Taipei 56 p

Hong Kong, SAR 56 p

Japan 55 p

Armenia 42 p

Netherlands 40 p

Australia 33 p

Scotland 31 p

Hungary 30 p

United States 30 p

New Zealand 29 p


Sweden 26 p

England 25 O

Malaysia 24 O

Estonia 24 O

Italy 24 O

Russian Federation 23 O

Slovenia 22 O



Moldova, Republic of 20 O

Israel 20 O

Lithuania 19 O

Romania 19 O

Latvia 19 O

Serbia and Montenegro 19 O

Cyprus 17 q

Bulgaria 16 q

Indonesia 15 q

Norway 14 q

Jordan 12 q

Philippines 11 q



Chile 9 q

Egypt 9 q

Bahrain 8 q


Morocco 7 q

Lebanon 6 q

Botswana 5 q

South Africa 4 q

Tunisia 2 q

Ghana 2 q

Saudi Arabia 0 q


Main Topic

A.ALgEBRAb. AlgebRAC.ALgEBRA


SolvingRoutineProblemsSolving Routine Problems

Reasoning


110

Student Responses


Sequenceoffigureswithtriangles:7thfigure(continued)Item Number: M022261B

Correct Response:

Incorrect Response:

111


Item Number: M022261C

SCORINgCorrect Response• Correctgeneral(i.e.,literal)expression,e.g.,2n2,orequivalentexpressedinwords.

• 2x502OR2x50x50OR100x50OR(50+50)x50ORequivalentexpressedinwords(disregarderrorsincomputation).

Partial Response• Derivesanswer(5000)withoutshowingwork.

• Otherpartiallycorrect.

Incorrect Response• 50x2OR100

• 50x50OR2,500


Sequenceoffigureswithtriangles:50thfigure

M022261




1 2

2 8

3

4


Answer: _______________



1

2

12

34

5

6

7

8




Chinese Taipei 49 p


Hong Kong, SAR 45 p

Singapore 44 p

Japan 44 p

Netherlands 36 p

Australia 26 p

Hungary 24 p

Scotland 22 p


England 20 p

United States 19 p

Sweden 17 p

New Zealand 16 O

Estonia 15 O



Italy 14 O

Latvia 13 O

Slovenia 13 O

Serbia and Montenegro 11 q

Lithuania 11 q

Romania 11 O

Malaysia 10 q

Israel 10 q

Cyprus 10 q

Norway 9 q

Russian Federation 9 q

Armenia 8 q

Indonesia 7 q

Chile 6 q

Jordan 5 q

Egypt 5 q



Philippines 4 q

Bulgaria 4 q

Bahrain 4 q


Morocco 2 q

Botswana 2 q

South Africa 1 q

Tunisia 1 q

Lebanon 1 q

Ghana 1 q

Saudi Arabia 0 q

Moldova, Republic of 0 q

Main Topic

A.ALgEBRAB.ALgEBRAC. AlgebRA


SolvingRoutineProblemsSolvingRoutineProblems

Reasoning


112

Student Responses


Sequenceoffigureswithtriangles/50thfigure(continued)Item Number: M022261C

Correct Response:

Partial Response:

113


Sequenceoffigureswithtriangles/50thfigure(continued)Item Number: M022261C

Student Responses (continued)

Incorrect Response:

114





TIMSS 2003 8th-Grade Mathematics Concepts and Mathematics ItemsM

032744

If the pattern on the grid below was continued, what letter would identifythe orientation of the tile in the cell labeled X?

Answer: _______________________

Questions for Geometry Tiling continue.

X


• D(includingdrawingoftileD).

Incorrect Response

• A,B,orC(includingdrawings).



Geometrytiling:identifycellwithletter

AlgebRA Patterns UsingConcepts

Japan 73 pKorea, Republic of 66 pSingapore 62 pSweden 57 pHong Kong, SAR 57 pNetherlands 55 pChinese Taipei 55 pEstonia 55 pHungary 54 pScotland 54 pAustralia 53 pNew Zealand 51 pBelgium (Flemish) 50 pUnited States 48 pEngland 47 pSlovak Republic 46 pLatvia 45 pMalaysia 44 pSlovenia 43 pRussian Federation 39 pNorway 36 OItaly 34 OIsrael 34 OInternational average 32 OBulgaria 30 ORomania 29 OLithuania 27 OCyprus 24 qChile 23 qBahrain 22 qSerbia and Montenegro 20 qJordan 16 qMoldova, Republic of 15 qPhilippines 14 qIran, Islamic Republic of 13 qMacedonia, Republic of 13 qIndonesia 11 qLebanon 10 qSouth Africa 8 qSaudi Arabia 8 qMorocco 7 qEgypt 7 qBotswana 7 qArmenia 6 qPalestinian Nat’l Auth. 3 qTunisia 2 q

115

Student Responses


Geometrytiling:identifycellwithletter(continued)Item Number: M032744

Correct Response:

116


Geometrytiling:identifycellwithletter(continued)Item Number: M032744

Incorrect Response:



Correct Response:

Cognitive Domain

117





M012029

(3, 6) , (6, 15) , (8, 21)

Which of these describes how to get the second number from the firstnumber in every ordered pair above?

a Add 3

b Subtract 3

c Multiply by 2

d Multiply by 2 and then add 3

e Multiply by 3 and then subtract 3

AlgebRA Relationships Reasoning


e

Setsoforderedpairsofnumbers

Korea, Republic of 85 pJapan 76 pHungary 75 pEstonia 74 pChinese Taipei 71 pSingapore 71 pHong Kong, SAR 71 pLatvia 71 pAustralia 70 pRussian Federation 69 pScotland 69 pUnited States 68 pNetherlands 68 pNew Zealand 67 pEngland 64 pLithuania 64 pBelgium (Flemish) 62 pSerbia and Montenegro 58 pIsrael 57 pSlovak Republic 56 pBulgaria 54 OSlovenia 53 OItaly 51 OMalaysia 51 OInternational average 50 OJordan 46 qSweden 45 qMacedonia, Republic of 42 qRomania 42 qNorway 40 qMoldova, Republic of 39 qBahrain 38 qBotswana 36 qIran, Islamic Republic of 35 qArmenia 34 qEgypt 33 qIndonesia 33 qPalestinian Nat’l Auth. 33 qPhilippines 31 qSaudi Arabia 26 qCyprus 25 qChile 24 qGhana 23 qLebanon 23 qSouth Africa 21 q

Correct Response:

118






012025

The graph represents the distance and time of a hike taken by Joshua and Liam.

If they both started from the same place and walked in the same direction,at what time did they meet?

a 8:00

b 8:30

c 9:00

d 10:00

e 11:00

8:00 8:30 9:00 9:30 10:00 10:30 11:00 11:30 12:00 12:30

Time

Dis

tance

(ki

lom

eter

s)

JoshuaLiam

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

AlgebRA Relationships SolvingRoutineProblems

Intersectionpointofdistance/timegraphs


D

Japan 96 pHong Kong, SAR 90 pKorea, Republic of 89 pEstonia 88 pSingapore 87 pHungary 84 pLithuania 84 pSweden 84 pRussian Federation 81 pNetherlands 81 pChinese Taipei 81 pEngland 81 pUnited States 80 pSlovenia 79 pLatvia 78 pItaly 75 pAustralia 75 pBelgium (Flemish) 73 pScotland 73 pNew Zealand 72 pIsrael 72 pSlovak Republic 70 pSerbia and Montenegro 68 pBulgaria 67 pNorway 64 OInternational average 62 OCyprus 58 ORomania 58 OMacedonia, Republic of 53 qMalaysia 53 qJordan 52 qArmenia 52 qChile 51 qBahrain 50 qEgypt 47 qMoldova, Republic of 47 qIndonesia 46 qLebanon 42 qBotswana 41 qPalestinian Nat’l Auth. 39 qSaudi Arabia 37 qPhilippines 31 qIran, Islamic Republic of 26 qGhana 21 qSouth Africa 19 qTunisia 14 q


Correct Response:

Cognitive Domain

119





b


Testscorefrequencytable

DATA DataInterpretation Reasoning

/

///

///// /

//

////

///

/

M01

2037

The table shows scores for a class on a 10-point test.

Test Score Tally Frequency

4

5

6

7

8

9

10 1

3

4

2

6

3

1

How many in the class had a score greater than 7 ?

a 2

b 8

c 10

d 12

e 20

Korea, Republic of 85 pNetherlands 77 pSlovenia 68 pBelgium (Flemish) 67 pSweden 65 pUnited States 65 pScotland 64 pSingapore 63 pLithuania 61 pIsrael 59 pNew Zealand 59 pEngland 58 pEstonia 58 pAustralia 56 pHungary 56 pSerbia and Montenegro 56 pNorway 55 pIndonesia 53 pLatvia 53 pRussian Federation 52 OBahrain 51 OChinese Taipei 51 OMacedonia, Republic of 51 OSlovak Republic 49 OHong Kong, SAR 48 OInternational average 48 OMalaysia 47 ORomania 47 OJordan 46 OItaly 45 OJapan 44 qCyprus 42 qEgypt 42 qIran, Islamic Republic of 42 qArmenia 39 qPhilippines 39 qPalestinian Nat’l Auth. 36 qTunisia 35 qBulgaria 34 qBotswana 33 qChile 33 qLebanon 31 qMoldova, Republic of 31 qGhana 27 qSaudi Arabia 26 qSouth Africa 22 qMorocco 21 q

Correct Response:

120






DATA Datainterpretation Reasoning

Howmanypencilssoldfrombargraph


C

M022189

The graph shows the number of pens, pencils, rulers, and erasers sold by astore in one week.

The names of the items are missing from the graph. Pens were the itemmost often sold, and fewer erasers than any other item were sold.More pencils than rulers were sold. How many pencils were sold?

a 40

b 80

c 120

d 140

Items Sold by Store

Num

ber

of

Item

s

0

20

40

60

80

100

120

140

160

Belgium (Flemish) 90 pChinese Taipei 89 pJapan 88 pHong Kong, SAR 88 pKorea, Republic of 87 pMalaysia 87 pEstonia 87 pSlovenia 86 pUnited States 86 pSweden 86 pNetherlands 85 pHungary 85 pScotland 84 pSingapore 83 pLatvia 82 pSlovak Republic 80 pRussian Federation 80 pItaly 80 pNorway 78 pEngland 78 pNew Zealand 78 pLithuania 77 pCyprus 76 pAustralia 76 pIsrael 70 OInternational average 67 OBulgaria 67 OBahrain 66 OSerbia and Montenegro 63 qMoldova, Republic of 62 qIran, Islamic Republic of 61 qMacedonia, Republic of 59 qRomania 59 qJordan 59 qMorocco 53 qArmenia 51 qChile 50 qEgypt 49 qIndonesia 49 qPalestinian Nat’l Auth. 48 qSaudi Arabia 45 qLebanon 42 qTunisia 40 qBotswana 37 qPhilippines 32 qSouth Africa 28 qGhana 24 q

121






032762

Betty talks for less than 2 hours per month. Which plan would be lessexpensive for her?

Less expensive plan ______________

Explain your answer in terms of both the monthly fee and free minutes.

Questions for Phone Plans continue.


• PlanBwithexplanationthatincludesfreeminutesusedandexplicitreferencetolowermonthlyfeeforPlanB.

Partial Response

• PlanBwithexplicitreferencetolowermonthlyfeeandnoreferencetofreeminutes.

Incorrect Response

• PlanBwithinadequate(onlyfreeminutes)ornoexplanation.

• PlanAwithorwithoutexplanation.



Phoneplans:leastexpensiveplanforBetty

DATA Datainterpretation Reasoning

Japan 49 pEngland 45 pAustralia 44 pEstonia 44 pKorea, Republic of 40 pSingapore 40 pHungary 39 pBelgium (Flemish) 38 pLithuania 37 pUnited States 37 pScotland 36 pIsrael 33 pNew Zealand 30 pNetherlands 28 pHong Kong, SAR 28 pSlovenia 27 pSweden 27 pMalaysia 27 pChinese Taipei 27 pSlovak Republic 26 pItaly 23 OLatvia 22 OInternational average 21 OJordan 20 OBahrain 18 ONorway 18 qRomania 16 qRussian Federation 15 qEgypt 14 qCyprus 13 qIndonesia 12 qSerbia and Montenegro 12 qChile 12 qBulgaria 12 qLebanon 11 qPhilippines 11 qMacedonia, Republic of 10 qSaudi Arabia 8 qMorocco 7 qSouth Africa 6 qPalestinian Nat’l Auth. 5 qIran, Islamic Republic of 4 qTunisia 4 qGhana 3 qBotswana 2 qArmenia 2 qMoldova, Republic of 1 q

122

Student Responses


Correct Response:

Partial Response:

Incorrect Response:

Phoneplans:leastexpensiveplanforBetty(continued)Item Number: M032762


Correct Response:

Cognitive Domain

123





A


graphofcoolingwater

DATA Datainterpretation SolvingRoutineProblems

M022135

A beaker of water which has reached boiling point is allowed to cool.The temperature of the water is recorded at five minute intervals, and atemperature-time graph is drawn.

Cooling Curve

About how many minutes did it take for the water to cool the first20 degrees?

a 3

b 8

c 37

d 50

100

80

60

40

20Tem

per

ature

(°C

)

Time (minutes)

0 5 10 15 20 25 30 35 40 45 50

Belgium (Flemish) 70 pSweden 62 pAustralia 59 pEstonia 57 pHungary 56 pScotland 55 pEngland 55 pNorway 54 pSingapore 54 pNetherlands 53 pUnited States 52 pNew Zealand 49 pLithuania 49 pLatvia 47 pChinese Taipei 45 pLebanon 40 pItaly 40 pSlovenia 39 pJapan 39 pRussian Federation 38 pIsrael 36 OIndonesia 35 OArmenia 35 OSlovak Republic 34 OMalaysia 33 OInternational average 33 OSerbia and Montenegro 33 OBulgaria 32 ORomania 30 OMoldova, Republic of 28 qHong Kong, SAR 26 qChile 25 qCyprus 21 qJordan 18 qIran, Islamic Republic of 18 qMacedonia, Republic of 17 qSouth Africa 14 qPalestinian Nat’l Auth. 14 qGhana 13 qBotswana 12 qKorea, Republic of 11 qBahrain 11 qMorocco 10 qPhilippines 10 qSaudi Arabia 9 qEgypt 8 qTunisia 4 q

124







• PlanA=140zedsandPlanB=375zeds,withworkshown.

Partial Response

• 140zedsand375zedswithnoworkshown.

• PlanAorplanBcorrectwithworkshownbutnotboth.

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegible,orofftask).


Phoneplans:costofplansforFrank


M032763

Frank talks for 5 hours per month at the night rate. What would each plancost him per month? Show your work.

Cost Per Month for Plan A: _______________ zeds

Cost Per Month for Plan B: _______________ zeds

Questions for Phone Plans continue.

Singapore 27 pJapan 19 pChinese Taipei 18 pHong Kong, SAR 15 pKorea, Republic of 15 pNetherlands 14 pSweden 12 pLithuania 11 pBelgium (Flemish) 11 pEstonia 10 pHungary 10 pEngland 8 OUnited States 8 pNew Zealand 7 OScotland 7 OSlovak Republic 7 OAustralia 7 OIsrael 6 OMalaysia 6 OInternational average 6 OLatvia 6 OSlovenia 5 ORussian Federation 5 ORomania 5 ONorway 5 OBulgaria 4 OSerbia and Montenegro 3 qItaly 3 qMoldova, Republic of 2 qJordan 1 qCyprus 1 qMacedonia, Republic of 1 qIndonesia 1 qSouth Africa 1 qArmenia 1 qPalestinian Nat’l Auth. 1 qPhilippines 1 qChile 0 qIran, Islamic Republic of 0 qEgypt 0 qLebanon 0 qBahrain 0 qGhana 0 qTunisia 0 qMorocco 0 qBotswana 0 qSaudi Arabia 0 q

125

Student Responses


Correct Response:

Inorrect Response:

Phoneplans:costofplansforFrank(continued)Item Number: M032763

126







• 150withworkshown.

