Modul JUJ Tahun 2010

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Projek Jawab Untuk Jaya 2010

MATHEMATICS SPM This module aims to prepare the Form five students for the SPM examination and also for the Form four students to reinforce as well as to enable them to master the selected topics. It also serves as a guidance for effective acquisition of the various mathematical skills.

At the end of each topic, sample answers are given. Discussions on common mistakes that result in the students’ failure to obtain full mark are included as well. This module suggests specific strategies for each chosen topic and strategies which can help the students in problem solving. It is hoped that this module can benefit all the Pahang students as well as helping them towards achieving excellent results in SPM Mathematics.

TABLE OF CONTENTS

1.1 Authentic Examination Format 1.2 Topical Analysis of SPM Paper 1 1.3 Topical Analysis of SPM Paper 2 1.4 Selected topical

(BONUS) 1full set of Paper 1 and Paper 2 questions

http://edu.joshuatly.com/ http://exammy.com/

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FORMAT OF ASSESSMENT INSTRUMENT MATHEMATICS 1449

NO TOPIC PAPER 1 (1449/1) PAPER 2 (1449/2) 1 Instrument type Objective questions Subjective questions

2 Item type Multiple Choice

Questions Open ended structure and limited response

3 Number of Questions

40 questions ( answer all)

Section A 11 questions (answer all) Section B 5 questions (choose 4)

4 Total Marks 40 Section A Total marks : 52 Section B Total marks : 48 (Each question 12 marks) Overall Total :100

5 Test Duration 1 hour 15 minutes 2 hours 30 minutes

6 Constructs Weights Knowledge - 45% Skills - 55%

Knowledge - 25% Skills - 70% Values - 5%

7 Context Scope Lower secondary school scope with continuation in the upper secondary.

All aspects of learning from Form 4 and Form 5.

Lower secondary school scope with continuation in the upper secondary.

All aspects of learning from Form 4 and Form 5.

8 Difficulty level Low - L Medium - M High - H

L : M : H = 5 : 3 : 2

L : M : H = 5 : 3 : 2

9 Additional Tools a. Scientific Calculator b. Four-figure Mathematical table b. Geometry Set

a. Scientific Calculator b. Four-figure Mathematical table b. Geometry Set


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2.LIST OF MATHEMATICS TOPICS 1449

No. FORM 1 – 3 FORM 4 FORM 5 1 Circles I and II Standard Form Number Bases

2 Polygons I and II Quadratic Expressions and Equations Graphs of Functions II

3 Solids and Volumes Sets Transformations III

4 Transformations I and II Mathematical Reasoning Matrices

5 Trigonometry I The Straight Line Variations

6 Algebraic Expressions I and II Statistics III Gradient and Area under

a Graph 7 Algebraic fractions Probability I Probability II 8 Algebraic Formulae Circles III Bearing

9 Linear Equations(1 and 2 unknowns) Trigonometry II Earth as a Sphere

10 Indices Angles of Elevation and Depression Plans and Elevations

11 Linear Inequalities Lines and Planes in 3 Dimensions

12 Statistics I and II

13 Arc Length & Area of Sector


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TOPICAL ANALYSIS OF SPM MATHEMATICS PAPER 1

Bil TOPIC FORM 2004 2005 2006 2007 2008 2009

1 Standard Form 4 1,2,3,4 1,2,3 1,2,3,4 1,2,3 1,2,3,4 1,2,3,4

2 Number Bases 5 5,6 4,5 5,6 4,5 5,6 5,6

3 Polygon II 3 7 6,7 7 6,7 7 7,8

4 Circles III 4 8 8 8 8 8 9

5 Transformation I 3 9,10. 9,10 9,10 9,10 9,10 10,11

6 Trigonometry I 3 13 - 11 - 12

7 Trigonometry II 4 11,12 11,12,13 12,13 11,12,13 11,12, 13 13

8 Lines and Planes in 3 Demension 4 14 14 14 14 14 14

9 Angles of Elevation and Depression

4 15,16 15 15,16 15 15 15,16

10 Bearing 5 18 16 17 16 16,17 17

11 Earth as a Sphere 5 17 17,18 18 17,18 18 18

12 Algebraic Expression II 2 20 19 19.20 19 19 19

13 Algebraic Expression III 3 19 20 - 21 20 20

14 Algebraic Formulae 3 21 21 21 20 21 21

15 Linear Equation I 2 22 22 22 22 22 22

16 Indices 3 23,24 23,24 23 23,24 23,24 23,24

17 Linear Inequalities 3 25,26 25 24 25 25,26

18 Statistic I 2 27 27 26,27 26 25 27

19 Statistic II 3 28 25 27 26,27 28

20 Statistic III 4 - 26 - - 29 21 Graph of Function II 5 29 28 28 28 30

22 Sets 4 30,31,32 29,30,31 29,30,31 29,30,31 29,30,31 30,31

23 The Straight Line 4 33,34 32,33 32,33 32,33 32,33 33,34

24 Probability I 4 35,36,37 34,35 34,35 34,35 34,35 35,36

25 Variations 5 38,39 36,37,38 36,37,38 36,37,38 36,37,38 37,38

26 Matrices 5 40 39,40 39,40 39,40 39,40 39,40


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TOPICAL ANALYSIS OF SPM MATHEMATICS PAPER 2 No. Form Topic 04 05 06 07 08 09 Part A (Question 1 to Question 11) 1. 1-3 Simultaneous Linear Equations 1 1 1 1 1 1(Q3) 2 4 Quadratic Equation 1 1 1 1 1 1(Q2) 3

4 Sets (Shade Venn diagrams) 1 - 1 - 1 5 Region for Inequalities - 1 - 1(Q1)

4. 4 Mathematical Reasoning (Statement, implications, argument, mathematical induction, converse )

1 1 1 1 1 1Q(5)

5. 4 The Straight Line ( parallel, equation,y-intercept)

1 1 1 1 1 1(Q6)

