sc specimen mathematics 06

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2006 School Certificate Specimen Test

MATHEMATICSIntroductionThis document accompanies the specimen test for the 2006 School Certificate test inMathematics. A mapping grid is also included with the test. It shows how eachquestion in the test relates to the relevant syllabus outcomes and content, and to the

performance bands used to report student achievement in the test.

In 2006, the first cohort of students studying the Mathematics Years 710 Syllabus (2002) will sit for the School Certificate Mathematics test. The scope of the test andthe test specifications have been reviewed for 2006, and this specimen test isindicative of the type of test that will be produced for 2006 and subsequent years.Because much of the content of the new syllabus is similar to that in the previoussyllabuses, many of the questions in past School Certificate Mathematics tests wouldcontinue to be suitable for tests from 2006. The inclusion of questions from past testsin the specimen paper reflects this.

The purpose of the School Certificate testsThe School Certificate credential marks the end of compulsory schooling. It recordsstudent achievement in the courses studied in Stage 5, and provides results in fivestate-wide tests in areas considered foundational to subsequent achievement. Further information about the School Certificate can be found on the Boards AssessmentResource Centre ( http://www.arc.nsw.edu.au/ ).

A major purpose of the School Certificate tests at the end of Year 10 is to strengthenthe foundation skills students need to pursue further learning or to succeed in theworkplace.

The scope of the School Certificate testsThe tests focus on foundational aspects of their related syllabuses, and do not cover allareas of the syllabus. The Mathematics test scope statement provides further details of the relationship between the School Certificate Mathematics test and the Mathematicssyllabus.

Specimen tests

Specimen tests are produced in accordance with the Boards Principles for Setting School Certificate Tests and Developing Marking Guidelines in a Standards-

Referenced Framework , published in Board Bulletin Volume 10 Number 1 (March2001). Questions are closely related to a subset of syllabus outcomes from the relatedcourse. The test as a whole is structured to show how appropriate differentiation of student performance at all levels on the performance scale can be obtained.

The Mathematics specimen testThe specimen test is an example of the type of test that could be prepared within theSchool Certificate Mathematics test specifications . Tests in Mathematics will be basedon a representative sample of syllabus outcomes. The mapping grid accompanying thespecimen test shows how the test as a whole samples a range of content and
http://www.boardofstudies.nsw.edu.au/http://www.boardofstudies.nsw.edu.au/http://www.boardofstudies.nsw.edu.au/schoolcertificate/sc_pbd.htmlhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/sc_pbd.htmlhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.arc.nsw.edu.au/http://www.arc.nsw.edu.au/http://www.boardofstudies.nsw.edu.au/schoolcertificate/maths_scope_specs_06.htmlhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/maths_scope_specs_06.htmlhttp://www.boardofstudies.nsw.edu.au/bulletins/pdf_doc/bbv10_1.pdfhttp://www.boardofstudies.nsw.edu.au/bulletins/pdf_doc/bbv10_1.pdfhttp://www.boardofstudies.nsw.edu.au/bulletins/pdf_doc/bbv10_1.pdfhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/maths_scope_specs_06.htmlhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/maths_scope_specs_06.htmlhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/maths_scope_specs_06.htmlhttp://www.boardofstudies.nsw.edu.au/bulletins/pdf_doc/bbv10_1.pdfhttp://www.boardofstudies.nsw.edu.au/bulletins/pdf_doc/bbv10_1.pdfhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/maths_scope_specs_06.htmlhttp://www.arc.nsw.edu.au/http://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/schoolcertificate/sc_pbd.htmlhttp://www.boardofstudies.nsw.edu.au/http://www.boardofstudies.nsw.edu.au/


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outcomes, and allows all students the opportunity to demonstrate their level of achievement.

The range and balance of outcomes tested in the School Certificate tests in 2006 andsubsequent years may differ from those addressed in the specimen test.

There are a number of points to note in considering the Mathematics specimen test: The School Certificate Mathematics test will be based on the Working

Mathematically strand of the syllabus, as it relates to the content strands up toand including Stage 5.1. Note that some syllabus topics in the Stage 5.1content have not previously been within the scope of the School CertificateMathematics test. Trigonometry (MS5.1.2), Coordinate Geometry (PAS5.1.2),Rational Numbers (NS5.1.1) and Algebraic Techniques (PAS5.1.1) (includingindex laws and scientific notation) are topics in this category.