Partial Response

• 150withnoworkshown.

• Correctmethodbutwithcalculationerror.

• 1230withcalculationsleadingto30.

Incorrect Response



Phoneplans:minutestalkbyDarlene


Singapore 28 pKorea, Republic of 22 pHong Kong, SAR 21 pChinese Taipei 20 pJapan 19 pNetherlands 17 pBelgium (Flemish) 13 pSweden 12 pEstonia 11 pEngland 11 pHungary 9 pLithuania 9 pAustralia 8 OUnited States 8 pSlovak Republic 8 ONew Zealand 7 OInternational average 6 OLatvia 6 OScotland 6 OSlovenia 5 OIsrael 5 ORomania 5 ONorway 5 ORussian Federation 4 qMalaysia 4 qGhana 3 qBulgaria 3 qItaly 3 qMoldova, Republic of 2 qJordan 2 qCyprus 2 qSerbia and Montenegro 2 qMacedonia, Republic of 1 qIndonesia 1 qSouth Africa 1 qBahrain 1 qLebanon 0 qTunisia 0 qIran, Islamic Republic of 0 qChile 0 qPhilippines 0 qArmenia 0 qPalestinian Nat’l Auth. 0 qMorocco 0 qBotswana 0 qEgypt 0 qSaudi Arabia 0 q

M032764

Darlene signed up for the Plan B, and the cost of one month of service was75 zeds. How many minutes did she talk that month? Show your work.

Minutes talked ______________

End of Phone Plans section.

127

Student Responses


Phoneplans:minutestalkbyDarlene(continued)Item Number: M032764

Correct Response:

Partial Response:

Incorrect Response:

Correct Response:

128






C


Comparisonoftwoaveragescores

DATA DataInterpretation UsingConcepts

Chinese Taipei 90 pKorea, Republic of 90 pSingapore 88 pHong Kong, SAR 87 pMalaysia 84 pJapan 81 pSlovak Republic 78 pLithuania 76 pNetherlands 76 pLatvia 75 pTunisia 75 pSlovenia 74 pUnited States 74 pBulgaria 73 pIsrael 73 pScotland 73 pEstonia 72 pHungary 72 pMoldova, Republic of 72 ORomania 72 pSerbia and Montenegro 72 pRussian Federation 70 OAustralia 69 OBelgium (Flemish) 69 OItaly 69 OInternational average 68 OMacedonia, Republic of 68 OSweden 66 OArmenia 65 OCyprus 65 OIran, Islamic Republic of 64 OMorocco 64 OChile 62 qNorway 61 qPhilippines 61 qEgypt 60 qEngland 60 qNew Zealand 60 qBahrain 58 qIndonesia 56 qBotswana 53 qJordan 52 qPalestinian Nat’l Auth. 51 qGhana 43 qSouth Africa 43 qSaudi Arabia 38 q

M012006

Joe had three test scores of 78, 76, and 74, while Mary had scores of 72, 82,and 74. How did Joe’s average (mean) score compare with Mary’s average(mean) score?

a Joe’s was 1 point higher.

b Joe’s was 1 point lower.

c Both averages were the same.

d Joe’s was 2 points higher.

e Joe’s was 2 points lower.


Correct Response:

Cognitive Domain

129





DATA DataInterpretation UsingConcepts

Piegraphofcropdistribution


D

Korea, Republic of 93 pJapan 92 pNetherlands 88 pAustralia 86 pBelgium (Flemish) 86 pSweden 85 pHong Kong, SAR 85 pChinese Taipei 84 pLatvia 84 pSingapore 83 pSlovak Republic 82 pEngland 82 pEstonia 82 pSlovenia 82 pLithuania 82 pHungary 81 pNew Zealand 81 pUnited States 81 pScotland 81 pIsrael 79 pNorway 78 pRussian Federation 78 pCyprus 76 pItaly 74 ORomania 72 OInternational average 71 OTunisia 71 OBulgaria 70 OEgypt 69 OMoldova, Republic of 67 OMorocco 67 OJordan 66 qMacedonia, Republic of 65 qSerbia and Montenegro 65 qIran, Islamic Republic of 64 qMalaysia 63 qBahrain 63 qPalestinian Nat’l Auth. 61 qArmenia 60 qChile 57 qSaudi Arabia 52 qBotswana 51 qPhilippines 50 qLebanon 49 qIndonesia 45 qGhana 41 qSouth Africa 33 q

M012014

The graph shows the distribution of crops grown in a certain country.

According to the information in the graph, which of these statements is true?

a More oats are grown than wheat.

b Corn is more than one-half of the country’s crop.

c Oats are more than one-third of the country’s crop.

d The total crop of oats and wheat is greater than the corn crop.

Wheat Corn

OatsOther

Correct Response:

130






b


Mostlikelysectoronspinner

DATA UncertaintyandProbability Reasoning

Hong Kong, SAR 87 pChinese Taipei 85 pNetherlands 85 pJapan 82 pSweden 81 pBelgium (Flemish) 81 pEngland 79 pSingapore 79 pKorea, Republic of 79 pUnited States 78 pAustralia 78 pHungary 76 pScotland 76 pIsrael 74 pSlovenia 74 pNorway 73 pEstonia 73 pLatvia 71 pNew Zealand 71 pSlovak Republic 69 pCyprus 69 pLithuania 67 pSerbia and Montenegro 66 pMalaysia 65 pBulgaria 60 ORussian Federation 60 OInternational average 60 OItaly 58 ORomania 57 OMacedonia, Republic of 54 qArmenia 47 qMoldova, Republic of 46 qJordan 46 qPhilippines 43 qIran, Islamic Republic of 43 qEgypt 43 qLebanon 42 qPalestinian Nat’l Auth. 41 qBahrain 40 qMorocco 39 qChile 38 qIndonesia 37 qBotswana 34 qSaudi Arabia 34 qGhana 34 qSouth Africa 34 qTunisia 31 q

M022252

The figure below shows a spinner with 24 sectors. When someone spins thearrow, it is equally likely to stop on any sector.

1

8 of the sectors are blue,

1

24 are purple,

1

2 are orange, and

1

3 are red. If a

person spins the arrow, on which color sector is the spinner LEAST likely tostop?

a blue

b purple

c orange

d red


Correct Response:

Cognitive Domain

131





Hong Kong, SAR 81 pSingapore 80 pNetherlands 78 pChinese Taipei 77 pKorea, Republic of 75 pBelgium (Flemish) 71 pJapan 66 pEstonia 61 pSweden 61 pUnited States 60 pHungary 56 pAustralia 56 pNew Zealand 55 pLithuania 55 pItaly 55 pScotland 53 pRussian Federation 52 pLatvia 50 OMalaysia 49 OEngland 49 OIsrael 47 OInternational average 47 ONorway 46 OSlovak Republic 45 OSerbia and Montenegro 44 OMoldova, Republic of 44 OSlovenia 44 OBulgaria 43 OCyprus 43 qLebanon 41 qArmenia 39 qTunisia 39 qJordan 39 qRomania 38 qEgypt 38 qMacedonia, Republic of 36 qIran, Islamic Republic of 35 qIndonesia 34 qChile 32 qPalestinian Nat’l Auth. 32 qPhilippines 31 qMorocco 28 qBotswana 28 qSaudi Arabia 26 qBahrain 23 qSouth Africa 23 qGhana 23 q

DATA UncertaintyandProbability Reasoning

Inaschooltherewere1200students


C

M03

2271

In a school there were 1,200 students (boys and girls). A sample of 100

students was selected at random, and 45 boys were found in the sample.

Which of these is most likely to be the number of boys in the school?

a 450

b 500

c 540

d 600

Correct Response:

132






DATA UncertaintyandProbability SolvingRoutineProblems

Numberofstudentsfromprobability


e

Korea, Republic of 89 pSingapore 87 pChinese Taipei 86 pJapan 86 pHong Kong, SAR 84 pNetherlands 82 pBelgium (Flemish) 79 pSweden 71 pMalaysia 69 pScotland 66 pEngland 63 pArmenia 62 pAustralia 60 pLatvia 59 pUnited States 58 pEstonia 57 pItaly 56 pHungary 55 pIsrael 54 pNew Zealand 54 OCyprus 53 OSlovenia 53 OLithuania 52 ORussian Federation 51 ONorway 50 OBulgaria 50 OInternational average 50 OSlovak Republic 50 OSerbia and Montenegro 46 OIndonesia 42 qRomania 39 qIran, Islamic Republic of 37 qJordan 33 qEgypt 33 qBotswana 32 qMacedonia, Republic of 32 qPhilippines 32 qMoldova, Republic of 31 qPalestinian Nat’l Auth. 28 qLebanon 28 qGhana 28 qSouth Africa 26 qBahrain 24 qChile 23 qTunisia 22 qSaudi Arabia 18 qMorocco 18 q

M022146

In an eighth-grade class of 30 students, the probability that a student

chosen at random will be less than 13 years old is

1

5. How many students in

the class are less than 13 years old?

a Two

b Three

c Four

d Five

e Six

133







• LinedrawnfromAto(approximate)midpointofBC.

Incorrect Response

• LinedrawnfromCorB.



DrawalinetodividetriangleABC

geOMeTRy CongruenceandSimilarityKnowingFactsandProcedures

Singapore 88 pJapan 86 pKorea, Republic of 84 pHong Kong, SAR 79 pArmenia 77 pRussian Federation 73 pBelgium (Flemish) 72 pChinese Taipei 71 pLatvia 71 pLithuania 70 pEstonia 69 pIsrael 66 pBahrain 65 pRomania 62 pBulgaria 61 pSlovak Republic 60 pNetherlands 59 pMoldova, Republic of 56 OLebanon 55 OAustralia 55 OUnited States 54 OSlovenia 53 OTunisia 53 OHungary 53 OMalaysia 52 OInternational average 52 OCyprus 51 OEngland 48 ONew Zealand 48 OJordan 47 qScotland 47 OItaly 45 qIran, Islamic Republic of 43 qNorway 42 qMorocco 41 qSerbia and Montenegro 40 qEgypt 40 qSaudi Arabia 39 qPalestinian Nat’l Auth. 36 qMacedonia, Republic of 35 qIndonesia 26 qSweden 20 qChile 19 qBotswana 14 qPhilippines 11 qSouth Africa 7 q

M032403

The triangle ABC has AB = AC.

Draw a line to divide triangle ABC into two congruent triangles.

A

C

B

134

Student Responses


DrawalinetodividetriangleABC(continued)Item Number: M032403

Correct:

Incorrect:


Correct Response:

Cognitive Domain

135





geOMeTRy CongruenceandSimilarity Reasoning

Propertyofcongruenttrapezoids


A

Korea, Republic of 86 pEstonia 84 pJapan 83 pHong Kong, SAR 81 pSingapore 81 pChinese Taipei 79 pLatvia 77 pRussian Federation 77 pLithuania 74 pBelgium (Flemish) 73 pSlovak Republic 73 pNetherlands 69 pUnited States 69 pHungary 69 pSlovenia 68 pRomania 68 pItaly 67 pBulgaria 67 pAustralia 66 pIsrael 66 pScotland 64 OMalaysia 64 OMoldova, Republic of 63 OSweden 62 OMorocco 62 OTunisia 62 ONew Zealand 61 OCyprus 61 OInternational average 60 OMacedonia, Republic of 60 OArmenia 59 ONorway 58 OEngland 57 OIndonesia 56 OSerbia and Montenegro 56 qLebanon 55 qBahrain 54 qJordan 48 qIran, Islamic Republic of 45 qSaudi Arabia 39 qChile 39 qPalestinian Nat’l Auth. 37 qEgypt 35 qBotswana 34 qPhilippines 30 qGhana 25 qSouth Africa 24 q

M012015

ABCD is a trapezoid.

Another trapezoid, GHIJ (not shown), is congruent (the same size and shape)to ABCD. Angles G and J each measure 70°. Which of these could be true?

a GH = AB

b Angle H is a right angle.

c All sides of GHIJ are the same length.

d The perimeter of GHIJ is 3 times the perimeter of ABCD.

e The area of GHIJ is less than the area of ABCD.

B

A

70˚

C

D

70˚

Correct Response:

136






geOMeTRy CongruenceandSimilarity UsingConcepts

Falsestatementofcongruenttriangles


b

Korea, Republic of 86 pJapan 85 pChinese Taipei 82 pEstonia 82 pHong Kong, SAR 79 pLatvia 78 pBulgaria 74 pRussian Federation 74 pLithuania 73 pNetherlands 72 pSingapore 72 pCyprus 69 pBelgium (Flemish) 68 pSlovak Republic 68 pRomania 64 pArmenia 62 pIsrael 62 pSweden 62 pSlovenia 61 pItaly 58 OMorocco 58 OBahrain 57 OInternational average 56 OMoldova, Republic of 56 OIndonesia 55 OUnited States 55 OJordan 54 OIran, Islamic Republic of 53 OMalaysia 50 qTunisia 49 qEgypt 46 qNorway 46 qHungary 45 qLebanon 45 qMacedonia, Republic of 45 qPalestinian Nat’l Auth. 44 qScotland 44 qAustralia 43 qNew Zealand 42 qSerbia and Montenegro 41 qPhilippines 39 qEngland 35 qSaudi Arabia 35 qChile 28 qSouth Africa 26 qBotswana 25 q

M012005

In square EFGH, which of these is FALSE?

a ∆EIF and ∆EIH are congruent.

b ∆GHI and ∆GHF are congruent.

c ∆EFH and ∆EGH are congruent.

d ∆EIF and ∆GIH are congruent.

I

H G

FE


Correct Response:

Cognitive Domain

137





geOMeTRy CongruenceandSimilarity UsingConcepts

Identifysimilartriangles


D

Korea, Republic of 83 pHong Kong, SAR 76 pSingapore 75 pJapan 70 pChinese Taipei 68 pRussian Federation 61 pNetherlands 60 pBelgium (Flemish) 59 pIran, Islamic Republic of 54 pHungary 51 pMalaysia 51 pLithuania 50 pLatvia 49 pEstonia 46 pUnited States 46 pLebanon 46 OItaly 44 OEngland 43 OInternational average 42 OJordan 41 OPhilippines 41 OSweden 41 OAustralia 40 ORomania 39 OSerbia and Montenegro 38 OPalestinian Nat’l Auth. 38 qMoldova, Republic of 38 ONew Zealand 37 qSlovak Republic 37 qArmenia 36 qIsrael 36 qMacedonia, Republic of 36 qCyprus 34 qNorway 34 qEgypt 34 qIndonesia 33 qBulgaria 31 qSlovenia 30 qScotland 29 qBahrain 27 qChile 25 qGhana 23 qBotswana 23 qSouth Africa 21 qMorocco 21 qTunisia 16 qSaudi Arabia 12 q

M032261

Which of the following triangles is similar to the triangle shown above?

a b

c d

8 cm 10 cm

12 cm

10 cm

12 cm

15 cm 10 cm

14 cm

12 cm

12 cm8 cm

6 cm

24 cm

16 cm

20 cm

Correct Response:

138






b


Sumofanglesequalto180degrees

geOMeTRy LinesandAnglesKnowingFactsandProcedures

Japan 83 pKorea, Republic of 81 pHong Kong, SAR 79 pSingapore 72 pChinese Taipei 67 pEstonia 63 pBelgium (Flemish) 62 pLatvia 56 pRussian Federation 54 pAustralia 49 pLithuania 49 pEngland 48 OIsrael 47 OBulgaria 47 OMoldova, Republic of 47 OHungary 47 OSlovak Republic 46 OBahrain 46 ONetherlands 45 ONew Zealand 45 OSerbia and Montenegro 43 OInternational average 43 OArmenia 43 OCyprus 42 OScotland 41 OSlovenia 41 ORomania 41 OMalaysia 41 OLebanon 38 qEgypt 37 qUnited States 37 qItaly 36 qMacedonia, Republic of 35 qPalestinian Nat’l Auth. 34 qNorway 34 qSweden 32 qIndonesia 31 qJordan 29 qTunisia 28 qMorocco 28 qPhilippines 26 qIran, Islamic Republic of 25 qChile 25 qSouth Africa 23 qGhana 22 qSaudi Arabia 22 qBotswana 19 q

M022142

In this figure, PQ and RS are parallel.