6. 5 Probability II 1 1 1 1 1 1(Q9) 7. 1-3 Arc Length & Area of Sector 1 1 1 1 1 1(Q10) 8. 1-3 Volume of Solids a. Pyramids and half cylinders - - 1 b. Cones and Cylinders 1 1 - c. Cones and cuboids d. Pyramid and prism 1 1 e. Cones and hemisphere 1(Q8) 9. 5 Matrices ( Inverse, matrix equation ) 1 1 1 1 1 1(Q7) 10. 5 Gradient and Area Under a Graph a. Speed-Time Graph - 1 1 1 1 1(Q11) b. Distance-Time graph 1 - - 1 11. 4 Lines & Planes in 3 Dimensions (angle

between 2 planes) 1 1 1 1 1 1(Q4)

Part B (Question 12 to 16 - Choose any four) 12. 5 Graphs of Functions II a. Quadratic - 1 1 b. Cubic - - - 1 1(Q12) c. Reciprocal 1 - - 1 13. 5 Transformations III ( combined ) 1 1 1 1 1 1(Q13) 14. 5 Earth as a Sphere 1 1 1 1 1 1(Q16) 15. 5 Plans and elevations a. Prism and cuboids 1 1(Q15) b. Cuboids and half cylinder, prism - 1 - 1 c. Prism and prism - - 1 1 16. 4 Statistics III a. Raw data, frequency table, mean,

frequency polygon, modal class 1

1

1

1 1 1(Q14a)

b. Ogive 1 - - 1 c. Histogram - 1 1 1(Q14b) d. Frequency Polygon - - - 1 e. Communication 1 1 - 1 1(Q14c) Total Questions 16 16 16 16 16


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Question Allocation (Mathematics SPM 2007)

Form Number of questions Paper 1 % Paper 2 Marks % Total %

1-3 13 32.5 3 14 12.50 28.57 4 16 40.0 6 33 29.46 39.28 5 11 27.5 7 65 58.04 32.14 Total 40 100.00 16 112 100.00 100.00

Question Allocation (Mathematics SPM 2008)


1-3 12 30.00 3 14 12.50 18.75 4 19 47.50 6 33 29.46 40.98 5 09 22.50 7 65 58.04 40.27 Total 40 100.00 16 112 100.00 100.00

Question Allocation (Mathematics SPM 2009 )


1-3 15 37.50 3 14 12.50 18.75 4 16 40.00 6 33 29.46 40.98 5 09 22.50 7 65 58.04 40.27 Total 40 100.00 16 112 100.00 100.00


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TOPICAL EXERCISE

1. SETS

PAPER 1 Given set F = {2, 3, 4} set G = {2,4,5,6} and set H = {4,6}.Which of the following is true? Diberi set F = {2, 3, 4} set G = {2,4,5,6} dan H = {4,6}.Yang manakah benar? A H G C H F B G F D F G 2 In the figure above, is an universal set. Set B’ is Rajah di atas, ialah set semester. Set B’ ialah A {2, 4, 7} C {3, 9, 10} B {5, 6, 8} D {3, 5, 6, 8, 9, 10} 3 In the diagram above, is an universal set. n ( P Q ) = A 2 C 7 B 4 D 8 4 Given S = { factors of 12} and T = {prime numbers that is less than 10}

the elements of set S T are A {1} C { 3, 4, 6 } B {2, 3 } D {2, 3, 4, 5, 6, 12}

.8

A B

.2

.7 .4

.5 .6

.9 .10

.3

P Q

.a .f

.k .b

.j .c .h

.r


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5 It is given that A = {a, b, c}, the number of subsets of A is A 4 C 7 B 6 D 8 6 Given that = {x:x is an integer, 12 x 40}, A = { multiples of 8 } and

B = {integers that contain digit 4}, A B = A {24, 34, 40} C {24, 40} B {14, 24, 40} D {14, 40} 7 Given that = P Q R, P Q , Q R = and R P. The Venn diagram that represents

these relationship is A B C D 8

In the above diagram, n (P Q) = n (R). The value of x is

A 2 C 4 B 3 D 5

Q P R

Q

R P

Q P R

Q

P R

P Q R

5 x + 7 3 2x

4


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9 Diagram below is a Venn diagram showing the number of students in sets P, Q, and R. It is given that set P = {English Society members}, set Q = {Science Society members}, set R = {Mathematics Society members} and the universal set, = P Q R

If the number of students who joined both the Science Society and the Mathematics Society is 11, find the number of students who joined only two societies. A 12 C 16 B 14 D 22

10 Given = P Q R. .Which of the following Venn diagrams represents ( PQ’) R’ ?

A C B D

R Q

5 x

6

4

3

2x

7

P Q

R

P Q

R

P Q

R

P Q

R


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SET PAPER 2 1 The Venn diagram below shows sets R, S and T.Given the universal set = R S T. On

each of the diagrams, shade the region which represents Gambarajah Venn di bawah menunjukkan set R, S dan T. Diberi set semesta = R S

T.Lorek pada setiap gambar rajah, kawasan yang mewakili (a) R ’ S ’ (b) ( R S ) T

2 The Venn diagram below shows sets P, Q and R.Given the universal set = P Q R.

On the diagrams, Gambar rajah Venn di bawah menunjukkan set P, Q dan R. . Diberi set semesta = P Q

R..Di atas rajah, (a) shade set P Q ’ (b) shade set PQ R’ Lorek set P Q ’ lorek set PQ R’

R

S T

R S

T

P Q R P Q R


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3 The Venn diagram in the answer space show sets A, B, and C such that the universal set, = A B C. On the Venn diagram in the answer space, shade

Gambar rajah Venn pada ruang jawapan menunjukkan sets A,B,dan Cdi mana set semesta = A B C.Di atas gambar rajah Venn di ruang jawapan, lorek

(a) A B (b) A’ (B C) Answer:

(a) (b)

4 Given that the universal set, = {x : 20 x 30, x is an integer}, P = { x: x is a multiple

of 4}, Q = { x: x is a number such that the sum of its digits is less than 7} and R = {x: x > 27}. Diberi set semesta = {x : 20 x 30, x ialah integer}, P = { x: x ialah gandaan 4},Q = { x: x jumlah antara digit-digit kurang dari 7} dan R = {x: x > 27}.

(a) List all the elements of the sets P and Q. Senaraikan semua unsur bagi set P dan Q. (b) Find /Cari the set P Q ’. (c) Find/Cari n (P Q’) Answer: (a) ……………….……….… (b) .……………………….… ( c) ………………..…………

A B

C

A B

C


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The Venn diagram shows the universal set , set P, set Q and set R. List all the elements for the following sets. Gambar rajah Venn menunjukkan set semesta , set P, set Q dan set R.Senaraikan semua unsur bagi set yang berikut.