The simple interest formula, I = PRT , (Mathematics Years 710 syllabus

(2002), NS5.1.2 Consumer Arithmetic, page 70) has been added to theformulae sheet. Calculators are not to be used in Section 1 of the test. Number sense and

mental computation are fundamentals emphasised in Section 1, reflecting thesyllabus advice that students maintain and develop their mental arithmeticskills, rather than relying on their calculators for every calculation(Mathematics Years 710 syllabus (2002), page 5).

A short break will occur following the expiry of working time for Section 1.During this period responses to Section 1 will be collected, and preparationsmade for the commencement of Section 2. Calculators may be used in

Section 2. In Section 2 Part A, there are five questions in a multiple correct-incorrect

format. These questions have four alternatives, of which one, two, three, or allfour, may be correct. These questions assist students to see that manyquestions in mathematics may have several answers, and reward students for the ability to discern these possibilities. This format directs students toconsider and choose an appropriate response for each alternative.

The four questions in Section 2 Part B, worth 5 marks each, are made up of parts. The number of parts and their mark values may vary from year to year.
http://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/manuals/equipment_list.htmlhttp://www.boardofstudies.nsw.edu.au/manuals/equipment_list.htmlhttp://www.boardofstudies.nsw.edu.au/manuals/equipment_list.htmlhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdfhttp://www.boardofstudies.nsw.edu.au/syllabus_sc/pdf_doc/mathematics_710_syllabus.pdf


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General Instructions

Reading time: 5 minutes Working time: 2 hours There will be a short break

between Section 1 and Section 2 Write using black or blue pen You may use a pencil to draw

or complete diagrams Attempt ALL questions Calculators may be used in

Section 2 only A formulae sheet is provided

with this paper Write your Centre Number

and Student Number at thetop of pages 3 and 35

Total marks 100

Section 1Pages 310

25 marksTime allowed for this section is 30 minutes

Questions 125 25 marks

Section 2Pages 1242

75 marksTime allowed for this section is 1 hour and30 minutes

This section has TWO parts

Part A Questions 2680 55 marksPart B Questions 8184 20 marks

Mathematics2006 School Certificate Specimen Test


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2

Formulae

For use in both SECTION 1 and SECTION 2

Circumference of a circle diameter or r= 2 aadius

Area of a circle

C d C r= =

=

2

rradius squared

Area of a parallel

A r=

2

oogram base perpendicular height

Ar

=

= A bh

eea of a rhombus half the product of the di= aagonals

Area of a trapezium ha

A xy=

=

12

llf the perpendicular height the sum of the parallel sides

Volume of

A h a b= +( )

12

aa prism base area height

Volume of

=

= V Ah

a cylinder radius squared height=

=

V r h2

= Simple interest principal annual intere est rate number of years

Pythagor

= I PRT

aas theorem states: In a right-angled tria angle, the hypotenuse squared is equal tothe sum of the squares ofthe other two sides

c a b2 2 2= +

Board of Studies NSW 2006


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25 marksTime allowed for this section is 30 minutes

Answer Questions 125 in the spacesprovided

Calculators are NOT to be used in thisSection

There will be a short break betweenSection 1 and Section 2

Centre Number

Student Number

Section 1


Mathematics


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4

Answer the questions in the spaces provided.

1 What number is halfway between 3 and 7?

.............................................................................................................................................

.............................................................................................................................................

2 112

15

=

.............................................................................................................................................

.............................................................................................................................................

3 O is the centre of the circle. Use the words from the list to complete the sentences below.

The shaded area is called ...............................................................................................

This area is bounded by two radii and .......................................................................

4 1.8 0.03 =

.............................................................................................................................................

.............................................................................................................................................

an arc

a chord

a sector

O


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5 Sergio said If I toss 2 coins, I can get 2 heads, or 2 tails, or a head and a tail.

Therefore the probability that I get 2 heads is 13

.

Sergio is incorrect. Write a brief reason why he is incorrect.

.............................................................................................................................................

.............................................................................................................................................