Of the following, which pair of angles has the sum of 180°?

a ∠ 5 and ∠ 7

b ∠ 3 and ∠ 6

c ∠ 1 and ∠ 5

d ∠ 1 and ∠ 7

e ∠ 2 and ∠ 8

P

R

Q

S

1 2

4 3

5 68 7

139







• 60

Incorrect Response

• 30OR50[140°–110°or140°–90°]

• 55[110÷2]



Measureofangleinadjacentangles

geOMeTRy LinesandAngles Reasoning

Korea, Republic of 63 pJapan 60 pSingapore 58 pHong Kong, SAR 57 pChinese Taipei 49 pHungary 44 pNorway 41 pRussian Federation 40 pArmenia 39 pLatvia 37 pBelgium (Flemish) 36 pSlovak Republic 36 pEstonia 36 pSerbia and Montenegro 35 pRomania 34 pBulgaria 34 pIsrael 32 pMoldova, Republic of 32 OMalaysia 32 pNetherlands 28 ONew Zealand 28 OInternational average 28 OLithuania 27 OMacedonia, Republic of 26 OAustralia 26 OLebanon 26 OItaly 25 OSlovenia 25 OEngland 23 qUnited States 22 qCyprus 21 qSweden 20 qTunisia 18 qScotland 17 qPalestinian Nat’l Auth. 16 qIndonesia 16 qBahrain 16 qEgypt 15 qJordan 13 qMorocco 11 qPhilippines 11 qIran, Islamic Republic of 11 qChile 10 qBotswana 9 qSaudi Arabia 6 qSouth Africa 4 q

M022202

In the figure, the measure of ∠POR is 110°, the measure of ∠QOS is 90°,and the measure of ∠POS is 140°.

What is the measure of ∠QOR?

Answer: _______________

S

R

Q

PO

140

Student Responses


Correct Response:

Incorrect Response:

Measureofangleinadjacentangles(continued)Item Number: M022202


Correct Response:

Cognitive Domain

141





geOMeTRy LinesandAngles SolvingRoutineProblems

Sumofanglesfromintersectinglines


C

Korea, Republic of 84 pSingapore 84 pHong Kong, SAR 83 pChinese Taipei 82 pJapan 78 pMalaysia 69 pEstonia 67 pLatvia 66 pRussian Federation 64 pBelgium (Flemish) 59 pSerbia and Montenegro 59 pIsrael 58 pRomania 58 pSlovenia 58 pBulgaria 57 pNetherlands 57 pLebanon 55 pLithuania 54 OAustralia 52 OMoldova, Republic of 52 OSlovak Republic 52 OEngland 50 OInternational average 50 OItaly 50 OHungary 48 OIran, Islamic Republic of 48 OUnited States 47 OCyprus 46 qNew Zealand 46 OMacedonia, Republic of 45 qArmenia 44 qEgypt 43 qSweden 43 qScotland 41 qTunisia 41 qJordan 40 qPalestinian Nat’l Auth. 40 qIndonesia 38 qNorway 34 qBahrain 33 qMorocco 33 qChile 32 qPhilippines 27 qBotswana 26 qSaudi Arabia 26 qGhana 21 qSouth Africa 16 q

M012039

In the figure, PQ and RS are intersecting straight lines.

What is the value of x + y ?

a 15

b 30

c 60

d 180

e 300

S

QR

x˚ y˚

P

150˚

Correct Response:

142






geOMeTRyLocations

andSpatialRelationshipsKnowingFactsandProcedures

Pointonalinedefinedbytwopoints


D

Netherlands 66 pEngland 62 pScotland 56 pKorea, Republic of 56 pSingapore 56 pChinese Taipei 54 pSweden 53 pAustralia 51 pUnited States 51 pJapan 50 pNorway 49 pHong Kong, SAR 47 pHungary 46 pLithuania 44 pNew Zealand 44 pBelgium (Flemish) 43 pRussian Federation 42 pEstonia 40 pMalaysia 38 OLatvia 37 OCyprus 36 OInternational average 35 OSlovenia 35 OIsrael 34 OSerbia and Montenegro 31 OIndonesia 31 qSlovak Republic 30 qChile 29 qEgypt 28 qMorocco 28 qRomania 28 qMacedonia, Republic of 27 qItaly 26 qJordan 26 qMoldova, Republic of 25 qBulgaria 24 qArmenia 23 qLebanon 23 qBotswana 22 qPhilippines 22 qPalestinian Nat’l Auth. 21 qBahrain 21 qIran, Islamic Republic of 20 qGhana 19 qSaudi Arabia 19 qSouth Africa 19 qTunisia 8 q

M022016

A straight line passes through the points (2,3) and (4,7). Which of thesepoints is also on the line?

a (0,2)

b (1,2)

c (2,4)

d (3,5)

e (4,5)


Correct Response:

Cognitive Domain

143





geOMeTRyLocations

andSpatialRelationshipsKnowingFactsandProcedures

Whichpointcouldhavecoordinates(2,-4)


C

Chinese Taipei 87 pJapan 86 pKorea, Republic of 83 pEstonia 81 pRussian Federation 79 pSingapore 77 pNetherlands 75 pHong Kong, SAR 74 pHungary 74 pLithuania 73 pLatvia 72 pUnited States 72 pMalaysia 71 pIran, Islamic Republic of 69 pBelgium (Flemish) 68 pEngland 67 pLebanon 66 pScotland 65 pIsrael 62 pSerbia and Montenegro 61 pBulgaria 60 ORomania 59 OSlovenia 58 OMacedonia, Republic of 58 ONew Zealand 58 OAustralia 58 OItaly 57 OInternational average 56 OJordan 55 OArmenia 53 OMoldova, Republic of 53 OIndonesia 53 OEgypt 47 qSweden 45 qSlovak Republic 43 qNorway 43 qPhilippines 41 qBahrain 38 qPalestinian Nat’l Auth. 34 qSaudi Arabia 32 qMorocco 31 qCyprus 30 qTunisia 28 qSouth Africa 28 qBotswana 26 qChile 25 qGhana 19 q

M032588

In the coordinate plane above, which point could havecoordinates (2,−4)?

a P

b Q

c R

d S

y

x

P Q

S R

O

Correct Response:

144






geOMeTRyLocations

andSpatialRelationshipsUsingConcepts

Whichcouldbefoldedtomakea3-Dfigure


D

Japan 97 pChinese Taipei 96 pKorea, Republic of 94 pHong Kong, SAR 94 pSingapore 94 pNetherlands 89 pMalaysia 89 pNew Zealand 88 pEstonia 87 pBelgium (Flemish) 87 pAustralia 86 pEngland 86 pScotland 86 pHungary 85 pLithuania 83 pSlovak Republic 81 pSerbia and Montenegro 77 pUnited States 76 pSweden 76 pSlovenia 75 pItaly 73 pLatvia 72 ONorway 71 OBulgaria 70 ORussian Federation 69 OIndonesia 68 OInternational average 68 ORomania 68 OChile 67 OCyprus 63 qMacedonia, Republic of 63 qIsrael 62 qMorocco 61 qLebanon 59 qTunisia 58 qIran, Islamic Republic of 55 qJordan 52 qPalestinian Nat’l Auth. 51 qMoldova, Republic of 49 qBahrain 46 qPhilippines 46 qBotswana 43 qSaudi Arabia 40 qArmenia 40 qEgypt 31 qSouth Africa 28 qGhana 24 q

M032489

Which of these could be folded to make a shape like the 3-D figure above?

a

b

c

d


Correct Response:

Cognitive Domain

145





geOMeTRySymmetry

andTransformationsReasoning

Centerpointofrotationofrectangle

Japan 79 pChinese Taipei 76 pKorea, Republic of 75 pHong Kong, SAR 73 pSlovenia 71 pEstonia 71 pNetherlands 65 pSingapore 64 pHungary 63 pEngland 63 pBelgium (Flemish) 62 pLatvia 61 pSweden 60 pNew Zealand 59 pLithuania 58 pItaly 58 pSlovak Republic 54 pAustralia 54 pIsrael 54 pMalaysia 54 pRussian Federation 52 pSerbia and Montenegro 50 ONorway 49 OUnited States 49 OInternational average 47 OBulgaria 47 OMoldova, Republic of 46 ORomania 46 OScotland 45 OJordan 44 OArmenia 40 qCyprus 39 qIran, Islamic Republic of 37 qPalestinian Nat’l Auth. 34 qBahrain 34 qLebanon 32 qEgypt 31 qIndonesia 29 qTunisia 29 qMacedonia, Republic of 28 qMorocco 28 qChile 28 qPhilippines 25 qBotswana 23 qSaudi Arabia 18 qSouth Africa 18 qGhana 13 q


C

M022154

Rectangle PQRS can be rotated (turned) onto rectangle UVST.

What point is the center of rotation?

a P

b R

c S

d T

e V

P

VU

T S R

Q

146







• Allcellsarecorrectwithsymmetricalgeometricpatternaboutbothaxes,PQandRS(lettersordrawings).

Partial Response

• Withrespecttoatleastoneoftheoriginaltilestheotherthreetilesarecorrect.

Incorrect Response

• LettersplacedsymmetricallywithrespecttobothPQandRS.



Geometrytiling:produceapatternusingletters

geOMeTRySymmetry

andTransformationsReasoning

Lithuania 16 pJapan 14 pKorea, Republic of 12 pSingapore 11 pHong Kong, SAR 10 pScotland 9 pEngland 9 pChinese Taipei 9 pNetherlands 8 pSlovenia 8 pEstonia 7 pAustralia 7 ONew Zealand 7 OBelgium (Flemish) 7 pUnited States 6 OMorocco 5 ORussian Federation 5 OMalaysia 5 OInternational average 4 OHungary 4 OSlovak Republic 3 OLatvia 3 ONorway 3 OMoldova, Republic of 3 OSweden 3 OIndonesia 2 qRomania 2 qIsrael 2 qBulgaria 2 qItaly 1 qArmenia 1 qLebanon 1 qMacedonia, Republic of 1 qSouth Africa 1 qEgypt 1 qChile 1 qPhilippines 1 qIran, Islamic Republic of 1 qBotswana 1 qJordan 1 qBahrain 1 qCyprus 0 qSerbia and Montenegro 0 qTunisia 0 qPalestinian Nat’l Auth. 0 q

M032745

Continue to identify the tiles as shown above. On the grid below, write theletters A, B, C, or D to make a symmetrical pattern where PQ and RSwould be lines of symmetry. Arrange the tiles to make a pattern.

End of Geometry Tiling section.

CA DB

P

S

Q

R

D

C

B

A

147

Student Responses


Correct Response:

Geometrytiling:produceapatternusingletters(continued)Item Number: M032745

148


Partial Response:


Student Responses (Continued)

149


Incorrect Response:

Student Responses (Continued)


150







• Bothquadrantscorrectlyshaded(patternshadedordemarcatedinsomewaymakingsymmetricalpatternaboutbothaxes,ABandCD).

Incorrect Response

• Oneofthetwoquadrantscorrectlyshaded.



Geometrytiling:makesasymmetricalpattern

geOMeTRySymmetry

andTransformationsUsingConcepts

Scotland 85 pNetherlands 82 pKorea, Republic of 82 pNew Zealand 80 pEngland 80 pSingapore 77 pAustralia 76 pHong Kong, SAR 75 pHungary 69 pJapan 68 pChinese Taipei 68 pUnited States 67 pBelgium (Flemish) 65 pLithuania 63 pSlovenia 60 pLatvia 60 pJordan 59 pMalaysia 56 pSlovak Republic 54 ORussian Federation 53 OCyprus 51 OEstonia 50 OItaly 50 OInternational average 49 OBulgaria 48 ONorway 46 OSweden 46 ORomania 44 OBahrain 43 qIsrael 42 qSerbia and Montenegro 41 qPalestinian Nat’l Auth. 41 qIndonesia 39 qMorocco 38 qIran, Islamic Republic of 34 qSaudi Arabia 34 qPhilippines 34 qEgypt 31 qTunisia 25 qMacedonia, Republic of 25 qBotswana 20 qLebanon 18 qSouth Africa 17 qArmenia 13 qChile 13 qMoldova, Republic of 1 q

M032743

There are several ways of arranging the tiles so that they form patterns.The grid below has been shaded to show how tiles can be placed on some ofthe squares. The pattern can be continued so that AB and CD are lines ofsymmetry.

Shade in all the remaining squares on the grid so that the resulting patternis symmetrical about line AB, and also is symmetrical about line CD.

Questions for Geometry Tiling continue.

A

B

C D

151

Student Responses


Geometrytiling:makesasymmetricalpattern(continued)Item Number: M032743

Correct Response:

152


Incorrect Response:


Geometrytiling:makesasymmetricalpattern(continued)Item Number: M032743


Correct Response:

Cognitive Domain

153





GeOMeTRyTwo-andThree-

DimensionalShapesSolvingRoutineProblems

Angleinoverlappingcongruenttriangles


D

Korea, Republic of 84 pHong Kong, SAR 81 pJapan 80 pSingapore 79 pChinese Taipei 73 pEstonia 67 pBelgium (Flemish) 66 pLatvia 63 pBulgaria 60 pIsrael 57 pRussian Federation 55 pLebanon 55 pScotland 54 pSlovak Republic 54 pLithuania 51 pHungary 50 OAustralia 47 OEngland 47 OEgypt 47 OMalaysia 47 OInternational average 45 OArmenia 45 OMoldova, Republic of 45 OCyprus 44 ONetherlands 44 OSerbia and Montenegro 43 ONew Zealand 42 OJordan 42 OItaly 42 OTunisia 41 qBahrain 41 qSweden 40 qPalestinian Nat’l Auth. 39 qIran, Islamic Republic of 37 qSlovenia 37 qUnited States 36 qMacedonia, Republic of 33 qNorway 32 qIndonesia 31 qMorocco 31 qChile 30 qSaudi Arabia 26 qSouth Africa 21 qGhana 20 qBotswana 20 qRomania 18 qPhilippines 15 q

M01

2026

In this figure, triangles ABC and DEF are congruent with BC = EF .

What is the measure of angle EGC ?

a 20°

b 40°

c 60°

d 80°

e 100°

B E C F

G

40˚ 60˚

A D



154




SCORINGCorrect Response

• 60degrees

Incorrect Response

• 120degrees



Theanglebyaregularhexagon


DimensionalShapesSolvingRoutineProblems

Japan 73 pChinese Taipei 70 pKorea, Republic of 68 pHong Kong, SAR 64 pSingapore 62 pHungary 59 pSlovenia 52 pNorway 50 pSerbia and Montenegro 46 pRomania 45 pBelgium (Flemish) 45 pSlovak Republic 43 pArmenia 42 pRussian Federation 42 pNetherlands 40 pMacedonia, Republic of 39 pMoldova, Republic of 39 pEstonia 37 OLatvia 33 OMalaysia 33 OInternational average 33 OItaly 32 OBulgaria 32 OLithuania 31 OEngland 30 OTunisia 29 qLebanon 28 qNew Zealand 27 qAustralia 27 qIsrael 26 qSweden 24 qIran, Islamic Republic of 24 qJordan 23 qPalestinian Nat’l Auth. 23 qEgypt 23 qScotland 23 qBahrain 22 qSaudi Arabia 21 qUnited States 20 qCyprus 19 qIndonesia 17 qGhana 16 qBotswana 14 qChile 9 qMorocco 9 qPhilippines 6 qSouth Africa 5 q

M032693

The figure above is a regular hexagon. What is the value of x?