(a) ( P R)’ (b) Q R P Answer: (a) ……………………………………………………………………………. (b) …………………………………………………………………………….

6 The Venn diagram shows the universal set , set P, set Q and set R. Gambar rajah Venn menunjukkan set semesta set , set P, set Q and set R. (a) Simplify/Ringkaskan the set PR. (b) State the set which represents the shaded region. Nyatakan set yang mewakili kawasan yang berlorek

Answer: (a) ………………………………………..

(b) ……………………………………….

P Q R .2 .3 .7 .1

.6

.4

.5

P Q R


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7 In the following Venn diagrams, = J K L .State the set which is represented by the shaded region.

Dalam rajah berikut,gambar rajah Venn, = J K L. Nyatakan set yang mewakili kawasan yang berlorek

(a) (b)

Answer:

(a) ……………………………... (b) ……………………………... 8. Given that set E = {5, 6} , set F = {3, 4, 5, 6, 8, 9} , set G = {1, 2, 3, 6, 8} and = E F G . Diberi set E = {5, 6} , set F = {3, 4, 5, 6, 8, 9} , set G = {1, 2, 3, 6, 8} dan = E F G .

(a) Draw a Venn diagram to show the relations between set E , F, and G . Lukis gambar rajah Venn menunjukkan hubungan antara set E , F, and G

(b) List the elements of set F G. Senaraikan unsur-unsur bagi set F G. (c) Find/Cari n (E F’). Answer:

(a)

(b) …………………………

(c) …………………………

J

L K

J K

L


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9. Given ={ x: 20 x 35, x is an integer, set P ={x:x is a multiple of 5}, set Q ={x: x is an even number}

Diberi ={ x: 20 x 35, x ialah integer, set P ={x:x ialah gandaan 5}, set Q ={x: x ialah nombor genap}

(a) List all the elements of set P and Q. Senaraikan semua element bagi set P and Q. (b) Find/Cari

(i) n(P Q) (ii) n(P Q)’

Answer:

(a) …………………………….. (b)(i) …………………………….. (ii) …………………………..…

10 The Venn diagram below shows the universal set , set X, set Y, set Z. In the diagram, shade the region which represents the set.

Gambarajah Venn di bawah menunjukkan set semesta set , set X, set Y, set Z. Dalam rajah lorek kawasan set yang diberi.

(a) X Z (b) (Y Z X)’

X Y

Z X Y

Z


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2. PROBABILITY PAPER 1 1 A box contains 8 black balls, 6 yellow balls and some blue balls.A ball is chosen at random

from the box. The probability of choosing a yellow ball is 31 . The probability of choosing

the blue ball is Sebuah kotak mengandungi 8 biji bola hitam dan beberapa biji bola biru.Sebiji bola dipilih

secara rawak daripada kotak itu.Kebarangkalian untuk mendapatkan bola kuning ialah

31 .Kebarangkalian untuk mendapatkan bola biru ialah

A 91 C

32

B 92 D

94

2 There are 45 packets of mango juice and orange juice in a refrigerator. A packet of drink is

chosen at random from the refrigerator. The probability that a packet of orange juice is

chosen is 52 . How many packets of oranges need to be added to the refrigerator so that the

probability of choosing a packet of orange juice is 21 ?

Terdapat 45 kotak jus mangga dan jus oren di dalam sebuah peti sejuk.Satu kotak minuman dipilih secara rawak daripada peti sejuk. Kebarangkalian sekotak jus oren dipilih ialah

52 .Berapakah bilangan jus oren yang perlu ditambahkan ke dalam peti sejuk supaya

kebarangkalian sekotak jus oren dipilih ialah 21

A 5 C 8 B 6 D 9 3 There are 150 people in a theatre.Given that the probability of a chair being seated by a

person is 31 , find the total numbers of chairs in the theatre.

Terdapat 150 orang di dewan teater.Diberi kebarangkalian kerusi yang diduduki ialah

31 ,cari bilangan kerusi di dewan teater itu.

A 50 C 300 B 150 D 450


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4 The diagram shows six numbered cards.

If a card randomly selected, state the probability that the number is a multiple of 3. Rajah menunjukkan enam keping kad nombor.Sekeping kad dipilih secara rawak,Nyatakan kebarangkalian bahawa kad yang dipilih itu ialah nombor gandaan 3.

A 61 C

21

B 41 D

32

6 Among a class of 38 students, 21 of them are girls.If 4 new boys joined the class and a

student randomly selected from the class, state the probability of selecting a boy. Diantara 38 orang pelajar dalam sebuah kelas, 21 adalah perempuan,4 pelajar lelaki baru

masuk dan seorang pelajar lelaki dipilih secara rawak,nyatakan kebarangkalian seorang pelajar lelaki dipilih.

A 31 C

53

B 21 D

43

7 Paul has a collection of stamps from Perak, Sabah and Sarawak.12 of the stamps are from

Perak.He picks a stamp at random.The probability of picking a stamp from Sabah is 72 and

the probability of picking a stamp from Sarawak is 32 .Calculate the total number of stamps

in his collection. Paul mempunyai koleksi setem dari Perak,Sabah dan Sarawak.12 keping daripada setem itu

ialah dari Perak.Dia memilih sekeping setem secara rawak.Kebarangkalian sekeping setem

dariSabah dipilih ialah 72 dan kebarangkalian sekeping setem dari Sarawak dipilih ialah

32 .Hitung jumlah bilangan setem dalam koleksinya.

A 252 C 278 B 260 D 350

12 14 18

20 21 51


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8 The table shows three types of favourite drink of a group of students. Jadual menunjukkan tiga jenis minuman kegemaran sekumpulan pelajar

Type of drink Number of students Coffee x Tea 14 Milo 26

A students is picked at random from the group.The probability of picking a students who likes

coffee is72 .Calculate the value of x.

Seorang pelajar dipilih secara rawak daripada kumpulan tersebut.Kebarangkalian seorang

pelajar yang suka minuman kopi ialah 72 .Hitung nilai x.