6 In a survey, students are asked how many mobile phone calls they have madethat day. The results are shown in the cumulative frequency histogram andpolygon below.

Use the graph to find the median number of calls made.

.............................................................................................................................................

7 Which number in the box is:

The number is ..................................................................................................................

486 888

639

762 572

smaller than 870AND greater than 540AND evenAND divisible by 3?

60

40

50

30

20

10

0 1 2 30

Calls

C u m u

l a t i v e

f r e q u e n c y

5


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8 Tides alternate between low and high. The time between low tide and high tideat Browns Beach is 6 hours and 10 minutes. There is a low tide at 7:13 am.

When will the next low tide occur?

.............................................................................................................................................

.............................................................................................................................................

9 Calculate the sum

2 + 4 + 16 + 18 + 2 + 4 + 16 + 18 + 2 + 4 + 16 + 18

.............................................................................................................................................

.............................................................................................................................................

10 If 12 167 = 2004then 24 = 2004

The value of is ...........................................................................................................

11 Arrange these scores into a stem-and-leaf plot.

14, 17, 20, 22, 23, 23, 24, 33

12 In Question 11, the mean of the scores is 22. Change any one of the scores to makethe mean 23.

Old score New score

changes to

LeafStem

1

2

3

6


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13 This diagram shows a trapezium.

Calculate the perimeter of the trapezium.

.............................................................................................................................................

.............................................................................................................................................

14 Khadija thought of a number. She doubled the number, then subtracted five. Theresult was 63.

What was the number Khadija thought of?

.............................................................................................................................................

.............................................................................................................................................

15 Write a number in the box so that the expression

+ 3_________

8

has a value between 1 and 2.

16 A sequence is formed by adding the two previous numbers together. Fill in thetwo missing numbers in this sequence.

4, ................, ................, 22

17 Write 2 3 as a fraction.

.............................................................................................................................................

10 cm

4 cm

13 cm

NOT TOSCALE

7


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18 What is the greatest number of 60 cent chocolates I can buy with $10?

..............................................................................................................................................

..............................................................................................................................................

19 Adele sells cosmetics. She is paid by commission.

Briefly explain the meaning of commission.

..............................................................................................................................................

..............................................................................................................................................

20 By measuring appropriate lengths, calculate the area of this triangle in squarecentimetres. Show all your measurements on the diagram.

.......................................................................................................................................................

.......................................................................................................................................................

8


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21 Write the next line of this pattern.

1 2 3 4 + 1 = 52

2 3 4 5 + 1 = 112

3 4 5 6 + 1 = 192

4 5 6 7 + 1 = 292

.........................................................................................................

22

Triangle ABC has angles 2 m, 3m and 4 m as shown.

Use an equation, or a calculation, to show that m = 20.

.............................................................................................................................................

.............................................................................................................................................

23 Complete the next line in the pattern.

3 102 = 300

3 101 = 30

3 100 = 3

3 101 = 0.3

3 =

NOT TOSCALE

C

A B2m

4m

3m

9


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24 $500 is invested for 2 years at 10% per annum, compounded annually.

Calculate the total interest earned.

.............................................................................................................................................

.............................................................................................................................................

25 More than one triangle can be constructed with sides 6 cm and 8 cm and an angleof 40. XYZ is one example.

Construct a triangle that is NOT congruent to XYZ, and that has sides 6 cm and8 cm and an angle of 40.

End of Section 1

X Z

Y

6 cm

8 cm

40

10



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Section 2

75 marksTime allowed for this section is 1 hourand 30 minutes

This section has TWO parts

Part A Questions 2680 55 marksPart B Questions 8184 20 marks

Calculators may be used in this section

Do not commence Section 2 until you areinstructed to do so


Mathematics


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12

Part A


Use the Section 2 Part A Answer Sheet for Questions 2680.

Instructions for answering multiple-choice questions

For Questions 2675, select the alternative A, B, C or D that best answers thequestion. Fill in the response oval completely.

Sample: 2 + 4 = (A) 2 (B) 6 (C) 8 (D) 9

A B C D

If you think you have made a mistake, put a cross through the incorrectanswer and fill in the new answer.