Answer: _______________

x˚

155

Student Responses


Correct Response:

Incorrect Response:

Theanglebyaregularhexagon(continued)Item Number: M032693

Correct Response:

156






C


ThesizeofanglePRQ


DimensionalShapesUsingConcepts

Korea, Republic of 70 pChinese Taipei 70 pHungary 69 pTunisia 66 pJapan 64 pMalaysia 62 pHong Kong, SAR 59 pNorway 58 pSlovak Republic 58 pLebanon 58 pSerbia and Montenegro 58 pEstonia 56 pBelgium (Flemish) 54 pSlovenia 52 pRussian Federation 51 ORomania 51 OMacedonia, Republic of 50 OSingapore 49 pBulgaria 48 OLatvia 46 OInternational average 46 ONew Zealand 45 OMoldova, Republic of 44 ONetherlands 44 OSaudi Arabia 43 OLithuania 43 OPalestinian Nat’l Auth. 42 OEngland 42 OItaly 41 qMorocco 40 qJordan 39 qGhana 38 qEgypt 38 qChile 37 qAustralia 37 qArmenia 36 qIran, Islamic Republic of 36 qScotland 35 qSweden 35 qBahrain 35 qIsrael 34 qUnited States 34 qBotswana 34 qCyprus 34 qIndonesia 32 qSouth Africa 29 qPhilippines 25 q

M032689

In the figure above, an arc of a circle with center P has been drawn to cutthe line at Q. Then an arc with the same radius and center Q was drawn tocut the first arc at R. What would be the size of angle PRQ ?

a 30º

b 45º

c 60º

d 75º

P Q

R


Correct Response:

Cognitive Domain

157





MeaSuReMeNT AttributesandUnitsKnowingFactsandProcedures

250 ml bottles filled by 400 liters


C

Singapore 68 pNetherlands 59 pBelgium (Flemish) 55 pSweden 54 pMalaysia 53 pLatvia 51 pEstonia 50 pAustralia 49 pLithuania 49 pRomania 48 pHungary 48 pHong Kong, SAR 47 pRussian Federation 46 pSlovak Republic 44 pJapan 44 pMoldova, Republic of 43 OItaly 42 ONorway 42 OEngland 42 OArmenia 42 ONew Zealand 41 OSlovenia 41 OKorea, Republic of 41 OChinese Taipei 41 OCyprus 41 OScotland 40 OBulgaria 39 OInternational average 39 OSerbia and Montenegro 38 OIsrael 38 OUnited States 33 qPhilippines 32 qIndonesia 32 qSouth Africa 31 qPalestinian Nat’l Auth. 30 qLebanon 30 qChile 29 qJordan 29 qMacedonia, Republic of 29 qEgypt 29 qIran, Islamic Republic of 28 qTunisia 27 qBahrain 27 qBotswana 25 qSaudi Arabia 25 qMorocco 22 qGhana 20 q

M02

2005

The number of 250 milliliter bottles that can be filled from 400 liters of

water is

a 16

b 160

c 1,600

d 16,000

Correct Response:

158






Whichisleastamountoftime


Chinese Taipei 66 pKorea, Republic of 63 pHungary 63 pSingapore 60 pBelgium (Flemish) 59 pJapan 54 pHong Kong, SAR 54 pSlovenia 54 pSlovak Republic 52 pNetherlands 52 pLatvia 51 pArmenia 50 pSerbia and Montenegro 49 pEstonia 48 pMacedonia, Republic of 48 pRussian Federation 47 pUnited States 47 pMalaysia 47 OMoldova, Republic of 45 OItaly 45 OBulgaria 44 OSweden 44 OInternational average 43 ORomania 43 OLithuania 42 OIsrael 41 OTunisia 41 OAustralia 41 OLebanon 40 OCyprus 39 qEngland 39 ONorway 39 qJordan 38 qScotland 38 qPalestinian Nat’l Auth. 37 qNew Zealand 36 qEgypt 36 qChile 35 qSaudi Arabia 35 qPhilippines 35 qIran, Islamic Republic of 35 qSouth Africa 32 qBahrain 32 qMorocco 32 qGhana 27 qIndonesia 26 qBotswana 26 q


B

M02

2188

Which of these is the LEAST amount of time?

a 1 day

b 20 hours

c 1,800 minutes

d 90,000 seconds


Correct Response:

Cognitive Domain

159






The unit used for a soccer field

Estonia 90 pSweden 89 pNew Zealand 89 pItaly 88 pSingapore 88 pHungary 88 pAustralia 87 pSlovak Republic 87 pChile 87 pBelgium (Flemish) 86 pNetherlands 86 pLatvia 86 pRomania 86 pLithuania 84 pSerbia and Montenegro 84 pBulgaria 84 pRussian Federation 83 pHong Kong, SAR 82 pChinese Taipei 82 pJapan 82 pEngland 82 pMoldova, Republic of 82 pScotland 81 pNorway 80 pMalaysia 77 OUnited States 76 OMacedonia, Republic of 76 OInternational average 75 OKorea, Republic of 74 OSlovenia 74 OIsrael 73 OArmenia 71 qCyprus 69 qTunisia 68 qIndonesia 66 qBahrain 66 qMorocco 64 qJordan 64 qEgypt 62 qBotswana 61 qPhilippines 60 qPalestinian Nat’l Auth. 58 qLebanon 56 qSaudi Arabia 55 qIran, Islamic Republic of 52 qSouth Africa 52 qGhana 35 q


C

M032699

Which of these units would usually be used for an area the size of a soccerfield?

a square centimeters

b cubic centimeters

c square meters

d cubic meters

Correct Response:

160







Measureoftheareaofatriangle

Japan 84 pSingapore 81 pEstonia 78 pChinese Taipei 76 pBelgium (Flemish) 75 pRussian Federation 75 pHong Kong, SAR 73 pSlovenia 71 pSweden 70 pNetherlands 70 pLithuania 70 pKorea, Republic of 69 pHungary 68 pSlovak Republic 67 pSerbia and Montenegro 67 pItaly 67 pMalaysia 64 pRomania 62 pLatvia 61 pNew Zealand 57 OMoldova, Republic of 56 OInternational average 55 OLebanon 55 ONorway 54 OBulgaria 52 OMacedonia, Republic of 52 OAustralia 52 OCyprus 52 OEngland 51 OScotland 48 qBotswana 48 qUnited States 47 qEgypt 46 qJordan 45 qIndonesia 44 qArmenia 44 qIsrael 43 qTunisia 43 qPalestinian Nat’l Auth. 42 qBahrain 37 qChile 36 qGhana 34 qSouth Africa 34 qSaudi Arabia 32 qMorocco 30 qPhilippines 27 qIran, Islamic Republic of 22 q


C

M032732

Which of these could be the measure of the area of a triangle?

a 2 cm

b 3 m

c 5 cm2

d 8 m3


Correct Response:

Cognitive Domain

161





MeaSuReMeNTTools,Techniques,

andFormulasKnowingFactsandProcedures

Actuallengthofboxfromroundedmeasure

Korea, Republic of 90 pHungary 89 pNetherlands 88 pHong Kong, SAR 87 pSingapore 87 pBelgium (Flemish) 82 pSlovak Republic 81 pChinese Taipei 80 pSweden 80 pScotland 76 pEngland 75 pAustralia 73 pRussian Federation 73 pLatvia 70 pEstonia 67 pUnited States 67 pNew Zealand 65 pIsrael 64 pJapan 64 pMalaysia 62 pNorway 61 pRomania 58 pSerbia and Montenegro 55 pSlovenia 53 OItaly 52 OInternational average 50 OArmenia 45 qMacedonia, Republic of 42 qMoldova, Republic of 42 qJordan 39 qChile 38 qCyprus 37 qBahrain 33 qPalestinian Nat’l Auth. 33 qEgypt 30 qIndonesia 30 qBulgaria 28 qLebanon 23 qPhilippines 23 qLithuania 21 qBotswana 20 qIran, Islamic Republic of 15 qSaudi Arabia 13 qSouth Africa 13 qGhana 8 qMorocco 8 qTunisia 7 q


D

M012003

The length of a box is 9 cm to the nearest centimeter. Which of these couldbe the actual length of the box?

a 10 cm

b 9.9 cm

c 9.6 cm

d 8.6 cm

Correct Response:

162








Lengthofpipefrommeterscale

Singapore 95 pHong Kong, SAR 94 pJapan 93 pEstonia 91 pChinese Taipei 90 pKorea, Republic of 89 pNetherlands 89 pBelgium (Flemish) 87 pHungary 86 pMalaysia 86 pSweden 86 pLatvia 83 pRussian Federation 82 pLithuania 81 pScotland 81 pEngland 80 pNew Zealand 79 pSlovak Republic 79 pSlovenia 79 pAustralia 78 pItaly 74 pNorway 74 pUnited States 73 pBulgaria 72 pIsrael 72 pSerbia and Montenegro 72 pMacedonia, Republic of 70 OInternational average 67 OLebanon 64 OMoldova, Republic of 64 ORomania 64 OBotswana 61 qCyprus 61 qChile 58 qArmenia 54 qIndonesia 54 qMorocco 50 qTunisia 49 qIran, Islamic Republic of 48 qPhilippines 42 qSouth Africa 40 qGhana 39 qJordan 38 qPalestinian Nat’l Auth. 34 qBahrain 32 qEgypt 31 qSaudi Arabia 27 q


C

M012038

Meters (m)

What is the length of the pipe being measured?

a 0.085 m

b 0.805 m

c 0.85 m

d 8.5 m

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0


Correct Response:

Cognitive Domain

163







Areaofpavedwalkwayaroundpool

Singapore 86 pHong Kong, SAR 82 pKorea, Republic of 77 pChinese Taipei 77 pJapan 76 pMalaysia 60 pNetherlands 57 pEstonia 53 pBelgium (Flemish) 51 pSlovak Republic 50 pSweden 48 pAustralia 46 pItaly 45 pNew Zealand 44 OLithuania 43 pHungary 43 pEngland 40 OSlovenia 40 OUnited States 40 OCyprus 39 OScotland 39 OInternational average 38 OSerbia and Montenegro 38 OLatvia 38 OBulgaria 38 ORussian Federation 38 OIsrael 37 OEgypt 33 qMoldova, Republic of 33 qNorway 32 qRomania 30 qIran, Islamic Republic of 28 qArmenia 28 qJordan 26 qIndonesia 25 qBahrain 23 qPalestinian Nat’l Auth. 22 qMacedonia, Republic of 20 qLebanon 19 qChile 19 qTunisia 18 qMorocco 18 qSaudi Arabia 17 qBotswana 16 qPhilippines 16 qSouth Africa 16 qGhana 13 q


C

M02

2021

A rectangular shaped swimming pool has a paved walkway around it as

shown.

What is the area of the paved walkway?

a 100 m2

b 161 m2

c 710 m2

d 1,610 m2

70 m

23 m

50 m

18 mPool

Walkway

Correct Response:

164







andFormulasReasoning

Orangesarepackedinboxes

Japan 62 pNetherlands 61 pSweden 57 pSingapore 57 pBelgium (Flemish) 56 pAustralia 56 pEngland 55 pKorea, Republic of 55 pChinese Taipei 55 pHungary 55 pLatvia 54 pScotland 53 pRussian Federation 53 pEstonia 53 pHong Kong, SAR 51 pSlovenia 51 pSlovak Republic 51 pNew Zealand 51 pLithuania 50 pUnited States 50 pNorway 48 pBulgaria 46 OItaly 45 OInternational average 44Serbia and Montenegro 43 OCyprus 42 OMoldova, Republic of 42 OMacedonia, Republic of 41 OChile 40 qIsrael 39 qBotswana 37 qMalaysia 37 qRomania 36 qMorocco 35 qPhilippines 35 qLebanon 34 qBahrain 32 qEgypt 32 qTunisia 31 qIndonesia 31 qIran, Islamic Republic of 31 qSouth Africa 31 qArmenia 31 qJordan 29 qGhana 29 qPalestinian Nat’l Auth. 28 qSaudi Arabia 28 q


B

M03

2647

Oranges are packed in boxes. The average diameter of the oranges is 6 cm,

and the boxes are 60 cm long, 36 cm wide, and 24 cm deep.

Which of these is the BEST approximation of the number of oranges that

can be packed in a box?

a 30

b 240

c 360

d 1,920


Correct Response:

Cognitive Domain

165





B


Singapore 81 pJapan 65 pChinese Taipei 62 pHong Kong, SAR 62 pKorea, Republic of 62 pNetherlands 56 pBelgium (Flemish) 56 pSweden 54 pEstonia 53 pLatvia 52 pAustralia 50 pRussian Federation 47 pEngland 46 pSlovak Republic 45 pSerbia and Montenegro 45 pNew Zealand 45 pIsrael 44 pBulgaria 43 pRomania 43 pItaly 42 pMalaysia 41 ONorway 40 OMoldova, Republic of 39 OUnited States 39 OLithuania 38 OInternational average 37 OScotland 37 OHungary 37 OCyprus 36 OSlovenia 33 qArmenia 31 qIran, Islamic Republic of 28 qMacedonia, Republic of 27 qChile 27 qTunisia 26 qLebanon 23 qJordan 22 qPalestinian Nat’l Auth. 19 qEgypt 18 qBahrain 18 qBotswana 17 qSouth Africa 16 qSaudi Arabia 14 qMorocco 14 qPhilippines 14 qIndonesia 13 qGhana 13 q

Lengthofrectanglefromwidth/perimeter


andFormulasSolvingRoutineProblems

M012030

A thin wire 20 centimeters long is formed into a rectangle. If the width ofthis rectangle is 4 centimeters, what is its length?

a 5 centimeters

b 6 centimeters

c 12 centimeters

d 16 centimeters



166





• 7:25

• Otherresponseequivalentto7:25.

Incorrect Response

• 7:20

• 7:30

• 6:25



Netherlands 91 pBelgium (Flemish) 85 pHungary 84 pEngland 80 pSweden 78 pSingapore 78 pScotland 76 pAustralia 72 pNorway 71 pNew Zealand 68 pHong Kong, SAR 67 pSlovenia 67 pItaly 65 pRomania 63 pJapan 63 pIsrael 63 pSlovak Republic 59 pChinese Taipei 59 pEstonia 58 pCyprus 58 pKorea, Republic of 57 pUnited States 55 pMalaysia 51 pLatvia 46 OInternational average 45 OLebanon 45 OMoldova, Republic of 42 ORussian Federation 41 OSerbia and Montenegro 36 qBulgaria 36 qArmenia 35 qLithuania 34 qChile 29 qTunisia 20 qEgypt 20 qJordan 19 qMacedonia, Republic of 18 qIndonesia 18 qPalestinian Nat’l Auth. 16 qMorocco 15 qIran, Islamic Republic of 15 qBahrain 14 qBotswana 11 qSaudi Arabia 9 qSouth Africa 8 qPhilippines 8 qGhana 4 q



Time when finish homework

M022148

Kris begins her homework at 6:40. If it takes Kris three-quarters of an hourto do her homework, at what time will she finish?

Answer: _______________

167

Student Responses


Correct Response:

Incorrect Response:

Time when finish homework (continued)Item Number: M022148



168





• 49

Incorrect Response

• 1



5squares:areaofonesquare



Singapore 89 pHong Kong, SAR 88 pKorea, Republic of 87 pJapan 86 pArmenia 84 pChinese Taipei 83 pEstonia 69 pNetherlands 69 pRussian Federation 68 pBelgium (Flemish) 67 pSlovenia 66 pScotland 63 pUnited States 60 pMalaysia 60 pHungary 60 pBulgaria 59 pRomania 58 pTunisia 57 pMoldova, Republic of 57 pItaly 57 pSlovak Republic 57 pLithuania 57 pAustralia 56 OInternational average 51 OLebanon 49 OSweden 48 OEngland 47 OSerbia and Montenegro 47 qIsrael 47 qEgypt 46 qNew Zealand 45 qJordan 45 qCyprus 43 qMacedonia, Republic of 41 qIran, Islamic Republic of 38 qBahrain 37 qIndonesia 33 qPhilippines 32 qNorway 32 qMorocco 31 qPalestinian Nat’l Auth. 30 qBotswana 28 qChile 24 qSaudi Arabia 15 qGhana 10 qSouth Africa 8 qLatvia

M022227

The figure consists of 5 squares of equal area. The area of the whole figureis 245 cm2.