A 12 C 24 B 16 D 28 9 It is given that set M = {2, 3, 4, 5, 6, 7, 8, 9, 10}. A number is chosen at random from the

set. Find the probability that the number chosen is a factor of 32. Diberi set M = {2, 3, 4, 5, 6, 7, 8, 9, 10}.Satu nombor dipilih secara rawak daripada set. Cari kebarangkalian bahawa nombor yang dipilih itu ialah faktor bagi 32.

A 31 C

92

B 32 D

94

10 Subject Commerce Arts Science Number of students

80 90 110

The table shows the subjects taken by a group of students.A student is chosen at random, find the probability that he takes Commerce or Arts. Jadual menunjukkan mata pelajaran yang diambil oleh sekumpulan pelajar.Seorang pelajar dipilih secara rawak, cari kebarangkalian pelajar yang mengambil mata pelajaran Perdagangan dan Pendidikan Seni.

A 2811 C

2817

B 2816 D

989


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PROBABILITY PAPER 2 1 The table shows the number of buttons in a container. Jadual menunjukkan bilangan butang di dalam sebuah bekas.

Colour Quantity Red 12 Blue 15 Green x Yellow 5

A button is picked at random and its colour is noted. The probability that a blue button is picked is 10

3 Sebiji butang dipilih secara rawak dan warnanya dicatat.Kebarangkalian butang biru

dipilih ialah 103

(a) Find the value of x Cari nilai x (b) Find the probability that either a red or yellow button is picked.

Cari kebarangkalian sebiji butang merah atau sebiji butang kuning dipilih.

Answer:

(a)………………………………… (b)…………………………………. 2 A bag contains 5 yellow cards,4 red cards and 3 blue cards, all of the same size. A card is

drawn at random from the bag. Sebuah beg mengandungi 5 kad kuning, 4 kad merah, dan 3 kad biru yang sama saiz.Sekeping kad dipilih secara rawak daripada beg. (i) Find the probability that the card is yellow.

Cari kebarangkalian kad kuning dipilih. (ii) If a card is drawn with replacement of 600 times, find the number of times the card is

yellow. Jika sekeping kad dipilih dan dikembalikan sebanyak 600 kali,cari berapa kali kad kuning dipilih.

Answer: (i)……………………………….. (ii) ……………………………….


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3 The diagram shows three numbered cards in box P and two cards with letters in box Q. Gambar menunjukkan tiga kad nombor dalam kotak P dan dua kad huruf dalam kotak Q.

A card is picked at random from box P and then a card is picked at random from box Q.By listing the sample of all the possible outcomes of the event, find the probability that Sekeping kad dipilih secara rawak dari kotak P dan sekeping kad dipilih dari kotak Q.Dengan menyenaraikan sampel semua kesudahan perisriwa yang mungkin, cari kebarangkalian bahawa (a) a card with an even number and the card labelled L are picked. satu kad nombor genap dan kad berlabel L dipilih (b) a card with number which is a multiple of 2 or the card labelled A are picked. satu kad nombor gandaan 2 atau kad berlabel A dipilih. Answer:

(a) (b) 4 The table shows the masses of a group of students in a school.

Jadual menunjukkan berat badan sekumpulan pelajar sekolah. Mass (kg) 41- 45 46 -50 51 - 55 56 - 60

Number of students

12 32 20 16

If a student is randomly selected from the group,find the probability that the mass of the selected student is Jika seorang pelajar dipilih secara rawak daripada kumpulan pelajar itu,cari kebarangkalian berat badan pelajar

(a) in the modal class (b) more than 50kg (a) dalam kelas mod (b) lebih daripada 50kg

1 6 8 A L

P Q


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Diagram above shows 11 letter cards which are put in a box. Rajah di atas menunjukkan 11 kad huruf di dalam sebuah kotak. Two cards are picked at random from the box, one by one, without returning the first card to the box.Calculate the probability that Dua kad dipilih secara rawak daripada kotak,satu demi satu, dengan kad pertama tidak dikembalikan.Hitung kebarangkalian (a) the first card picked is labelled T and

the second card picked is not labelled T. kad pertama dipilih bertanda T dan kad kedua dipilih tidak bertanda T

(b) the first and the second card picked have the same letter Kad pertama dan kedua dipilih ialah sama nombor Answer: (a) ……………………………

(b) ……………………………. 6 A fair dice and a fair coin are tossed simultaneously.By listing the sample of all the possible

outcomes of the event,find the probability of obtaining Sebiji dadu dan sekeping duit syiling dilambungkan secara serentak.Cari kebarangkalian

mendapat a) the number 6 with the dice

nombor 6 pada dadu itu b) heads with the coin

angka pada duit syiling itu c) the number 4 with the dice and heads with the coin

nombor 4 pada dadu itu dan angka pada duit syiling.

Answer:

(a) ……………………………. (b) ……………………………..

(c) …………………………….

M A T H E M

A T I C S


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7 Fruit Durian Banana Number of people

x 60

The table shows the number of people who likes durian or bananas. A person is chosen at

random from the group and the probability of choosing a person who likes banana is 41 .

Jadual menunjukkan bilangan orang yang suka buah durian dan buah pisang.Seorang dipilih secara rawak dari kumpulan itu dan kebarangkalian seorang yang suka pisang

dipilih ialah is 41

Find/Cari the value of x. (a) 15 people who likes durians join the group.Find the probability of choosing a person who likes bananas. 15 orang yang suka pisang ditambah dalam kumpulan itu.Cari kebarangkalian seorang yang dipilih suka pisang. Answer: (a)……………………………….. (b)………………………………..

8 The table above shows the probabilities that Krishnan and Halim will join the Science

stream or the Arts stream after completing form three. Jadual di atas menunjukkan kebarangkalian Krishnan dan Halim masuk ke Aliran Sains

atau Aliran Sastera selepas tamat Tingkatan 3. Calculate the probability that Hitung kebarangkalian bahawa Calculate the probability that

Student

The probability of joining the

Science stream

Arts stream.

Krishnan 32

61

Halim 103

52


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(a) Krishnan and Halim will join the Science Stream Krishnan dan Halim akan masuk Aliran Sains

(b) one of them joins the Science stream and the other joins the Arts stream. Salah seorang memilih Aliran Sains dan seorang lagi memilih aliran Sastera

Answer:

(a) ……………………………….