A B C D

If you change your mind and have crossed out what you consider to be thecorrect answer, then indicate the correct answer by writing the word correctand drawing an arrow as follows.

correct

A B C D


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13

26 Simplify 2 2 23.

(A) 25 (B) 26 (C) 45 (D) 46

27 In scientific notation, 0.0043 is written as

(A) 4.3 102 (B) 4.3 103 (C) 4.3 102 (D) 4.3 103

In which of the solids is the cross-section a triangle?

(A) I only (B) II only

(C) Both I and II (D) Neither I nor II

29 Abdul wrote the following lines of working to solve the following equation:

5x + 7 = 16

Line 1 5x = 16 7

Line 2 5x = 9

Line 3 x = 95

Line 4 x = 1 49

In which line did he make an error?

(A) Line 1 (B) Line 2 (C) Line 3 (D) Line 4

I II

28


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14

30 Maureen was born on 26 November 1990. What was her age on 26 August 2004?

(A) 13 years 8 months (B) 13 years 9 months

(C) 14 years 8 months (D) 14 years 9 months

31 Michelle drew a circle inside a rectangle. She drew a diameter of the circle andextended it. When she extended the diameter, it was a diagonal of the rectangle.

Which of the following could be Michelles drawing?

32 Which of the following scales would be the most appropriate to make a scaledrawing of a police car on a piece of paper the same size as this page?

(A) 1 : 25 (B) 1 : 100 (C) 1 : 250 (D) 1 : 1000

33 The possible three-child families are

BBB, BBG, BGB, BGG, GBB, GBG, GGB, GGG

where B = boy, G = girl.

What is the probability that in a three-child family there will be AT LEAST ONEgirl?

(A) 38 (B) 48 (C) 68 (D) 78

34 Expand and simplify 3( t 1) t + 1

(A) 2t + 4 (B) 2t 4 (C) 2t 2 (D) 2t

(A) (B) (C) (D)


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15

35 For this triangle, what is the value of sin ?

(A) 513

(B) 125

(C) 1213

(D) 1312

36 Which of the following could represent the probability of an event that is LIKELYto occur?

(A) 19

(B) 25

(C) 12

(D) 45

37 Peta sells cars. She earns $270 per week plus 5% commission on her total weeklysales over $40 000.

What is the value of her sales in a week when she earns $860?

(A) $11 800

(B) $17 200

(C) $51 800

(D) $57 200

NOT TOSCALE

5

1213


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16

38 Alice is going to use this pattern to pave her courtyard.

She is going to pave an area of 12 m 2. How many 20 cm 10 cm pavers will sheneed?

(A) 75 (B) 150 (C) 240 (D) 600

39 Darren has $ x in his bank account, and he saves $ y every week. How much will be in his account after n weeks?

(A) x + yn (B) xn + yn (C) xn + y (D) x + y + n

40 Helenas home repayments increased from $962.22 to $984.24 per fortnight.

How much extra will Helena repay each year?

(A) $264.24 (B) $528.48 (C) $572.52 (D) $1145.04

41 Using a protractor, find the size of x.

(A) 70 (B) 110 (C) 250 (D) 290

x

20 cm

10 cm

NOT TOSCALE


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17

42 The diagram shows the price of oranges in four shops.

In which shop are oranges cheapest per kilogram?

(A) Shop 1 (B) Shop 2 (C) Shop 3 (D) Shop 4

(A) 6a3

(B) 6a4

(C) 6a5

(D) 6a6

44 Gertrude normally works four-hour shifts. She is paid $8.50 per hour normaltime, and $12.50 per hour for any time she works over four hours.

Gertrude works a shift from 9:15 am to 2:15 pm. What is her total pay?

(A) $42.50 (B) $46.50 (C) $62.50 (D) $71.50

3a 2 4a 3

2a43 Simplify

Shop 1 Shop 2 Shop 3 Shop 4


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18

45 EFGH is a parallelogram. MH is perpendicular to EF.

Which of the following lengths are sufficient information to find the area of EFGH ?