A. Find the area of one square.

Answer: _______________ cm2

B. Find the length of one side of one square.

Answer: _______________ cm

C. Find the perimeter of the whole figure in centimeters.

Answer: _______________ cm

169

Student Responses


Correct Response:

Incorrect Response:

5squares:areaofonesquare(continued)Item Number: M022227A



170





• 7 (or 49)

• Correctsquarerootofincorrectanswertoparta.

Incorrect Response

• 1–onlyiftheanswertopartAisnot1.

• Indication of division of area of one square (as obtained in part a) by 4 (e.g., 12.25, 49/4, etc.).

• 24.5 or other indication of division by 2.



5squares:lengthofoneside



Singapore 80 pHong Kong, SAR 78 pKorea, Republic of 70 pChinese Taipei 65 pArmenia 62 pRomania 45 pRussian Federation 43 pItaly 43 pJapan 42 pEstonia 39 pNetherlands 38 pBelgium (Flemish) 37 pSerbia and Montenegro 36 pMoldova, Republic of 35 pHungary 35 pMalaysia 34 pLithuania 33 pBulgaria 32 OUnited States 29 OSlovak Republic 29 OSlovenia 29 OInternational average 28 OScotland 27 OAustralia 26 OEngland 23 OSweden 23 qNew Zealand 23 qCyprus 21 qIsrael 20 qMacedonia, Republic of 20 qEgypt 20 qLebanon 18 qLatvia 17 qJordan 16 qPalestinian Nat’l Auth. 16 qIndonesia 15 qBahrain 14 qNorway 11 qIran, Islamic Republic of 11 qPhilippines 10 qTunisia 9 qMorocco 8 qSaudi Arabia 8 qChile 6 qBotswana 4 qSouth Africa 3 qGhana 2 q

M022227



Answer: _______________ cm2


Answer: _______________ cm


Answer: _______________ cm

171

Student Responses


Correct Response:

Incorrect Response:

5squares:lengthofoneside(continued)Item Number: M022227B



172





• 84

• 12,oncondition1wastheresponseforpartb.

• Other responses consistent with answer to part b, using multiplication by 12 (e.g., 147, 294, etc.).

Incorrect Response

• An answer that is 4 times the response to part b.

• Indicationofmultiplicationby12butmultiplicationisincorrect.

• 245 [Confusion between area and perimeter].


Item Number: M022227C

5 squares: perimeter whole figure



Singapore 72 pHong Kong, SAR 58 pKorea, Republic of 53 pChinese Taipei 51 pJapan 47 pArmenia 42 pMalaysia 38 pNetherlands 38 pAustralia 30 pScotland 27 pEngland 27 pEstonia 26 pBelgium (Flemish) 25 pHungary 24 pSlovenia 24 pSlovak Republic 24 pNew Zealand 23 ORussian Federation 23 OUnited States 23 OItaly 22 OLithuania 22 OSweden 21 OInternational average 20 OSerbia and Montenegro 18 OLatvia 17 OCyprus 17 ONorway 16 OMoldova, Republic of 16 ORomania 16 qBulgaria 14 qIsrael 12 qMacedonia, Republic of 8 qTunisia 7 qIndonesia 5 qChile 5 qEgypt 5 qJordan 5 qBahrain 4 qPalestinian Nat’l Auth. 4 qBotswana 3 qLebanon 3 qMorocco 2 qIran, Islamic Republic of 2 qSouth Africa 2 qPhilippines 2 qSaudi Arabia 2 qGhana 1 q

M022227



Answer: _______________ cm2


Answer: _______________ cm


Answer: _______________ cm

173

Student Responses


Correct Response:

Incorrect Response:

5 squares: perimeter whole figure (continued)Item Number: M022227C



174





• 64 kph or 64 or equivalent.

Incorrect Response

• Incorrect(includingcrossedout/erased,straymarks,illegibleorofftask).


Carrally:averagespeed

a. MeaSuReMeNTB.MeASUReMeNT

Tools, Techniques, and Formulas

Tools,Techniques,andFormulas

Solving Routine Problems

Reasoning

Singapore 78 pHong Kong, SAR 76 pNetherlands 70 pRussian Federation 67 pArmenia 65 pEstonia 64 pChinese Taipei 59 pJapan 59 pHungary 59 pLithuania 56 pUnited States 55 pBelgium (Flemish) 54 pLatvia 50 pSlovak Republic 49 pSweden 45 pKorea, Republic of 43 pScotland 43 pItaly 42 pMoldova, Republic of 38 OEngland 37 ONorway 37 OAustralia 36 OIsrael 36 ONew Zealand 35 OInternational average 35 OSerbia and Montenegro 34 OSlovenia 33 OMalaysia 29 qRomania 29 qBulgaria 28 qTunisia 27 qMacedonia, Republic of 26 qJordan 24 qIndonesia 22 qBotswana 21 qPalestinian Nat’l Auth. 18 qCyprus 16 qLebanon 15 qChile 15 qPhilippines 14 qBahrain 12 qIran, Islamic Republic of 8 qEgypt 7 qSouth Africa 7 qMorocco 6 qSaudi Arabia 2 qGhana 2 q

M032649

In a car rally two checkpoints are 160 km apart. Drivers must travel fromone checkpoint to the other in exactly 2.5 hours to earn maximum points.

A. What must the average speed be to travel the 160 km in this time?

Answer: _______________

B. A driver took 1 hour to travel through a 40 km hilly section at thebeginning of the course.

What must the average speed, in kilometers per hour, be for theremaining 120 km if the total time between checkpoints is to be2.5 hours?

Answer: _______________

175

Student Responses


Correct Response:

Incorrect Response:

Carrally:averagespeed(continued)Item Number: M032649A



176





• 80kphor80

Incorrect Response

• 5, 2, 120 or 48 shown.



Carrally:averagespeedforonesection

A.MeASUReMeNTB. MeaSuReMeNT

Tools,Techniques,andFormulas

Tools, Techniques, and Formulas

SolvingRoutineProblems

Reasoning

Armenia 54 pSingapore 52 pNetherlands 50 pHong Kong, SAR 47 pChinese Taipei 39 pEstonia 35 pRussian Federation 34 pHungary 33 pJapan 33 pBelgium (Flemish) 30 pSweden 28 pLithuania 27 pKorea, Republic of 27 pLatvia 24 pUnited States 24 pScotland 23 pEngland 22 OAustralia 22 OSlovak Republic 21 ONew Zealand 19 ONorway 19 OInternational average 18 OIsrael 17 OMoldova, Republic of 17 OBulgaria 17 OSlovenia 16 OItaly 15 ORomania 13 qSerbia and Montenegro 10 qMacedonia, Republic of 8 qMalaysia 7 qCyprus 6 qJordan 6 qIran, Islamic Republic of 5 qTunisia 5 qChile 5 qEgypt 4 qBotswana 4 qBahrain 4 qIndonesia 4 qPalestinian Nat’l Auth. 4 qSouth Africa 3 qLebanon 2 qPhilippines 2 qSaudi Arabia 2 qGhana 1 qMorocco 1 q

M032649

In a car rally two checkpoints are 160 km apart. Drivers must travel fromone checkpoint to the other in exactly 2.5 hours to earn maximum points.

A. What must the average speed be to travel the 160 km in this time?

Answer: _______________

B. A driver took 1 hour to travel through a 40 km hilly section at thebeginning of the course.

What must the average speed, in kilometers per hour, be for theremaining 120 km if the total time between checkpoints is to be2.5 hours?

Answer: _______________

177

Student Responses


Correct Response:

Incorrect Response:

Carrally:averagespeedforonesection(continued)Item Number: M032649B

Correct Response:

178







andFormulasUsingConcepts

Volumesofstacksofblocks

Korea, Republic of 88 pSingapore 86 pHong Kong, SAR 83 pJapan 81 pChinese Taipei 81 pNetherlands 78 pAustralia 73 pEstonia 69 pSlovak Republic 68 pBelgium (Flemish) 67 pScotland 67 pLithuania 66 pLatvia 64 pMalaysia 62 pSlovenia 62 pNew Zealand 60 pHungary 58 pEngland 58 pRussian Federation 57 pNorway 56 pItaly 55 pUnited States 50 OInternational average 50 OSweden 50 OIsrael 49 OBulgaria 48 OMoldova, Republic of 48 ORomania 46 OSerbia and Montenegro 45 qArmenia 42 qCyprus 42 qBahrain 41 qPhilippines 35 qLebanon 34 qMacedonia, Republic of 33 qSaudi Arabia 32 qIndonesia 32 qPalestinian Nat’l Auth. 30 qJordan 29 qChile 27 qMorocco 26 qBotswana 26 qTunisia 26 qIran, Islamic Republic of 26 qEgypt 24 qSouth Africa 22 qGhana 20 q


a

M012013

All the small blocks are the same size. Which stack of blocks has a differentvolume from the others?

a b

c d


Correct Response:

Cognitive Domain

179





D


Singapore 82 pHong Kong, SAR 82 pKorea, Republic of 75 pChinese Taipei 74 pJapan 73 pNetherlands 65 pBelgium (Flemish) 61 pEstonia 53 pRussian Federation 51 pItaly 51 pSlovak Republic 51 pHungary 48 pMalaysia 48 pLatvia 46 pLithuania 45 pSweden 45 pScotland 44 pEngland 43 OSerbia and Montenegro 43 OAustralia 42 ONew Zealand 41 OSlovenia 41 ORomania 39 OInternational average 39 OUnited States 39 OBulgaria 38 OCyprus 37 OArmenia 36 OLebanon 35 ONorway 35 qIsrael 34 qMoldova, Republic of 33 qTunisia 30 qMacedonia, Republic of 30 qIran, Islamic Republic of 27 qJordan 25 qIndonesia 24 qEgypt 21 qBahrain 20 qMorocco 19 qPalestinian Nat’l Auth. 18 qChile 18 qBotswana 16 qPhilippines 15 qGhana 10 qSouth Africa 10 qSaudi Arabia 10 q


andFormulasUsingConcepts

TheareaoftherectangleABCD

M032678

In the figure above, ABCD is a rectangle, and circles P and Q each have aradius of 5 cm. What is the area of the rectangle?

a 50 cm2

b 60 cm2

c 100 cm2

d 200 cm2

5 cm

P Q

A

D

B

C

Correct Response:

180






NuMBeR FractionsandDecimalsKnowingFactsandProcedures

Pairofnumbersbracketing2.25


B

Korea, Republic of 77 pSingapore 71 pBelgium (Flemish) 63 pLithuania 61 pHong Kong, SAR 61 pChinese Taipei 60 pRussian Federation 58 pHungary 58 pEstonia 57 pIsrael 57 pSlovak Republic 55 pJapan 55 pSweden 55 OUnited States 54 pSerbia and Montenegro 54 OSlovenia 53 ORomania 52 OItaly 52 OAustralia 52 OLatvia 52 OPhilippines 52 ONetherlands 51 OScotland 51 ONorway 51 OCyprus 51 OInternational average 50 OBulgaria 50 OMalaysia 50 OEngland 50 OMoldova, Republic of 48 ONew Zealand 47 OBotswana 46 qArmenia 46 OSaudi Arabia 46 qLebanon 45 qGhana 44 qMacedonia, Republic of 44 qTunisia 43 qMorocco 41 qEgypt 40 qBahrain 40 qSouth Africa 39 qChile 39 qPalestinian Nat’l Auth. 39 qJordan 38 qIran, Islamic Republic of 38 q

M012016

In which of these pairs of numbers is 2.25 larger than the first number butsmaller than the second number?

a 1 and 2

b 2 and

52

c

52

and

114

d

114

and 3


181






• 30

Incorrect Response

• 30 kg [incorrect unit]

• 6/5 [6 x 1/5]

• 4 [4/5 more needed to complete 1 kg]

• 5 [5 scoops = 1 kg flour]

• 6 [from stem]



Scoops of flour needed to fill bag


Singapore 79 pHong Kong, SAR 76 pChinese Taipei 75 pNetherlands 74 pKorea, Republic of 68 pJapan 62 pBelgium (Flemish) 62 pSweden 60 pAustralia 53 pUnited States 52 pScotland 51 pEstonia 51 pLatvia 51 pHungary 51 pEngland 50 pRussian Federation 49 pIsrael 48 pMalaysia 47 pNew Zealand 46 pSlovenia 46 pArmenia 45 pLithuania 43 pSlovak Republic 43 pNorway 39 ORomania 39 OSerbia and Montenegro 38 OBulgaria 38 OInternational average 38 OCyprus 37 OMoldova, Republic of 37 OItaly 34 OIndonesia 26 qMacedonia, Republic of 22 qIran, Islamic Republic of 20 qTunisia 18 qEgypt 17 qJordan 16 qLebanon 15 qChile 13 qPhilippines 13 qBahrain 11 qBotswana 11 qPalestinian Nat’l Auth. 10 qMorocco 8 qSouth Africa 7 qSaudi Arabia 7 qGhana 6 q

M022156

A scoop holds

1

5 kg of flour. How many scoops of flour are needed to fill a

bag with 6 kg of flour?

Answer: _______________

182

Student Responses


Correct Response:

Incorrect Response:

Scoops of flour needed to fill bag (continued)Item Number: M022156


Correct Response:

Cognitive Domain

183






Addition/multiplicationwithfractions

Chinese Taipei 82 pKorea, Republic of 80 pJapan 75 pSingapore 72 pHong Kong, SAR 69 pEgypt 58 pRomania 54 pItaly 53 pBelgium (Flemish) 53 pSlovenia 51 pSlovak Republic 51 pHungary 50 pEstonia 50 pMalaysia 48 pBulgaria 48 pRussian Federation 48 pLatvia 46 pSerbia and Montenegro 45 pLithuania 44 pArmenia 42 OInternational average 40 OLebanon 40 OIsrael 40 ONetherlands 40 OMoldova, Republic of 39 OCyprus 36 qUnited States 36 qJordan 35 qIran, Islamic Republic of 34 qBahrain 29 qAustralia 28 qIndonesia 28 qEngland 28 qNew Zealand 28 qPalestinian Nat’l Auth. 27 qMacedonia, Republic of 27 qTunisia 26 qScotland 26 qMorocco 25 qBotswana 24 qSweden 22 qPhilippines 22 qChile 21 qNorway 21 qSouth Africa 18 qSaudi Arabia 16 q


e

M022199

3

5

3

10

4

15+ × =( )

a

3

51

b

1

6

c

6

25

d

11

25

e

17

25

Correct Response:

184






NuMBeR FractionsandDecimals Reasoning

Numberofmen/womenatmeeting

Korea, Republic of 89 pJapan 87 pNetherlands 86 pBelgium (Flemish) 83 pSingapore 81 pSweden 79 pNorway 77 pChinese Taipei 77 pMalaysia 74 pHong Kong, SAR 73 pHungary 71 pItaly 70 pSlovenia 68 pSlovak Republic 68 pEstonia 67 pScotland 67 pEngland 67 pBulgaria 67 pAustralia 66 pIsrael 65 pCyprus 64 pSerbia and Montenegro 63 pNew Zealand 63 OLatvia 62 OLithuania 60 OInternational average 59 ORussian Federation 57 OMoldova, Republic of 56 OIran, Islamic Republic of 56 OUnited States 52 qChile 51 qJordan 51 qIndonesia 50 qRomania 48 qBahrain 46 qPalestinian Nat’l Auth. 46 qMorocco 46 qEgypt 46 qMacedonia, Republic of 45 qBotswana 42 qTunisia 40 qArmenia 40 qSaudi Arabia 37 qGhana 31 qPhilippines 27 qLebanon 24 qSouth Africa 23 q


a

M022191

Two-thirds of the people present at the beginning of a meeting are men.Nobody leaves but 10 more men and 10 more women arrive at the meeting.Which of the following statements is true?

a There would then be more men than women at the meeting.

b There would then be the same number of men as there are women atthe meeting.

c There would then be more women than men at the meeting.

d From the information given, you cannot tell whether there would bemore women or men.