(b) ………………………………

9 A survey conducted in a class shows that 20 students are not tongue rollers and y students are tongue- rollers.A student is picked at random from the class.The probability of picking a

student who can roll his tongue is 73

Suatu tinjauan ke atas pelajar dalam sebuah kelas menunjukkan 20 orang pelajar ialah bukan penggulung lidah dan y orang pelajar penggulung lidah.Kebarangkalian seorang

pelajar yang boleh menggulung lidah dipilih ialah 73 .

(a ) If a student is picked at random from the class,find the probability that he cannot roll his tongue. Jika seorang pelajar dipilih daripada kelas itu, cari kebarangkalian dia tidak boleh menggulung lidahnya. (b) Calculate the value of y.

Hitung nilai y.

Answer:

(a) ……………………………… (b) ………………………………

10 A box contains 1 red and 2 yellow identical balls.A ball is picked at random from the box

and its colour is noted and then returned to the box.Then the second ball is picked. Sebuah kotak mengandungi 1 biji bola merah dan 2 biji bola kuning yang serupa. Sebiji

bola dipilih secara rawak daripada kotak itu dengan warnanya dicatat dan bola itu dikembalikan semula ke dalam kotak itu.Kemudian,sebiji bola kedua dipilih.


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(a) Draw a tree diagram to represent the possible outcomes using R to represent the red ball and Y1 and Y2 to represent the yellow balls.

Lukis gambar rajah pokok untuk mewakili kesudahan yang mungkin dengan menggunakan R untuk mewakili bola berwarna merah dan Y1 danY2 untuk mewakili bola berwarna kuning.

(b) Find the probability that both balls picked at random are red or yellow Cari kebarangkalian kedua-dua bola yang dipilih secara rawak ialah bola berwarna

merah atau kuning. Answer: (a)

(b) 3. THE STRAIGHT LINES PAPER 1 1 The gradient of the straight line 5x + 7y = 14 is Kecerunan bahi garis lurus 5x + 7y = 14 ialah

A 57

C 75

B 75

D 57

2 Diagram below shows a straight line MN on a Cartesian plane Rajah di bawah menunjukkan garis lurus MN di atas satah Cartesan. The gradient of MN is Kecerunan MN ialah

A 3 C 31

B 31

D 3

N(0,3)

M(-9, 0)

0

y

x


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3 The graph in the diagram below shows a straight line JK with gradient 52

Graf dalam rajah di bawah menunjukkan garis lurus JK dengan kecerunan 52

Calculate the x-intercept of JK

A – 15 C 10 B 8 D 15 4 Find the y-intercept of the straight line 3x – 5y = 15.

A 53

C – 3

B 53

D 3

5 A straight line with a gradient of 3 passess through the point (2,0).

The y-intercept of the line is

A 23 C – 6

B 23

D 6

6 The gradient of QR is – 4 and the distance of PQ is 15 units. Find the x-intercept of PQ

A -9 C 49

J(0,6)

K

0

y

x

R(1,8)

P 0

y

x

Q


25


B -12 D 4

15

7. The straight line RS has gradient of 2. The coordinates of R are (0,6). The x-intercept of RS is

A – 3 C 31

B 31

D 3

8 The coordinates of point T(-1,1) and the gradient of the straight line TU is 2. The coordinates of point U could be A (3, 3) C (3,–1) B (3, 9) D (3,–7) 9 Given that the straight line y = mx + 6 is parallel to the straight line 4y – 9x =16, find the value of m.

A 9 C 49

B 4 D 49

10 The straight lines 4x – 3y = 9 and x – 2y = – 4 intersect at point A. Find the coordinates at point A. A (6, 5) C (–6, 5) B (6, –5) D (–6, –5) THE STRAIGHT LINES PAPER 2

1 Base on diagram above, find

(i) gradient of PQ

(ii) x-intercept for PQ

(iii) the equation of PR O

Q(3,5)

P(0,6)

x R

y


26


2 Base on diagram above, find

(i) the gradient of AB

(ii) the equation of ECF

(iii) x-intercept for ECF

3 The diagram above, 6OP units.

(i) find the gradient of PR

(ii) find the y-intercept of PQ

4 In the diagram , line DE is parallel to the line GF. Given the equation of straight line DG is x + 3y = 14 and the gradient of GF is -2, Find

(a) the value of h,

(b) the coordinate F

(c) the equation of straight line DE 5 In the diagram below, the gradient of the

straight line MN is 32

Find

(a) the value of p (b) the equation of straight line LN

y

B(-3,3) C(5,4)

F

A(2,6)

E

x

P

R

O

Q(7,8)

y

x

x

y

D(-4,6)

G(h,4)

E O F

3

y

-5

● N(6, p) M

L


27


6 Diagram below, JKLM is a trapezium and JK is

parallel to ML

Find

(i) the x-intercept for the straight line JK

(ii) the equation of the straight line ML

(iii) the coordinate M

7 In diagram below, the graph shows that PQ, QR, and RS are straight lines. P is on the y-axis. OP is parallel to QR and PQ is parallel to RS.

The equation of PQ is y = –2x + 5 (a) State the equation of the straight line QR (b) Find the equation of the straight line RS and hence , state its y-intercept.

8

P(0,6)

Q O

y

x

O Q

P●

● R

● (8, -7)

x

y

s

y K (2,5)

J(-4,2)

L(4,3)

M O x


28


Diagram above, the gradient of PQ is23

. Line

RS is parallel to the line PQ and passes through a point (-5,3). Find i) the coordinate of Q ii) the equation of RS. 9 y = mx + c is the equation of a straight line AB, where m and c are constants.Find the value of m and of c

if the straight line AB is parallel to y = 3x + 5 and passes through the point (4, 3).

10 Given two points A and B with coordinates (0,1) and (1,3) respectively, (a) calculate the gradient of the straight line AB (b) find the equation of the straight line AB (c) find the value of h if the point (10,h) lies on the straight line AB produced. 4. MATRICES PAPER 1

1 Given that

8362

243

ww

w ’

find the value of w.

Diberi bahawa

8362

243

ww

w , cari nilai w.

A 1 C -1

B 2 D -2

2

64

0312

A

01868

C

714


29


B

51868

D

1214

3 Given that 2 ,46

010321

M find the matrices of M.

Diberi bahawa 2 ,46

010321

M Cari matriks M

A

4041

C

412213

B

4021

D

41243

4 Given that 71

221x

1511 , find the value of x

Diberi bahawa 71

221x

1511 , Cari nilai x

A 11 C -3 B 3 D -11

5 Given

e21

35

3

e0

, the value of e.