(A) The lengths of HG and EH only

(B) The lengths of HG and MH only

(C) The lengths of the diagonals EG and HF only

(D) The lengths of EH and MH only

46 What is the area of this shape?

(A) 417 cm 2 (B) 459 cm2 (C) 507 cm2 (D) 639 cm 2

47 Using trigonometry, calculate the size of the smallest angle in this triangle,correct to the nearest degree.

(A) 31 (B) 37 (C) 41 (D) 49

NOT TOSCALE

35

4

22 cm

25 cm

15 cm

13 cm

NOT TO

SCALE

H

E M F

G


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19

48 The diagram shows part of a number line. Which point is closest to 3.15?

(A) P (B) Q (C) R (D) S

49 When he climbed a 60 m tree, Ross climbed 140 rungs on his ladder. He plans toclimb a 75 m tree.

How many rungs will be on the ladder?

(A) 155 (B) 175 (C) 200 (D) 215

50 The diagram is the net of a rectangular prism, drawn to a scale 1: 2.

What is the volume of the prism?

(A) 27 cm3 (B) 54 cm3 (C) 108 cm3 (D) 432 cm 3

SCALE 1 : 2

2.7

P Q R S

3.7


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20

51 Barbara wrote each letter of her name on separate cards.

She placed the cards face down on a table. She is going to turn over two cards atthe same time.

In how many ways can she turn over two cards that have the same letter onthem?

(A) 3 (B) 4 (C) 5 (D) 10

What is the perimeter of this rectangle?

(A) 3x + 10 (B) 4x + 20(C) 5x + 10 (D) 6x + 20

53 The balances show relationships between the masses of three types of object.

Which of the following shows the three objects arranged from heaviestto lightest?

(A) , , (B) , ,

(C) , , (D) , ,

2x

x + 1052


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22

What are the values of x and y?

(A) x = 40, y = 70 (B) x = 55, y = 55

(C) x = 50, y = 60 (D) x = 70, y = 40

57 A discount voucher offered 25% discount, up to a maximum discount of $15.Daniel bought goods to the value of $80, and Naomi bought goods to the value

of $40. They each had a discount voucher.How much more money did Daniel pay than Naomi?

(A) $5 (B) $10 (C) $30 (D) $35

The shaded design is made from four of the small triangles.

What is the perimeter of the design?

(A) 4c + 4b + 4a (B) 4c + 4b 4a

(C) 4a 4b + 4c (D) 4a2 + 4b2 + 4c2

a

bc

58

110

x

y

56


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23

59 In the diagram, lengths BC, CD and BD are equal and BEA is a right angle.

What is the size of x?

(A) 30 (B) 35 (C) 45 (D) 60

60 David earns $7.67 an hour for an 8 hour shift. John earns $6.97 an hour andreceives a $5.60 meal allowance for an 8 hour shift.

Which of the following statements about their earnings for an 8 hour shiftis correct ?

(A) They receive the same amount.

(B) David receives $5.60 more than John.

(C) John receives $4.90 more than David.

(D) John receives $11.20 more than David.

C

D

B

A Ex

NOT TOSCALE


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63 Michael won $240. He donated one third of his winnings to charity. He divided

the remainder between his savings account and his investment account in the

ratio 3 : 5.

How much did he deposit in his savings account?(A) $30 (B) $60 (C) $90 (D) $100

64 The time in Maitland is 12

hour ahead of the time in Broken Hill. The time in

Albany is 1 12

hours behind the time in Broken Hill.

When the time in Maitland is 13:30, what is the time in Albany?

(A) 11:30 (B) 12:30 (C) 14:30 (D) 15:30

65 The annual membership fee at Jerrys golf club is $345, and it costs $15 to playeach game. Jerrys golf budget for 2006 is $900.

How many games of golf will Jerry be able to play at his club in 2006?

(A) 23 (B) 37 (C) 60 (D) 83

Which statement is true?

(A) = (B) =

(C) = (D) , and are all equal

In PQR , sides PQ and RQare equal, and side PR isshorter than side PQ .

P

QR

NOT TOSCALE

66


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26

What is the modal class for this set of data?

(A) 46 (B) 79 (C) 1012 (D) 1315

68 Kevin and Jim are playing a game using a spinner. A player wins when the

spinner stops on his colour. Kevin always chooses white, and Jim alwayschooses green.

Which spinner should Kevin choose so that he has the greatest chance of beating Jim?