Correct Response:

Cognitive Domain

185





NuMBeR FractionsandDecimals SolvingRoutineProblems

Fractionofhourbetweentwotimepoints

Singapore 85 pHong Kong, SAR 80 pKorea, Republic of 77 pChinese Taipei 77 pSweden 73 pEngland 68 pNetherlands 67 pJapan 67 pBelgium (Flemish) 66 pHungary 66 pAustralia 65 pSlovak Republic 64 pScotland 63 pUnited States 62 pLatvia 62 pIsrael 61 pMalaysia 61 pNew Zealand 60 pSlovenia 58 pNorway 57 pBulgaria 56 pCyprus 56 pEstonia 55 ORussian Federation 53 OInternational average 52 OMoldova, Republic of 52 OArmenia 50 OLithuania 50 OSerbia and Montenegro 48 OJordan 46 qRomania 43 qPalestinian Nat’l Auth. 43 qEgypt 43 qItaly 41 qLebanon 40 qPhilippines 40 qMacedonia, Republic of 40 qBahrain 40 qIran, Islamic Republic of 38 qIndonesia 38 qSaudi Arabia 30 qBotswana 29 qChile 28 qSouth Africa 27 qMorocco 26 qGhana 24 qTunisia 20 q


B

M012027

What fraction of an hour has passed between 1:10 a.m. and 1:30 a.m.?

a

15

b

13

c

12

d

23

e

34

Correct Response:

186







Fraction birthdays in first half of year

Korea, Republic of 90 pSingapore 90 pHong Kong, SAR 86 pNetherlands 82 pChinese Taipei 79 pBelgium (Flemish) 76 pSweden 76 pEngland 75 pMalaysia 75 pIsrael 74 pUnited States 72 pNorway 71 pAustralia 69 pNew Zealand 69 pScotland 69 pJapan 68 pEstonia 62 pSlovenia 60 pCyprus 59 pHungary 58 pItaly 57 pLatvia 57 pLithuania 57 ORussian Federation 55 OSlovak Republic 54 OInternational average 52 OIran, Islamic Republic of 46 qBulgaria 43 qRomania 41 qBotswana 40 qMoldova, Republic of 38 qJordan 37 qChile 36 qIndonesia 36 qEgypt 35 qLebanon 33 qMacedonia, Republic of 31 qPalestinian Nat’l Auth. 31 qSerbia and Montenegro 31 qTunisia 31 qBahrain 30 qPhilippines 28 qArmenia 27 qMorocco 21 qSouth Africa 21 qGhana 20 qSaudi Arabia 15 q


D

M012041

In a group of children, 16 have birthdays during the first half of the year,and 14 have birthdays during the second half of the year. What fraction ofthe group have birthdays during the first half of the year?

a

1430

b

1416

c

1614

d

1630

e

3016


Correct Response:

Cognitive Domain

187






4/5 of books more than 2/3

Singapore 85 pKorea, Republic of 80 pHong Kong, SAR 78 pChinese Taipei 78 pMalaysia 69 pNetherlands 68 pJapan 66 pSweden 65 pBelgium (Flemish) 63 pScotland 61 pHungary 60 pEngland 57 pLatvia 57 pSlovenia 57 pItaly 56 pEstonia 54 pRomania 53 pAustralia 53 pSlovak Republic 52 OIsrael 52 OCyprus 51 OLithuania 50 ONew Zealand 50 OUnited States 50 OBulgaria 49 OSerbia and Montenegro 48 OInternational average 48 ORussian Federation 45 OMoldova, Republic of 44 ONorway 43 qMacedonia, Republic of 38 qArmenia 38 qIran, Islamic Republic of 38 qEgypt 37 qPhilippines 35 qIndonesia 35 qPalestinian Nat’l Auth. 34 qBotswana 33 qJordan 33 qChile 33 qLebanon 28 qBahrain 27 qSouth Africa 27 qGhana 25 qTunisia 25 qMorocco 24 qSaudi Arabia 24 q


C

M022004

A teacher and a doctor each have 45 books. If

4

5 of the teacher’s books and

2

3 of the doctor’s books are novels, how many more novels does the teacher

have than the doctor?

a 2

b 3

c 6

d 30

e 36

Correct Response:

188







TimeforBettytorunrace

Singapore 88 pKorea, Republic of 87 pMalaysia 81 pNetherlands 81 pHungary 80 pChinese Taipei 80 pJapan 78 pRussian Federation 76 pHong Kong, SAR 75 pSlovak Republic 74 pUnited States 74 pSlovenia 73 pEstonia 72 pBelgium (Flemish) 71 pScotland 71 pMoldova, Republic of 69 pSerbia and Montenegro 68 pLatvia 67 pBulgaria 66 pLithuania 65 pRomania 64 OTunisia 63 OAustralia 63 OSweden 63 OItaly 62 OBotswana 61 OLebanon 61 OInternational average 61 OArmenia 60 OMacedonia, Republic of 59 OCyprus 59 OEgypt 58 OIsrael 58 OIndonesia 55 qEngland 54 qNew Zealand 53 qJordan 46 qNorway 46 qPhilippines 45 qMorocco 45 qBahrain 45 qIran, Islamic Republic of 44 qChile 42 qPalestinian Nat’l Auth. 37 qGhana 32 qSouth Africa 29 qSaudi Arabia 19 q


a

M022010

Alice ran a race in 49.86 seconds. Betty ran the same race in 52.30 seconds.How much longer did it take Betty to run the race than Alice?

a 2.44 seconds

b 2.54 seconds

c 3.56 seconds

d 3.76 seconds


Correct Response:

Cognitive Domain

189






Fuelremainingintankatendoftrip

Singapore 56 pChinese Taipei 50 pHong Kong, SAR 43 pKorea, Republic of 43 pJapan 38 pNetherlands 38 pMalaysia 34 pMoldova, Republic of 33 pLithuania 32 pHungary 32 pEstonia 31 pRomania 30 OBelgium (Flemish) 30 pRussian Federation 29 OAustralia 28 OArmenia 27 OLatvia 26 OInternational average 26 OSlovenia 26 OMacedonia, Republic of 25 OUnited States 25 OSlovak Republic 24 ONew Zealand 24 OIndonesia 23 OSweden 23 OJordan 23 OBulgaria 23 OCyprus 22 qSaudi Arabia 22 OIsrael 22 qSerbia and Montenegro 22 qItaly 21 qEgypt 21 qBotswana 20 qChile 20 qGhana 20 qEngland 20 qScotland 19 qMorocco 19 qTunisia 19 qSouth Africa 18 qIran, Islamic Republic of 18 qPalestinian Nat’l Auth. 17 qPhilippines 17 qBahrain 16 qNorway 16 qLebanon 12 q


a

M022127

A car has a fuel tank that holds 45 L of fuel. The car consumes 8.5 L of fuelfor each 100 km driven. A trip of 350 km was started with a full tank of fuel.How much remained in the tank at the end of the trip?

a 15.25 L

b 16.25 L

c 24.75 L

d 29.75 L

Correct Response:

190







JohnandCathytodivideanumberby100

Singapore 58 pBelgium (Flemish) 58 pEstonia 56 pJapan 56 pHong Kong, SAR 56 pKorea, Republic of 52 pRussian Federation 51 pHungary 51 pNetherlands 51 pChinese Taipei 46 pSlovak Republic 45 pLithuania 43 pIsrael 41 pSweden 41 pLatvia 37 ONew Zealand 36 OAustralia 35 OScotland 35 OInternational average 34 OItaly 34 OEngland 34 OCyprus 33 OSlovenia 32 OUnited States 32 OMoldova, Republic of 32 OSerbia and Montenegro 32 ONorway 31 ORomania 29 qArmenia 28 qEgypt 27 qMalaysia 27 qSaudi Arabia 26 qLebanon 26 qMacedonia, Republic of 23 qBahrain 23 qPhilippines 23 qMorocco 23 qChile 23 qIran, Islamic Republic of 22 qGhana 22 qBulgaria 22 qIndonesia 21 qPalestinian Nat’l Auth. 21 qSouth Africa 20 qTunisia 18 qBotswana 16 q


B

M032079

John and Cathy were told to divide a number by 100. By mistake Johnmultiplied the number by 100 and obtained an answer of 450.Cathy correctly divided the number by 100. What was her answer?

a 0.0045

b 0.045

c 0.45

d 4.5


Correct Response:

Cognitive Domain

191





NuMBeR FractionsandDecimals UsingConcepts

Numberofsquaresinshadedfraction

Singapore 88 pHong Kong, SAR 87 pBelgium (Flemish) 84 pKorea, Republic of 82 pNetherlands 80 pJapan 79 pChinese Taipei 78 pSweden 71 pMalaysia 67 pIsrael 67 pHungary 66 pAustralia 66 pScotland 63 pNorway 62 pEngland 62 pUnited States 61 pNew Zealand 60 pSlovenia 59 pEstonia 59 pCyprus 56 pLatvia 56 pRussian Federation 52 OSlovak Republic 52 OMoldova, Republic of 50 OItaly 50 OInternational average 49 OLithuania 47 OBulgaria 46 ORomania 45 OArmenia 42 qSerbia and Montenegro 42 qIran, Islamic Republic of 41 qMacedonia, Republic of 37 qJordan 32 qEgypt 30 qPalestinian Nat’l Auth. 29 qTunisia 26 qBahrain 25 qPhilippines 23 qLebanon 22 qMorocco 22 qChile 21 qIndonesia 21 qSaudi Arabia 19 qSouth Africa 16 qBotswana 16 qGhana 8 q


a

M012001

In the figure, how many MORE small squares need to be shaded so that

45

of

the small squares are shaded?

a 5

b 4

c 3

d 2

e 1



192





• A fraction with numerator smaller than 4 and denominator equal to 9, includes 3/9 = 1/3 OR 1/3.

• A fraction with numerator equal to 4 and denominator greater than 9, includes 4/10 = 2/5 OR 2/5.

• 3/8

• Othercorrectfraction

Incorrect Response

• 5/9

• 2/3

• Any fraction equivalent to 4/9.



Singapore 84 pKorea, Republic of 81 pJapan 81 pHong Kong, SAR 79 pChinese Taipei 77 pIsrael 74 pHungary 72 pArmenia 72 pAustralia 71 pSweden 70 pUnited States 69 pNetherlands 69 pEngland 68 pSlovak Republic 66 pNew Zealand 64 pNorway 64 pSlovenia 64 pEstonia 63 pBelgium (Flemish) 62 pRussian Federation 62 pScotland 60 pCyprus 60 pInternational average 54 ORomania 54 OBulgaria 54 OSerbia and Montenegro 52 OEgypt 52 OLatvia 52 OLithuania 50 OPalestinian Nat’l Auth. 50 qBotswana 49 qItaly 48 qJordan 48 qTunisia 47 qIran, Islamic Republic of 47 qMalaysia 43 qBahrain 41 qMoldova, Republic of 40 qSaudi Arabia 39 qChile 36 qMacedonia, Republic of 35 qSouth Africa 30 qLebanon 28 qIndonesia 26 qPhilippines 25 qMorocco 24 qGhana 21 q

Fraction less than 4/9


M022012

Write a fraction that is less than

4

9.

Answer: ______________________________

193

Student Responses


Fraction less than 4/9 (continued)Item Number: M022012

Correct Response:

Incorrect Response:

Correct Response:

194







Decimalroundedtonearesthundredth

Korea, Republic of 88 pSerbia and Montenegro 74 pRussian Federation 73 pLithuania 72 pHungary 72 pSlovak Republic 71 pBelgium (Flemish) 66 pUnited States 66 pEstonia 62 pMoldova, Republic of 55 pSweden 55 pSingapore 54 pItaly 54 pJapan 54 pLatvia 54 pNetherlands 54 pChinese Taipei 49 OSlovenia 49 OInternational average 47 OAustralia 47 OCyprus 46 OLebanon 45 OMalaysia 45 OPalestinian Nat’l Auth. 44 OIsrael 43 ONew Zealand 41 qEgypt 41 qScotland 41 qJordan 40 qEngland 40 qIndonesia 39 qPhilippines 38 qBulgaria 38 qIran, Islamic Republic of 37 qMorocco 37 qSaudi Arabia 36 qRomania 35 qNorway 33 qBahrain 32 qMacedonia, Republic of 32 qChile 30 qArmenia 29 qGhana 29 qHong Kong, SAR 29 qBotswana 28 qSouth Africa 22 q


D

M022144

Which of the following is 78.2437 rounded to the nearest hundredth?

a 100

b 80

c 78.2

d 78.24

e 78.244


Correct Response:

Cognitive Domain

195






Decimalsorderedgreatesttoleast


D

Singapore 79 pBelgium (Flemish) 74 pHong Kong, SAR 72 pNetherlands 66 pChinese Taipei 63 pEstonia 62 pMalaysia 62 pKorea, Republic of 59 pSweden 59 pLatvia 58 pJapan 53 pAustralia 53 pSlovak Republic 52 pLithuania 49 pRussian Federation 49 pScotland 48 OUnited States 48 pSlovenia 48 OItaly 47 OHungary 47 OBulgaria 47 OEgypt 46 ORomania 46 OMoldova, Republic of 44 OEngland 44 OInternational average 44 OArmenia 42 OLebanon 42 ONew Zealand 42 OCyprus 39 OIsrael 38 qMorocco 38 qChile 35 qNorway 35 qJordan 35 qSerbia and Montenegro 34 qTunisia 33 qMacedonia, Republic of 32 qIndonesia 29 qPalestinian Nat’l Auth. 29 qBahrain 27 qPhilippines 25 qSaudi Arabia 23 qGhana 20 qIran, Islamic Republic of 18 qBotswana 18 qSouth Africa 16 q

M022198

In which list are the numbers ordered from greatest to least?

a 0.233, 0.3, 0.32, 0.332

b 0.3, 0.32, 0.332, 0.233

c 0.32, 0.233, 0.332, 0.3

d 0.332, 0.32, 0.3, 0.233

Correct Response:

196







Thenumberclosestto10

Netherlands 97 pSweden 96 pEstonia 96 pSingapore 95 pLithuania 95 pBelgium (Flemish) 94 pKorea, Republic of 94 pMalaysia 93 pJapan 92 pSerbia and Montenegro 91 pNorway 91 pRussian Federation 91 pLatvia 90 pSlovak Republic 90 pItaly 90 pHong Kong, SAR 89 pScotland 89 pChinese Taipei 89 pCyprus 88 pHungary 88 pAustralia 88 pUnited States 87 pSlovenia 87 pNew Zealand 86 pBulgaria 85 pEngland 82 pMoldova, Republic of 82 pIsrael 81 pRomania 79 OMacedonia, Republic of 78 OInternational average 76 OTunisia 76 OMorocco 75 OIndonesia 74 OIran, Islamic Republic of 69 qChile 67 qLebanon 67 qArmenia 66 qJordan 55 qPalestinian Nat’l Auth. 50 qBahrain 49 qEgypt 48 qPhilippines 42 qBotswana 40 qSaudi Arabia 35 qSouth Africa 30 qGhana 24 q


B

M03

2760

Use the patterns in the previous table to answer the following questions.

A. Pat made a shape with a total of 64 tiles. How many were black and

how many were red?

Answer: ____________ black tiles ____________ red tiles

B. Pat made a shape that used 49 black tiles.

How many red tiles did Pat use in that shape?

Answer: ____________ red tiles

C. Next, Pat made a shape using 44 of the red tiles. How many black tiles

would Pat need to complete the black part of the shape?