Diberi

e21

35

3

e0

, n ilai e ialah

A 1 C -4

B 0 D -9

6 Given 3437

24

f . Find the value of f.

Diberi 3437

24

f . Cari nilai f.


30


A -3 C 2

B -1 D 3

7

14

35

A.

49

C

320

B

39

D

41

8

7452

1043

3612

=

A

91083

C

51021

B

91023

D

5281

9 T - ,12

040132

the matrix of T is

T - ,12

040132

matriks bagi T ialah

A

1336

C

1132

B

1132

D

1116

10 Given that

34

23

3012

k , ind the value of k.


31


Diberi bahawa

34

23

3012

k , Cari nilal k

A 1 C 4

B 2 D 8

MATRIX PAPER 2

1 M is a matrix where M

4523

=

1001

M ialah matriks di mana M

4523

=

1001

a) Find the matrix M Cari matriks M b) Write the following simultaneous linear equations as a matrix equation. Tulis persamaan linear serentak yang berikut dalam bentuk persamaan matriks: 3x – 2y = 7 5x – 4y = 9 Hence, calculate the values of x and y using matrices. Seterusnya,menggunakan kaedah matriks,hitung nilai x dan nilai y.

2 a) Find the inverse matrix of

6532

.

Cari matriks songsang bagi

6532

.

b) Using matrices, calculate the value of x and of y thay satisfy the following simultaneous linear equations:

Menggunakan kaedah matriks,hitung nilai x dan nilai y yang memuaskan persamaan linear serentak berikut:

265

132

yxyx

3 a) The inverse matrix of

6543

is m

356 p

, find the value of m and of p.

Matriks songsang bagi

6543

ialah m

356 p

, cari nilai m dan nilai p


32


b) Using matrices, calculate the value of x and of y that satisfy the following simultaneous linear equations. Menggunakan kaedah matriks,hitung nilai x dan nilai y yang memuaskan persamaan linear berikut.

3x – 4y = -1 5x – 6y = 2

4 P is a 2 x 2 matrix such that

1001

4321

P

P ialah matriks 2 x 2 dengan keadaan

1001

4321

P

a) Find the matrix P Cari matriks P b) Write the following simultaneous linearequations as a matrix equation: Tulis persamaan linear serentak yang berikut dalam bentuk persamaan matriks

643

82

yxyx

Hence, using matrices, calculate the value of x and of y. Seterusnya,menggunakan kaedah matriks,hitung nilai x dan nilai y . Seterusnya,menggunakan kaedah matriks,hitung

5 The inverse matriks of

6283

isk1

386

m.

It is given that matrix P =

3152

and

matrix Q = k

213 h

such that PQ =

1001


6283

ialahk1

386

m.

a) Find the value of m and of k Cari nilai bagi m dan k.

b) Write the following simultaneous linear as a matrix equation : Tulis persamaan linear serentak yang berikut dalam bentuk persamaan matriks. 2x – 5y = -17


33


x + 3y = 8

6 It is given that matrix M =

2143

.

Diberi bahawa matriks M =

2143

.

(a) Find the inverse matrix of M

Cari matriks songsang bagi M

(a) Write the following simultaneous linear equations as matrix equation: Tulis persamaan linear serentak yang berikut dalam bentuk persamaan matriks

621343

yxyx

Hence, using matrices, calculate the value of x and of y. Seterusnya,menggunakan kaedah matriks,hitung nilai x dan nilai y

7 (a) It is given that

n21

21 is inverse matrix of

2143

. Find the value of n.

Diberi bahawa

n21

21 adalah matriks songsang kepada

2143

.Cari nilai n.

(b) Write the following simultaneous linear equations as matrix equation:

Tulis persamaan linear serentak yang berikut dalam bentuk persamaan matriks:

22543

vuvu

Hence, using matrices, calculate the value of u and of v

Seterusnya,menggunakan kaedah matriks,hitung nilai u dan nilai v.

8 a) The inverse matrix of

4312

is m

214

p, find the value of m and p.


4312

iala m

214

p, cari nilai m dan p.


34


b) Using matrices, calculate the value of x and y which satisfy the following simultaneous linear equations.


2x + y = 4 3x – 4y = 17

9 Given that E =

2345

and F =

1084

k,

Diberi bahawa E =

2345

dan F =

1084

k,

a) Find the value of k where EF =

4004

Cari nilai k di mana EF =

4004

b) State the inverse matrix of E Nyatakan matriks songsang bagi E

Hence, using matrices, find the value of x and y which satisfy the following matrix equations.


2345

yx

=

46

10 a) Given that the inverse matrix of

2354

is

74

75

k

h, state the value of h and k.

b) Using matrices, calculate the values of x and y which satisfy both of the following equations. 4x + 5y = -1 3x + 2y = 8

5. STATISTICS PAPER 1


35


1. The pictograph shows the sale of magazines in a particular week. The number of sports magazines sold is not shown.

represents 12 copies of magazines

Entertainment magazines make up 25% of the total the sales that week. Calculate the number of sports magazines sold.

A 26 C 84

B 39 D 94

2 The pie chart shows the amount spent on five types of groceries in a shop on a particular day.

flour

margarine

salt

sugar

rice

Given that the total spent on these groceries is RM400. The amount spent on margarine is RM 80.Find the ratio of the amount spent on margarine to the amount spent on sugar.

A 1:5 C 3: 10

B 3:4 D 4: 15

3 The table shows the heights of samples of seedlings.

Calculate the mean height, in cm, of the seedlings.

A 13.06 C 14.56

B 13.56 D 15.56 4 The bar chart shows the scores of a group of pupils in a test.

Number of pupils

Fashion Entertainment Sports

Heights (in cm) 9 – 11 12 – 14 15 – 17 18- 20 No. of seedlings 5 6 10 4

120º

32º

40º


36


1 2 3 4 5 Score

State the modal score. A 6 C 3 B 5 D 2

5 The table is a cumulative frequency table which shows the height of 40 siakap fish caught by a fish breeder.

Which of the following is the correct calculation for the mean leight of the 40 siakap fish?