White

Blue White

Green

(A) (B)

(C) (D)

White

White

Blue

White

Green

Green

Green White

Blue

White

Red

Blue

White

Green

Class interval Cumulative frequency

134679

10121315

412182326

67


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27

69 Madi covered the front page of this examination paper with $2 coins. She placedas many coins on the page as possible without overlapping.

What is the approximate value of the coins?

(A) $140$218 (B) $220$276

(C) $278$330 (D) $332$380

70 Ervino took his family for dinner. The cost of each meal was: Ervino, $24;Chris, $18; Rebecca, $20; and Ben, $22. Ervino paid the total bill, using two ofthese discount vouchers.

What is the lowest total amount he could be required to pay?

(A) $61 (B) $62 (C) $64 (D) $65

71 Aisha is looking at a map of caves.

Jimbo cave is 90 m below ground level.Lateral cave is 50 m higher than Cathedral cave. Jimbo cave is 20 m lower than Lateral cave.

How far below ground level is Cathedral cave?

(A) 60 m (B) 120 m (C) 140 m (D) 160 m

Buy any main meal and receive a second main meal

for price (up to equal value)

1 2 Price Main Meal

1 2

1 2

ACTUAL SIZE


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28

72 What is the area of rectangle ABCD?

(A) 24 cm2

(B) 48 cm2

(C) 50 cm2

(D) 60 cm2

73 In a group of 19 boys, all play either tennis or rugby, and some play both. 14 boysplay tennis and 8 play rugby.

One of the boys is selected at random. What is the probability that he playstennis but not rugby?

(A) 519

(B) 619

(C) 1119

(D) 1419

74 The formula for the perimeter of a rectangle is

P = 2 + 2b.

What is the value of b when = 5 and P = 40?

(A) 15 (B) 25 (C) 30 (D) 35

A E B

D C10 cm

8 cm6 cm


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Section 2 (continued)

Instructions for answering Questions 7680

Questions 7680 contain options a, b, c and d. Each option may be Correct orIncorrect. In each question, one, two, three or four options may be Correct.

For Questions 7680, fill in the response ovals on the Section 2 Part AAnswer Sheet to indicate whether options a, b, c and d are Correct orIncorrect. You must fill in either the Correct or the Incorrect response oval foreach option.

Correct IncorrectSample: a. 2 + 4 = 4 + 2 a.

b. 2 4 = 4 2 b.c. 2 4 = 4 2 c.d. 2 4 = 4 2 d.

If you think you have made a mistake, put a cross through your answer andfill in your new answer.

Correct Incorrect

a.

If you change your mind and have crossed out what you consider to be theright answer, then indicate your intended answer by writing the wordanswer and drawing an arrow as follows.

answer

Correc t In correc t

a.

30


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76 The number of goals scored by Jims soccer team in eight matches is:

2, 2, 2, 3, 3, 4, 4, 5.

In its ninth game the team scored six goals.

Indicate whether each of the following is Correct or Incorrect.

a. The mean increased.

b. The mode increased.

c. The median increased.

d. The range increased.

77 Fatima is making a pattern of rectangles, using matches.


a. The number of matches Fatima needs is three times the number ofrectangles plus one.

b. The number of matches Fatima needs is four more than three times thenumber of rectangles.

c. The number of matches Fatima needs is four times the number ofrectangles minus one.

d. The number of matches Fatima needs is twice the number of rectanglesplus one more than the number of rectangles.

78 The minute hand of a clock is between 3 and 4 and the hour hand is between7 and 8.


a. The time on a digital watch could be 3:39.

b. The time on a digital watch could be 7:18.

c. The time on a digital watch could be 8:17.

d. The time on a digital watch could be 19:16.

31


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79 A bag contains red, black and yellow marbles. There are more red than blackmarbles, and there are more black than yellow marbles.

There are 3 yellow marbles and 10 red marbles. Chris draws a marble at random.


a. The probability of drawing a yellow marble could be .

b. The probability of drawing a black marble could be .

c. The probability of drawing a red marble could be .

d. The probability of drawing a red marble could be .

80 The perimeter of a rectangle is 24 cm.


a. The area of the rectangle could be 11 cm 2.

b. The area of the rectangle could be 27 cm 2.

c. The area of the rectangle could be 35 cm 2.

d. The area of the rectangle could be 40 cm 2.