Answer: ____________ black tiles


Correct Response:

Cognitive Domain

197





NuMBeR IntegersKnowingFactsandProcedures

Thevalueof1minus5times-2


a

Japan 74 pSingapore 70 pHong Kong, SAR 67 pChinese Taipei 66 pNetherlands 61 pBelgium (Flemish) 55 pKorea, Republic of 54 pSlovak Republic 52 pEstonia 52 pIsrael 52 pRomania 49 pNew Zealand 48 pRussian Federation 46 pBulgaria 46 pAustralia 45 pArmenia 44 pLatvia 42 pHungary 42 pLebanon 42 pMalaysia 39 OBotswana 39 OLithuania 38 OUnited States 38 OItaly 37 OEgypt 37 OSlovenia 36 OInternational average 35 OSerbia and Montenegro 33 OMoldova, Republic of 33 OMacedonia, Republic of 32 OEngland 25 qTunisia 24 qCyprus 23 qPhilippines 21 qJordan 19 qPalestinian Nat’l Auth. 19 qScotland 18 qSouth Africa 17 qBahrain 15 qIndonesia 12 qSaudi Arabia 12 qSweden 10 qChile 10 qIran, Islamic Republic of 10 qMorocco 6 qNorway 5 q

M032612

What is the value of 1 − 5 × (−2)?

a 11

b 8

c −8

d −9

Correct Response:

198






NuMBeR Integers UsingConcepts

Ifnisanegativeinteger

Korea, Republic of 78 pChinese Taipei 74 pRussian Federation 69 pJapan 68 pHong Kong, SAR 67 pSingapore 58 pHungary 53 pEstonia 51 pLatvia 49 pBelgium (Flemish) 48 pUnited States 48 pIsrael 48 pArmenia 47 pSlovak Republic 46 pSerbia and Montenegro 46 pNetherlands 44 OBulgaria 42 ORomania 41 OLebanon 41 OLithuania 40 OMalaysia 40 OInternational average 40 OMoldova, Republic of 39 OSlovenia 38 OEgypt 37 OAustralia 36 OCyprus 34 qItaly 32 qIran, Islamic Republic of 32 qPhilippines 32 qMacedonia, Republic of 32 qNew Zealand 31 qJordan 29 qPalestinian Nat’l Auth. 29 qSweden 28 qScotland 28 qIndonesia 27 qEngland 26 qSouth Africa 26 qNorway 25 qMorocco 25 qSaudi Arabia 25 qBahrain 22 qTunisia 22 qBotswana 22 qChile 18 q


C

M032643

If n is a negative integer, which of these is the largest number?

a 3 + n

b 3 × n

c 3 − n

d 3 ÷ n


Correct Response:

Cognitive Domain

199





NuMBeRRatio,Proportions,

andPercentKnowingFactsandProcedures

Percentdecreaseintraveltime


C

Singapore 70 pNetherlands 62 pHong Kong, SAR 61 pMalaysia 48 pSweden 47 pAustralia 46 pKorea, Republic of 45 pScotland 42 pEngland 42 pHungary 40 pChinese Taipei 40 pNew Zealand 40 pJapan 39 pSlovak Republic 38 pIsrael 38 pSlovenia 38 pBelgium (Flemish) 38 pEstonia 37 pLatvia 37 pUnited States 35 pLithuania 34 OCyprus 34 ONorway 34 ORussian Federation 32 OSerbia and Montenegro 32 OInternational average 31 OMoldova, Republic of 29 OBulgaria 28 ORomania 27 qJordan 22 qSouth Africa 21 qChile 21 qArmenia 20 qItaly 20 qMacedonia, Republic of 19 qBahrain 19 qIndonesia 19 qPalestinian Nat’l Auth. 18 qIran, Islamic Republic of 18 qBotswana 18 qLebanon 17 qEgypt 17 qPhilippines 17 qSaudi Arabia 17 qMorocco 15 qGhana 15 qTunisia 12 q

M022139

When a new highway is built, the average time it takes a bus to travel fromone town to another is reduced from 25 minutes to 20 minutes. What is thepercent decrease in time taken to travel between the two towns?

a 4%

b 5%

c 20%

d 25%

Correct Response:

200







andPercentKnowingFactsandProcedures

Theratiooftheshadedareatotheunshaded

Singapore 87 pChinese Taipei 81 pKorea, Republic of 80 pHong Kong, SAR 74 pMalaysia 72 pJapan 71 pSlovak Republic 56 pAustralia 55 pScotland 54 pLatvia 52 pEngland 52 pHungary 52 pNetherlands 51 pUnited States 50 pLithuania 50 pSlovenia 48 pSerbia and Montenegro 48 pRussian Federation 47 pIndonesia 45 OBulgaria 44 OBelgium (Flemish) 43 OEstonia 42 OInternational average 41 ONew Zealand 39 OIsrael 38 OCyprus 37 ORomania 37 OPhilippines 37 OMoldova, Republic of 37 OItaly 35 qMacedonia, Republic of 35 qSweden 31 qArmenia 28 qPalestinian Nat’l Auth. 27 qIran, Islamic Republic of 26 qEgypt 26 qSaudi Arabia 26 qNorway 23 qJordan 21 qChile 20 qBahrain 19 qBotswana 17 qSouth Africa 16 qMorocco 16 qLebanon 16 qTunisia 14 q


a

M032447

In the figure above, each of the smaller triangles has the same area. Whatis the ratio of the shaded area to the unshaded area?

a 5:3

b 8:5

c 5:8

d 3:5


201





A computer club had 40 members


• 48% with calculations shown.

Partial Response

• 24 girls

• Correctmethodbutcomputationalerror.

• 48% with no calculations shown.

Incorrect Response

• 50%




andPercentReasoning

M03

2233

A computer club had 40 members, and 60% of the members were girls.

Later, 10 boys joined the club. What percent of the members now are girls?

Show the calculations that led to your answer.

Answer: _______________

Singapore 64 pKorea, Republic of 44 pChinese Taipei 41 pHong Kong, SAR 29 pHungary 28 pMalaysia 23 pBelgium (Flemish) 21 pSweden 21 pSlovak Republic 19 pEstonia 19 pNetherlands 18 pLithuania 18 pJapan 16 pEngland 16 OScotland 14 OUnited States 14 OAustralia 13 OSlovenia 13 OIsrael 13 ONew Zealand 12 OInternational average 12 OLatvia 9 OSerbia and Montenegro 9 OArmenia 8 ORomania 7 qRussian Federation 6 qItaly 6 qBulgaria 6 qCyprus 4 qNorway 3 qChile 3 qIndonesia 3 qLebanon 3 qPhilippines 2 qSouth Africa 2 qIran, Islamic Republic of 2 qJordan 2 qPalestinian Nat’l Auth. 2 qEgypt 2 qMorocco 1 qBotswana 1 qTunisia 1 qMoldova, Republic of 1 qMacedonia, Republic of 1 qBahrain 0 qGhana 0 q

202

Student Responses


A computer club had 40 members (continued)Item Number: M032233

Correct Response:

Partial Response:

Incorrect Response:


Correct Response:

Cognitive Domain

203






andPercentSolvingRoutineProblems

LapsrunbyCarolandAlicefromratio


D

Singapore 75 pBelgium (Flemish) 69 pJapan 68 pChinese Taipei 66 pNetherlands 66 pSweden 62 pHong Kong, SAR 61 pSlovak Republic 59 pLatvia 55 pLithuania 55 pRussian Federation 54 pIsrael 53 pAustralia 52 ONorway 52 pEstonia 51 pKorea, Republic of 51 pIran, Islamic Republic of 48 OUnited States 48 OGhana 47 OInternational average 47 OSerbia and Montenegro 47 OSouth Africa 47 OCyprus 46 OLebanon 46 ONew Zealand 46 OSlovenia 46 OEngland 45 OScotland 45 OHungary 43 qMalaysia 43 OPalestinian Nat’l Auth. 43 qArmenia 42 qPhilippines 42 qTunisia 42 qJordan 41 qEgypt 40 qMoldova, Republic of 40 qBotswana 39 qRomania 37 qBulgaria 36 qMacedonia, Republic of 36 qItaly 35 qSaudi Arabia 35 qIndonesia 34 qMorocco 33 qChile 32 qBahrain 29 q

M012004

Alice can run 4 laps around a track in the same time that Carol can run3 laps. When Carol has run 12 laps, how many laps has Alice run?

a 9

b 11

c 13

d 16

Correct Response:

204






C


A shop increased its prices by 20%



Singapore 87 pHong Kong, SAR 86 pNetherlands 79 pChinese Taipei 74 pKorea, Republic of 74 pSlovak Republic 73 pHungary 72 pBelgium (Flemish) 72 pSweden 70 pEstonia 65 pJapan 63 pScotland 62 pMalaysia 62 pRussian Federation 61 pLithuania 58 pIsrael 58 pUnited States 57 pAustralia 55 pSlovenia 55 pRomania 54 OLatvia 54 OEngland 52 OSerbia and Montenegro 51 OInternational average 49 ONew Zealand 49 OItaly 49 ONorway 48 OBulgaria 47 OArmenia 45 qCyprus 45 qMoldova, Republic of 44 qChile 41 qTunisia 40 qMacedonia, Republic of 39 qIndonesia 34 qBotswana 32 qPhilippines 31 qLebanon 31 qMorocco 30 qEgypt 29 qBahrain 27 qPalestinian Nat’l Auth. 26 qJordan 25 qIran, Islamic Republic of 24 qSaudi Arabia 22 qSouth Africa 19 qGhana 16 q

M03

222 8

A shop increased its prices by 20%. What is the new price of an item which

previously sold for 800 zeds?

a 640 zeds

b 900 zeds

c 960 zeds

d 1,000 zeds


Correct Response:

Cognitive Domain

205







A machine uses 2.4 liters of gasoline


B

Singapore 89 pNetherlands 78 pHong Kong, SAR 77 pKorea, Republic of 75 pBelgium (Flemish) 74 pChinese Taipei 71 pMalaysia 68 pJapan 66 pEstonia 65 pLithuania 64 pSlovak Republic 63 pHungary 63 pSweden 60 pLebanon 55 pUnited States 55 pRussian Federation 54 pIsrael 53 pEngland 50 OScotland 50 OLatvia 50 OSlovenia 50 OAustralia 49 ORomania 48 OInternational average 47 OSerbia and Montenegro 45 OItaly 44 ONorway 44 OMoldova, Republic of 44 OCyprus 44 OBulgaria 43 ONew Zealand 42 OArmenia 41 qJordan 40 qMacedonia, Republic of 38 qEgypt 34 qIran, Islamic Republic of 31 qIndonesia 31 qPalestinian Nat’l Auth. 31 qTunisia 30 qChile 29 qPhilippines 27 qMorocco 27 qBotswana 23 qBahrain 23 qSaudi Arabia 22 qSouth Africa 17 qGhana 17 q

M032533

A machine uses 2.4 liters of gasoline for every 30 hours of operation.How many liters of gasoline will the machine use in 100 hours?

a 7.2

b 8.0

c 8.4

d 9.6

Correct Response:

206






D


Three brothers receive 45,000 zeds



Singapore 85 pHong Kong, SAR 73 pKorea, Republic of 71 pChinese Taipei 68 pSweden 67 pHungary 67 pEstonia 67 pNetherlands 66 pSlovak Republic 65 pBelgium (Flemish) 63 pJapan 60 pMalaysia 57 pEngland 55 pAustralia 55 pRomania 53 pIsrael 52 pRussian Federation 52 pNew Zealand 50 OLithuania 49 OItaly 48 OScotland 48 OSerbia and Montenegro 48 OUnited States 45 ONorway 45 OSlovenia 45 OInternational average 45 OCyprus 42 OChile 41 OMoldova, Republic of 40 OLatvia 37 qBulgaria 37 qMacedonia, Republic of 36 qIran, Islamic Republic of 35 qSouth Africa 32 qGhana 32 qPhilippines 29 qJordan 29 qArmenia 28 qPalestinian Nat’l Auth. 28 qIndonesia 27 qLebanon 26 qTunisia 24 qMorocco 22 qBotswana 21 qBahrain 21 qEgypt 20 qSaudi Arabia 18 q

M03

2727

Three brothers, Bob, Dan, and Mark, receive a gift of 45,000 zeds from their

father. The money is shared between the brothers in proportion to the

number of children each one has. Bob has 2 children, Dan has 3 children,

and Mark has 4 children.

How many zeds does Mark get?

a 5,000

b 10,000

c 15,000

d 20,000


Correct Response:

Cognitive Domain

207






andPercentUsingConcepts

3/25ofthepeopleintheaudiencewerechildren


a

Singapore 96 pHong Kong, SAR 90 pBelgium (Flemish) 87 pMalaysia 84 pNetherlands 79 pChinese Taipei 77 pKorea, Republic of 76 pEngland 71 pUnited States 70 pBotswana 70 pNew Zealand 67 pAustralia 67 pLatvia 65 pCyprus 64 pScotland 63 pIsrael 63 pSlovenia 61 pSweden 61 pJapan 60 pLithuania 59 OEstonia 57 OSlovak Republic 56 OHungary 55 OInternational average 55 ORussian Federation 52 OIndonesia 51 OBulgaria 50 ONorway 50 qRomania 49 qItaly 47 qSerbia and Montenegro 45 qEgypt 44 qArmenia 42 qMacedonia, Republic of 42 qPhilippines 42 qMoldova, Republic of 42 qGhana 41 qIran, Islamic Republic of 39 qPalestinian Nat’l Auth. 39 qJordan 39 qChile 39 qBahrain 36 qLebanon 34 qSouth Africa 33 qTunisia 30 qMorocco 29 qSaudi Arabia 25 q

M032570

At a play,

325

of the people in the audience were children.