A 40

)10(41)16(36)8(31)6(26

B 40

))40(41)30(36)14(31)46(26

C 40

)10(43)16(38)8(33)6(28

D 40

)40(43)30(38)14(33)6(28

Leight (cm)

26–30

31– 35

36– 40

41– 45

Cumulative Frequency

4 16 34 44


37


6 The table below shows the distribution of the scores of a group of pupils in a quiz.

The median score of the distribution is

A 1 C 2

B 1.5 D 2.5

7 Given that the mean for 3, 4, p, 7, 5, 6, 4 and 3 is 5. Find the value of p.

A 5 C 7 B 6 D 8

8 The table shows the number of goals scored by a soccer team in a certain number of matches.

Number of goals 0 1 2 3 4

Number of matches k 2 6 2 1

If the mean of the number of goals scored is 2, find the value of k.

A 1 C 3

B 2 D 4

9

Score Frequency 95 – 99 100 – 104 105 – 109

5 11 9

Which of the following statements

Score 0 1 2 3 4 5 Frequency 2 6 1 1 5 1


38


regarding the above frequency table is incorrect?

A The midpoint of the class 95 – 99 is 97. B The modal class is 100 – 104 . C The size of each class interval is 5. D The upper boundary of the class 105 –109 is 109

10 The frequency table shows the number of books in the bags of a group of students.

Given that the mode is 6 books, find the greatest possible value of a.

A 5 C 6

C 7 D 8

Number of books 2 3 4 5 6 Frequency 4 6 5 a 8


39


STATISTICS ANSWERS 1. SET Paper 1

1 A 2 D 3 C 4 B 5 D 6 C 7 B 8 C 9 C 10 D

Paper 2 1 (a) R ’ S ’

(b) ( R S ) T 2 (a) shade set P Q ’ (b) shade set PQ R’

3 (a) A B (b) A’ (B C)

R

S T

S

R S

T

P Q R

P Q R

A B

C

A B

C http://edu.joshuatly.com/ http://exammy.com/

40


4 (a) set P = {20, 24, 28} set Q = { 20, 21, 2, 23, 24, 30} (b) P Q’ = {25, 26, 27, 28, 29 } (c ) n (P Q’) = 1

5 (a) ( P R)’ = {4, 5, 7} (b) Q R P = {1, 2, 3} 6 (a) P R = { } (b) Q R’ 7 (a) J ’ L’ (b) J K L’ 8 (a) (b) {3, 6, 8} (c ) 4 9 (a) set P = {20, 25, 30, 35} set Q = {20, 22, 24, 26, 28, 30, 32, 34} (b) (i) 2 (ii) 6 10 (a) (b)

E F

G

6 5 9

3 8

1 2

X Y

Z

X Y

Z


PROBABILITY PAPER 1 1. B 2. D 3. D 4. D 5. D 6. B 7. A 8. B 9. A 10. C PAPER 2

1. Answer:

(a)…………………………………1/8 (b)………………………………….1/16

2. (i)………………………………..5/12 (ii) ………………………………250 3. Answer:

S = {(1,A), (1,L), (6,A), (6,L), (8,A),(8,L)} (a) 2/6 or 1/3 (b) 5/6 4. Answer (a) in the modal class (b) more than 50kg dalam kelas mod lebih daripada 50kg 2/5 9/20

5. Answer: (a) ……………………………18/110

(b) …………………………….9/55

6. Answer:

(a) S={(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H), (4,T),(5,H),(5,T),(6,H),(6,T)}

(b)…………………………….2/12 / 1/6 ©……………………………..6/12 / ½ (e)………………………….1/12

7. Answer: (a)………………………………..20 (b)……………………………….12/19

8. (c) ………………………………1/5. (b) ……………………………… 19/60


9.

(c) ………………………………4/7 (d) ………………………………15 Answer: (a)

(b) 95

THE STRAIGHT LINES PAPER 1 1. B 2. C 3. C 4. C 5. C 6. A 7. A 8. 9. C 10. A THE STRAIGHT LINES PAPER 2 1

(i) gradient of PQ (-1/3)

(ii) x-intercept for PQ (18)

(iii) the equation of PR ( y = 5/3x+6) 2.

(iv) the gradient of AB (3/5)

(v) the equation of ECF (y=3/5x+1)

(vi) x-intercept for ECF (-5/3 )

R

Y1

Y2

R

Y1

Y2

R

Y1

Y2

R

Y1

Y2

RR

RY1

RY2

Y1R

Y1Y1

Y1Y2

Y2R

Y2Y1

Y2Y2

y


3 (ii) find the gradient of PR (4/3)

(ii) find the y-intercept of PQ (y = 8x – 48 )

4 (a) the value of h, (h=2) (b) the coordinate F (4,0) (c) the equation of straight line DE (y = -2x + 2)

5 (a) the value of p (p = 7) (b) the equation of straight line LN(y = 2x – 7 ) 6

(iii) the x-intercept for the straight line JK (1/2)

(iv) the equation of the straight line ML(2y=x+2)

(iii) the coordinate M (-2,0) 7

(a) State the equation of the straight line QR (x = 5/2) (b) Find the equation of the straight line RS and hence , state its y-intercept. (y = -2x + 9),

c = 9 8

i) the coordinate of Q.(4, 0) ii) the equation of RS.(2y = -3x -9)

9 m = 3, c = -9 10 (a) calculate the gradient of the straight line AB (m = 2) (b) find the equation of the straight line AB(y= 2x+1) (c) find the value of h if the point (10,h) lies on the straight line AB produced.(21)


STATISTICS PAPER 1

1. A 2. B 3. C 4. D 5. D 6. B 7. D 8. A 9. D 10. B

PAPER 2 1 (a) The table shows the speed, in km h-1, of 56 cars on a road.

Speed ( km h-1 ) Frequency Midpoint 51 – 55 2 56 – 60 6 61 – 65 18 66 – 70 15 71 – 75 9 76 – 80 5 81 – 85 1

(i) Find the midpoints of the class intervals. (ii) Calculate the mean speed of the cars. (b) Complete the table given in the answer space below. (c) For this part of question, use the graph paper.

By using a scale of 2 cm to 5 km h-1 on the x axis and 2 cm to 5 cars on the y-axis, draw an ogive for the data.