1023

1022

721

317

32


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36/47 Board of Studies NSW 2006

BLANK PAGE

34


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Mathematics

Section 2 (continued)

Part B


Answer the questions in the spaces provided.

Question 81 (5 marks)

Please turn over

Print run

35

Centre Number

Student Number


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(a) Ted needs to choose a spinner for a game.

Ted makes the statement:Spinner A and Spinner B are equally likely to stop on an odd number.

Explain briefly why Teds statement is incorrect.

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(b) Ted decides to conduct a trial to test his statement.

He spins each spinner 10 times and records his results in the table, asshown.

Why would Teds trial NOT be an appropriate test of his statement?

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Question 81 continues on page 37

Spinner A Spinner B

Odd 6 5

Even 4 5

Total 10 10

1

2

38

9 5

7

Spinner B

5

76

8 2

1

Spinner A

1

Marks

36


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Marks

37

Question 81 (continued)

(c) Julie chooses a different spinner. It has 5 sectors of equal size numbered1, 2, 3, 4 and 5, as shown.

Julies teacher asked her to spin the arrow 100 times and record thenumber of times the arrow stopped on an odd number and the numberof times it stopped on an even number.

Julies results are shown in the table.

Why do you think Julies teacher said: I am surprised by these results.?

What results would you expect? Give mathematical reasons to justifyyour answer.

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End of Question 81

Odd 22

Even 78

Total 100

1

2

3

4

5

3


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The diagram shows a number plane. The line y = 2x + 8 crosses the x axis atC (4,0) and intersects line l at A (2,12).

(a) What is the equation of line l?

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(b) What is the y intercept of the line y = 2x + 8?

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(c) Show that the point (3,14) also lies on the line y = 2x + 8.

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1

1

1

Ol

x

y

A (2,12)

y = 2x + 8

C (4,0)

NOT TOSCALE

Marks

39


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(d) On the diagram, a circle is to be drawn with diameter AC.

(i) What are the coordinates of the centre of this circle?......................................................................................................................

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(ii) Calculate the radius of this circle.

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End of Question 83

1

1

Marks

40


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A square and a right-angled triangle are joined to form a pentagon, as shown.

(a) Calculate the area of this pentagon. Show all working.

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2

10 cm

14.8 cm

6 cm

NOT TOSCALE

8 cm

Marks

41


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(b) Another pentagon is formed from a square and a right-angled triangle.Measurements on this pentagon are given using pronumerals a, b, x

and y, as shown.

(i) Explain why an expression for the area of this pentagon is

12

ab + a2 + b2.

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(ii) Write an expression for the area of this pentagon in terms of x and y.

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End of test

1

2

x

y

b

aNOT TOSCALE

Marks

42



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Question Marks Strand TopicContent

Outcomes

WorkingMathematically

Outcomes

TargetedPerformance

BandsSection 2 Part A

26 1 Number Rational Numbers NS5.1.1 5.1.2 3427 1 Number Rational Numbers NS5.1.1 5.1.3 23

28 1 Space andGeometry

Properties of Solids SGS4.1 4.4 23

29 1 Patterns andAlgebra

Algebraic Techniques PAS4.4 5.1.4 23

30 1 Measurement Time MS4.3 4.3 3431 1 Space and

GeometryProperties of TwoDimensional Figures

SGS4.3 4.3 23

32 1 Number Fractions, Decimals andPercentages

NS4.3 4.2 45

33 1 Number Probability NS5.1.3 5.1.2 2334 1 Patterns and

AlgebraAlgebraic Techniques PAS4.4 4.2 34

35 1 Measurement Trigonometry MS5.1.2 5.1.3 2336 1 Number Probability NS4.4 4.3 2337 1 Number Consumer Arithmetic NS5.1.2 5.1.2 4538 1 Measurement Perimeter and Area MS4.1 5.1.2 4539 1 Patterns and