What percent of the audience was this?

a 12%

b 3%

c 0.3%

d 0.12%

Correct Response:

208






D


The closest to 11 squared plus 9 squared

NuMBeR WholeNumbersKnowingFactsandProcedures

Hong Kong, SAR 88 pLatvia 88 pHungary 85 pRussian Federation 84 pUnited States 82 pSlovak Republic 82 pEstonia 81 pSlovenia 81 pLebanon 80 pBelgium (Flemish) 80 pKorea, Republic of 80 pMalaysia 80 pChinese Taipei 80 pRomania 80 pSingapore 80 pSerbia and Montenegro 79 pItaly 79 pLithuania 77 pCyprus 74 pAustralia 73 pNetherlands 69 pMacedonia, Republic of 68 pBulgaria 67 pIndonesia 65 OEngland 64 OArmenia 64 OIsrael 63 OInternational average 61 OScotland 59 ONew Zealand 56 OTunisia 53 qJapan 50 qJordan 49 qPalestinian Nat’l Auth. 48 qMorocco 47 qPhilippines 45 qEgypt 44 qIran, Islamic Republic of 44 qChile 41 qBahrain 37 qSweden 36 qGhana 28 qBotswana 26 qSaudi Arabia 22 qSouth Africa 20 qMoldova, Republic of 18 qNorway 13 q

M032609

Which of these is closest to 11 92 2+ ?

a 20 + 20

b 20 + 80

c 120 + 20

d 120 + 80


Correct Response:

Cognitive Domain

209





NuMBeR WholeNumbersKnowingFactsandProcedures

Which equals 370 times 998 plus 370 times 2


a

Singapore 70 pHong Kong, SAR 69 pChinese Taipei 68 pHungary 61 pNetherlands 59 pEstonia 57 pLebanon 53 pIsrael 52 pEgypt 52 pBelgium (Flemish) 50 pRussian Federation 49 pAustralia 49 pUnited States 48 pLithuania 47 pMalaysia 47 pNew Zealand 46 pKorea, Republic of 43 ORomania 43 OBotswana 41 OScotland 40 OInternational average 39 OArmenia 38 OLatvia 38 OSlovak Republic 38 OJapan 37 OBulgaria 37 OMoldova, Republic of 37 OSlovenia 36 OItaly 35 OMacedonia, Republic of 34 OEngland 34 OPalestinian Nat’l Auth. 33 qTunisia 31 qPhilippines 30 qBahrain 28 qCyprus 24 qSweden 23 qSerbia and Montenegro 23 qNorway 22 qSaudi Arabia 22 qMorocco 21 qSouth Africa 21 qChile 18 qIndonesia 18 qJordan 17 qIran, Islamic Republic of 14 q

M03

2690

Which of these is equal to 370 × 998 + 370 × 2?

a 370 × 1,000

b 372 × 998

c 740 × 998

d 370 × 998 × 2

Correct Response:

210






C


Arrangements of 4-digit whole numbers

NuMBeR WholeNumbers SolvingRoutineProblems

Korea, Republic of 92 pSingapore 88 pChinese Taipei 87 pHong Kong, SAR 86 pJapan 85 pMalaysia 79 pLatvia 77 pSlovenia 75 pBelgium (Flemish) 75 pSweden 72 pBulgaria 71 pItaly 71 pRussian Federation 70 pRomania 70 pUnited States 70 pSerbia and Montenegro 70 pSlovak Republic 69 pEstonia 68 pAustralia 68 pMoldova, Republic of 67 pScotland 66 pIsrael 66 pHungary 65 pLithuania 65 pMacedonia, Republic of 64 pNetherlands 61 OEngland 60 OInternational average 59 OArmenia 57 ONew Zealand 56 OIran, Islamic Republic of 56 OCyprus 55 qEgypt 53 qTunisia 52 qJordan 50 qChile 50 qNorway 45 qPalestinian Nat’l Auth. 41 qLebanon 41 qBahrain 41 qIndonesia 40 qPhilippines 35 qBotswana 32 qMorocco 30 qGhana 22 qSouth Africa 21 qSaudi Arabia 21 q

M01

2028

The four digits above are to be arranged from largest to smallest to form a

four-digit number. The same four digits are then to be arranged from

smallest to largest to form another four-digit number. What is the

difference between the two resulting four-digit numbers?

a 3,726

b 4,726

c 8,082

d 8,182

e 8,192

9 1 4 5


Correct Response:

Cognitive Domain

211






Approximatenumberofmagazinessold


D

Korea, Republic of 74 pSingapore 74 pChinese Taipei 71 pNetherlands 69 pBelgium (Flemish) 69 pHong Kong, SAR 68 pAustralia 67 pHungary 66 pJapan 66 pSweden 63 pNew Zealand 62 pEstonia 62 pEngland 61 pSlovenia 60 pSlovak Republic 59 pUnited States 58 pMalaysia 58 pRussian Federation 58 pScotland 58 pNorway 58 pLithuania 57 pLatvia 57 pBulgaria 56 pIsrael 54 pItaly 53 pSerbia and Montenegro 50 OInternational average 49 ORomania 47 OCyprus 47 OMoldova, Republic of 44 OMacedonia, Republic of 42 qArmenia 39 qIndonesia 38 qTunisia 37 qPhilippines 36 qLebanon 36 qChile 36 qMorocco 33 qBahrain 31 qIran, Islamic Republic of 29 qJordan 28 qEgypt 23 qSaudi Arabia 23 qPalestinian Nat’l Auth. 21 qSouth Africa 20 qBotswana 19 qGhana 18 q

M02

2194

About 7,000 copies of a magazine are sold each week. Approximately how

many magazines are sold each year?

a 8,400

b 35,000

c 84,000

d 350,000

e 3,500,000



212





• 15

Incorrect Response

• 14 or 14.88



Theteachersplantosend6newslettersperyear


Armenia 60 pNetherlands 57 pSingapore 57 pHong Kong, SAR 53 pBelgium (Flemish) 46 pJapan 44 pChinese Taipei 44 pKorea, Republic of 43 pUnited States 36 pHungary 35 pSlovak Republic 33 pScotland 32 pEstonia 32 pSweden 30 pNew Zealand 29 pRussian Federation 29 pLithuania 29 pAustralia 28 pEngland 27 OSlovenia 24 OLatvia 22 OInternational average 21 OItaly 21 OBulgaria 20 OIsrael 20 ONorway 20 OCyprus 18 qRomania 14 qSerbia and Montenegro 13 qMacedonia, Republic of 11 qMoldova, Republic of 10 qMalaysia 8 qChile 8 qTunisia 8 qJordan 4 qLebanon 4 qPhilippines 3 qIndonesia 3 qSouth Africa 3 qIran, Islamic Republic of 3 qBahrain 3 qEgypt 3 qPalestinian Nat’l Auth. 2 qMorocco 1 qBotswana 0 qGhana 0 qSaudi Arabia 0 q

M032652

The teachers at Parkway School plan to send 6 newsletters per year toeach of the 620 families with children at the school. The newsletters eachneed 2 sheets of paper. The paper is sold in packs of 500 sheets.

What is the least number of packs of paper needed to print the schoolnewsletter for the year?

Answer: _______________

213

Student Responses


Theteachersplantosend6newslettersperyear(continued)Item Number: M032652

Correct Response:

Incorrect Response:



214





• 400 or equivalent.

Incorrect Response



Singapore 91 pNetherlands 88 pHong Kong, SAR 87 pBelgium (Flemish) 86 pKorea, Republic of 85 pEstonia 85 pChinese Taipei 83 pSweden 82 pMalaysia 81 pUnited States 78 pLatvia 78 pRussian Federation 78 pNew Zealand 77 pAustralia 76 pEngland 75 pHungary 72 pIsrael 72 pLithuania 72 pScotland 71 pItaly 71 pSlovenia 67 pMoldova, Republic of 66 pCyprus 66 pRomania 65 pBulgaria 63 OSlovak Republic 63 OJapan 61 OChile 61 OSerbia and Montenegro 61 OInternational average 61 ONorway 60 OMacedonia, Republic of 56 qIndonesia 49 qTunisia 48 qArmenia 47 qIran, Islamic Republic of 44 qLebanon 43 qJordan 43 qBahrain 41 qMorocco 39 qEgypt 36 qPhilippines 35 qPalestinian Nat’l Auth. 33 qBotswana 28 qSaudi Arabia 23 qSouth Africa 18 qGhana 11 q

Garden with 14 rows of 20 plants each

M032671

A garden has 14 rows. Each row has 20 plants. The gardener thenplants 6 more rows with 20 plants in each row.

How many plants are now there altogether?

Answer: _______________


215

Student Responses


Correct Response:

Incorrect Response:

Garden with 14 rows of 20 plants each (continued)Item Number: M032671

Item Index 1999Content Domain Page

Fractions and Number Sense

B08 Caloriesinportionoffoodfromratio 3

B09 Figureshowingequivalentfractions 4

B10 Smallestdecimalfraction 5

D09 Smallestsimplefraction 6

D12 EstimateofpointPonanumberline 7

F07 Averagespeedfromdistanceandtime 8

F09 Numberbetweentwodecimalfractions 9

F12 Fractionofacircleshaded 10

H08 Figureshowingfractionofshadedsquare 11

H09 Sumclosestto691+208 12

J12 Divisionoffractions 13

J14 Divisionofdecimals 14

J18 Distancebetweentownsfrommap 15

L09 Lengthofbuildingcomparedtocar 16

L10 Twohundredsixandnine-tenths 17

L18 Subtractionwiththreefractions 18

N11 Numberofcarsfromroundedvalue 19

N14 Listofequivalentfractions 20

N16 Numberofmarblesinbag 21

N17 Amountofpaintleft 22

N19 Shadein3/8ofsquaresingrid 23

P13 Estimateoftotalcarsinparkinglot 24

P14 Estimateofdistancefromexplosion 25

P15 Fractionofcherriesinbasket 26

P17 Writedecimalasfraction 27

R07 Subtractionofdecimalsto0.001 28

R08 Averageweightofsaltcrystals 29

R13 Subtractionof4-digitwholenumbers 30

R14 Howmuchmoneyleftifspent5/8 31

R15 Moneyfromtotalmagazinesales 32

T02A Number/fractionof2typesofboxes 33

T02B Number/fractionof2typesofboxes 34

T04 Heightofstackofpaperfromthickness 35

V01 Twopossibilitiesforactualheight 36

V03 Ratioofnitratetototalfertilizer 37

Algebra

B12 Equationrepresentingrelationship 38

D08 Valueofxfromequivalentratios 39

D10 Equationtodeterminecostofcards 40

F11 Find1/3ofnumberfromrelationship 41

H10 Equationfromx/ytable 42

H12 Symboliclinearequationofmagazines 43

J17 Missingnumberintable 44

L12 Distancetraveledbyelevator 45

Content Domain Page

Algebra (continued)

L14 Correctequationbasedonx/ytable 46

L15 Valuesinproportionalitytable 47

L17 Valueofxinmathematicalequation 48

N13 Valueofexpressionsubstitutingx=3 49

P09 Expressionequivalenttonxnxn 50

P11 Equivalentexpression:k+k+k+k+k 51

R10 Expressionwhena, b, carereal 52

R12 Operationsonnegativenumber 53

T01 Totalclubmembers:boysandgirls 54

V04A Sequenceoffigureswithcircles 55

V04B Sequenceoffigureswithcircles 56

V04C Sequenceoffigureswithcircles 57

Measurement

D11 Unitstomeasuremassofegg 58

F10 Measurementaccuracyofruler 59

J10 Areaofpatharoundgarden 60

L13 Mostpacestowalktoendofhallway 61

N15 Angleclosestto45degrees 62

P08 Ratioofwidth/perimeterinrectangle 63

P12 Lengthofstringpulledstraight 64

T03 Areaofrectangleinsideparallelogram 65

Geometry

B11 Cubefromfolded2-dimensionalnet 66

D07 Anglesinsymmetricpolygon 67

J11 NOTtrueforallrectangles 68

J15 Twosimilartriangles 69

J16 Pointongraphfromcoordinates 70

L16 Measureofangleinquadrilateral 71

N12 Positionofpointonnumberline 72

P10 Lengthofsidefromsimilartriangle 73

R11 Righttrianglestocoverrectangle 74

Data Representation, Analysis and Probability

B07 Graphshowinggreatestincrease 75

F08 Likelyresultoffifthcointoss 76

H07 Barcharthistogramoftraveltime 77

H11 Defectivebulbsfromrandomsample 78

J13 Interpretationofpictographofhouses 79

L11 Graphofhumidityinroom 80

N18 Probabilityofdrawingchip 81

P16 Day/timeintableatshowntemperature 82

R09 Timeforpendulumtoswing20times 83

V02 Cheapermagazinesubscription 84

Content Domain Page

Algebra

M012042 Valueof-3xgivenvalueofx 85

M022185 Subtractfractionsinvolvingx 86

M032036 Whichequals2xminus3 plus7xplus5y 87

M032557 Thevalueofa+2times(bplusc) 88

M022002 Threeconsecutiveevennumbers 90

M022251 Totalnumberofbooksthreeboyshave 91

M032044 Carlapaidxzedsfor3cartonsofjuice 92

M012040 Findnfromproportionalityequation 93

M022196 TrueexpressionforvaluesofL,K,M 94

M022253 Solveequationforx 95

M032728 Ifxplus3y equals11and2xplus3yequals13 97

M032208 Ifxminusyequals5andx/2equals3 98

M032210 Ifa/bequals70 99

M032545 7orangesand4lemonscost43zeds 100

M012002 Objectsbalancedonscale 102

M032046 Ifyequals3xplus2 103

M012017 Numberofmatchstickscontinuingpattern 104

M022008 Numbersinsequenceincreasingby4 105

M022261A Sequenceoffigureswithtriangles:filltable 107

M022261B Sequenceoffigureswithtriangles:7thfigure 109

M022261C Sequenceoffigureswithtriangles:50thfigure 111

M032744 Geometrytiling:identifycellwithletter 114

M012029 Setsoforderedpairsofnumbers 117

M012025 Intersectionpointofdistance/timegraphs 118

Data

M012037 Testscorefrequencytable 119

M022189 Howmanypencilssoldfrombargraph 120

M032762 Phoneplans:leastexpensiveplanforBetty 121

M022135 Graphofcoolingwater 123

M032763 Phoneplans:costofplansforFrank 124

M032764 Phoneplans:minutestalkbyDarlene 126

M012006 Comparisonoftwoaveragescores 128

M012014 Piegraphofcropdistribution 129

M022252 Mostlikelysectoronspinner 130

M032271 Inaschooltherewere1200students 131

M022146 Numberofstudentsfromprobability 132

Content Domain Page

Geometry

M032403 DrawalinetodividetriangleABC 133

M012015 Propertyofcongruenttrapezoids 135

M012005 Falsestatementofcongruenttriangles 136

M032261 Identifysimilartriangles 137

M022142 Sumofanglesequalto180degrees 138

M022202 Measureofangleinadjacentangles 139

M012039 Sumofanglesfromintersectinglines 141

M022016 Pointonalinedefinedbytwopoints 142

M032588 Whichpointcouldhavecoordinates(2,-4) 143

M032489 Whichcouldbefoldedtomakea3-Dfigure 144

M022154 Centerpointofrotationofrectangle 145

M032745 Geometrytiling:produceapatternusingletters 146

M032743 Geometrytiling:makesasymmetricalpattern 150

M012026 Angleinoverlappingcongruenttriangles 153

M032693 Theanglebyaregularhexagon 154

M032689 ThesizeofanglePRQ 156

Measurement

M022005 250mlbottlesfilledby400liters 157

M022188 Whichisleastamountoftime 158

M032699 Theunitusedforasoccerfield 159

M032732 Measureoftheareaofatriangle 160

M012003 Actuallengthofboxfromroundedmeasure 161

M012038 Lengthofpipefrommeterscale 162

M022021 Areaofpavedwalkwayaroundpool 163

M032647 Orangesarepackedinboxes 164

M012030 Lengthofrectanglefromwidth/perimeter 165

M022148 Timewhenfinishhomework 166

M022227A 5squares:areaofonesquare 168

M022227B 5squares:lengthofoneside 170

M022227C 5squares:perimeterwholefigure 172

M032649A Carrally:averagespeed 174

M032649B Carrally:averagespeedforonesection 176

M012013 Volumesofstacksofblocks 178

M032678 TheareaoftherectangleABCD 179

Continued

Item Index 2003

y

Content Domain Page

Number

M012016 Pairofnumbersbracketing2.25 180

M022156 Scoopsofflourneededtofillbag 181

M022199 Addition/multiplicationwithfractions 183

M022191 Numberofmen/womenatmeeting 184

M012027 Fractionofhourbetweentwotimepoints 185

M012041 Fractionbirthdaysinfirsthalfofyear 186

M022004 4/5ofbooksmorethan2/3 187

M022010 TimeforBettytorunrace 188

M022127 Fuelremainingintankatendoftrip 189

M032079 JohnandCathytodivideanumberby100 190

M012001 Numberofsquaresinshadedfraction 191

M022012 Fractionlessthan4/9 192

M022144 Decimalroundedtonearesthundredth 194

M022198 Decimalsorderedgreatesttoleast 195

M032670 Thenumberclosestto10 196

M032612 Thevalueof1minus5times-2 197

M032643 Ifnisanegativeinteger 198

M022139 Percentdecreaseintraveltime 199

M032447 Theratiooftheshadedareatotheunshaded 200

M032233 Acomputerclubhad40members 201

M012004 LapsrunbyCarolandAlicefromratio 203

M032228 Ashopincreaseditspricesby20% 204

M032533 Amachineuses2.4litersofgasoline 205

M032727 Threebrothersreceive45,000zeds 206

M032570 3/25ofthepeopleintheaudiencewerechildren 207

M032609 Theclosestto11squaredplus9squared 208

M032690 Whichequals370times998plus370times2 209

M012028 Arrangementsof4-digitwholenumbers 210

M022194 Approximatenumberofmagazinessold 211

M032652 Theteachersplantosend6newslettersperyear 212

M032671 Gardenwith14rowsof20plantseach 214

Item Index 2003

Documents

TIMSS Resource Kit