AlgebraAlgebraic Techniques PAS4.3 5.1.2 23

40 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3441 1 Space and

GeometryAngles SGS4.2 4.2 23

42 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3443 1 Patterns and

Algebra

Algebraic Techniques PAS5.1.1 5.1.2 34

44 1 Number Consumer Arithmetic NS5.1.2 5.1.2 2345 1 Measurement Perimeter and Area MS4.1 5.1.2 3446 1 Measurement Perimeter and Area MS5.1.1 4.2 2347 1 Measurement Trigonometry MS5.1.2 5.1.4 3448 1 Number Fractions, Decimals and

Percentages NS4.3 5.1.2 34

49 1 Number Fractions, Decimals andPercentages

NS4.3 5.1.2 23

50 1 Measurement Surface Area and Volume MS4.2 5.1.2 4551 1 Number Probability NS5.1.3 5.1.2 34

52 1 Patterns andAlgebra Algebraic Techniques PAS4.3 4.2 34


Algebraic Techniques PAS4.4 5.1.4 23

54 1 Measurement Surface Area and Volume MS4.2 5.1.2 3455 1 Data Data Representation DS4.1 5.1.3 2356 1 Space and

GeometryProperties of GeometricalFigures

SGS4.3 4.2 34

57 1 Number Consumer Arithmetic NS5.1.2 5.1.2 4558 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3459 1 Space and


SGS4.3 4.2 34

60 1 Number Consumer Arithmetic NS5.1.2 5.1.2 3461 1 Patterns and

AlgebraCoordinate Geometry PAS5.1.2 5.1.2 23


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Question Marks Strand TopicContent

Outcomes

WorkingMathematically

Outcomes

TargetedPerformance

Bands62 1 Data Data Analysis and

EvaluationDS4.2 5.1.2 45

63 1 Number Fractions, Decimals and

Percentages

NS4.3 5.1.2 34

64 1 Measurement Time MS4.3 5.1.2 2365 1 Number Consumer Arithmetic NS5.1.2 5.1.2 2366 1 Space and


SGS4.3 5.1.2 34

67 1 Data Data Represention andAnalysis

DS5.1.1 5.1.3 23

68 1 Number Probability NS5.1.3 5.1.2 4569 1 Measurement Perimeter and Area MS4.1 5.1.2 4570 1 Measurement Perimeter and Area MS5.1.1 5.1.2 4571 1 Number Integers NS4.2 5.1.2 3472 1 Measurement Perimeter and Area MS4.1 5.1.2 4573 1 Number Probability NS5.1.3 5.1.2 4574 1 Patterns and

AlgebraAlgebraic Techniques PAS4.4 5.1.2 23

75 1 Number Probability NS5.1.3 5.1.2 3476 1 Data Data Analysis and

EvaluationDS4.2 5.1.2, 5.1.4 435


Number Patterns PAS4.2 5.1.2, 5.1.4 35

78 1 Measurement Time MS3.5 5.1.2, 5.1. 2479 1 Number Probability NS5.1.3 5.1.2, 5.1.4 4680 1 Measurement Perimeter and Area MS4.1 5.1.2, 5.1.4 56

Section 2 Part B81(a) 1 Number Probability NS5.1.3 5.1.2, 5.1.3,

5.1.423

81(b) 1 Number Probability NS5.1.3 5.1.2, 5.1.3,5.1.4

24

81(c) 3 Number Probability NS5.1.3 5.1.2, 5.1.3,5.1.4

25

82(a) 2 Measurement Trigonometry MS5.1.2 5.1.2, 5.1.4 3582(b) 1 Measurement Trigonometry MS5.1.2 5.1.2, 5.1.4 2382(c) 2 Measurement Trigonometry MS5.1.2 5.1.2, 5.1.4 4683(a) 1 Patterns and

Algebra

Coordinate Geometry PAS5.1.2 5.1.2 45

83(b) 1 Patterns andAlgebra


83(c) 1 Patterns andAlgebra


83(d)(i) 1 Patterns andAlgebra

Coordinate Geometry PAS5.1.2 5.1.2, 5.1.4 56

83(d)(ii) 1 Patterns andAlgebra

Coordinate Geometry PAS5.1.2 5.1.2, 5.1.4 56

84(a) 2 Measurement Perimeter and Area MS5.1.1 5.1.2, 5.1.4 2484(b)(i) 2 Measurement Perimeter and Area MS5 1 1 5 1 2 5 1 4 46

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sc specimen mathematics 06