Hence, find (i) the median (ii) the interquartile range. 2. The data above shows the pocket money, in RM, per week of a group of 40 students. 10 13 18 7 19 5 21 21 18 16 18 10 15 19 20 8 4 14 12 6 9 20 20 15 8 10 16 11 13 17 9 11 19 15 17 12 14 11 16 17 (a) Based on the data, complete the table below.

Pocket money (RM) Frequency Midpoint 1 – 3 0 4 – 6


(b) Based on the table, (i) state the modal class, (ii) calculate the mean, of the data.

(c) For this part of the question, use a graph paper. By using a scale of 2 cm to RM 3 on the x-axis and 2 cm to 1 student on the y-axis,

draw a histogram and a frequency polygon on the same graph paper. 3. (a) The table above shows the scores of a group of players in the game.

Score 10 11 12 13 14 15 Frequency 4 7 3 X 5 8

(i) Given the median is 12.5, find the value of x. (ii) Given the mode is 15, find the maximum value of x. (b) The data shows the mass, in kg, of a group of students.

49 45 47 66 66 62 68 43 46 53 50 61 65 67 63 68 65 44 48 63 62 45 61 67 56 43 44 57 64 60 52 58 46 59 41 43 64 65 47 46 52 50 54 42 60

(i) Based on the data, complete the frequency table below.

Mass (kg) Frequency 41 – 44 65 – 68

(ii) For this part of question, use the graph paper.

(a) By using a scale of 2 cm to 4 kg on the x-axis and 2cm to 1 student on the y-axis, draw a histogram for the data.

(b) State one information obtained from the histogram.


4. The histogram shows the donations from a group of 40 students to a school fund.

(a) Based on the histogram, state the modal class of the data. (b) Complete the frequency table below.

Donation (RM) Frequency Cumulative frequency

Upper boundary

0 0 1 – 4 2

(c) For this part of question, use a graph paper.

(i) By using a scale of 2 cm to RM4 on the x-axis and 2 cm to 5 students on the y-axis, draw an ogive for the data.

(ii) From the ogive, find the inter quartile range.

0

2

4

6

8

10

12

14

0.5 4.5 8.5 12.5 16.5 20.5 24.5 28.5

Donation (RM)

Fre

qu

en

cy

0.5 4.5 8.5 12.5 16.5 20.5 24.5 28.5

32.5


5. The ogive shows the scores of a group of 48 students in a Mathematics test.

(a) Based on the ogive, calculate the percentage of students who scored more than 80. (b) Complete the table below.

Score Cumulative

frequency Frequency Midpoint

60 – 64 0 65 – 69

(c) Calculate the mean of the data.

(d) For this part of question, use the graph paper.

By using a scale of 2 cm to 5 scores on the x-axis and 2 cm to 2 students on the y- axis, draw a frequency polygon for the data

0

10

20

30

40

50

60

64.5 69.5 74.5 79.5 84.5 89.5 94.5 99.5

Score

Cu

mu

lati

ve

fre

qu

en

cy


6. The frequency table above shows the masses, in kg, of watermelons in a lorry.

Mass (kg)

Frequency

1.5 – 1.9 4 2.0 – 2.4 10 2.5 – 2.9 26 3.0 – 3.4 84 3.5 – 3.9 50 4.0 – 4.4 15 4.5 – 4.9 8 5.0 – 5.4 3

(a) From the table, state

(i) the size of the class interval, (ii) the midpoint of the modal class.

(b) (i) Based on the information, complete the table below.

Upper boundary 1.45 5.45

Cumulative Frequency 0 200

(ii) For this part of question, use a graph paper. By using a scale of 2 cm to 0.5 kg on the x-axis and 2cm to 20 watermelons on the y-axis, draw an ogive for the data. (iii) From the ogive, a) state the median of the data, b) find the number of watermelons with the weight less than 3.8 kg. 7. The cumulative frequency table shows the marks of a group of 40 students in a test.

Mark 60 – 64 65 – 69 70 – 74 75 – 79 80 – 84 85 – 89 90 – 94 Cumulative frequency 7 11 17 26 34 37 40

(a) Based on the information, complete the table in the answer corner.

(b) Find

(i) the size of the class interval, (ii) the modal class of the data, (iii) the midpoint of the modal class.

(c) Calculate the mean of the data.


(d) For this part of question, use the graph paper. By using a scale of 2 cm to 5 marks on the x-axis and 2 cm to 1 student on the y-axis, draw a histogram for the data.

8. The data shows the ages of a group of 40 workers in a factory.

38 41 32 39 32 50 31 38 36 51 31 27 44 30 49 28 26 31 22 36 32 33 34 43 31 27 46 41 35 35 34 31 40 35 25 27 50 37 33 45

(a) Find the range of the data. (b) Based on the data and by using a class interval of 5 years, complete the table below.

Ages (years) Frequency Midpoint 21 – 25 26 – 30

(c) From the table, (i) state the modal class, (ii) calculate the mean,of the data.

(d) For this part of question, use a graph paper. By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 workers on the y-axis, draw a frequency polygon for the data.

9. The data shows the ages of a group of 40 workers in a factory.

38 41 32 39 32 50 31 38 36 51 31 27 44 30 49 28 26 31 22 36 32 33 34 43 31 27 46 41 35 35 34 31 40 35 25 27 50 37 33 45

(a) Find the range of the data. (b) Based on the data and by using a class interval of 5 years, complete the table below.


Ages (years) Frequency Midpoint 21 – 25 26 – 30

(c) From the table, (i) state the modal class, (ii) calculate the mean, of the data. (d) For this part of question, use a graph paper. By using a scale of 2 cm to 5 years on the x-axis and 2 cm to 2 workers on the y-axis,

draw a frequency polygon for the data. 10. The frequency polygon shows the daily incomes, in RM, of 28 workers.

0

2

4

6

8

10

12

18 23 28 33 38 43 48

Daily income

Fre

qu

en

cy


(a) Based on the frequency polygon, complete the table below.

Daily income (RM)

Midpoint Upper boundary Frequency Cumulative

frequency

16 – 20 18 20.5 0 0

(b) Based on the table, (i) state the modal class, (ii) calculate the mean, of the data.

(c) For this part of question, use a graph paper.

(i) By using a scale 2 cm to RM5 on the x-axis and 2 cm to 4 workers on the y-axis,draw an ogive for the data.

(i) From the ogive, find the number of workers whose daily income is more

than RM38. STATISTICS Answer/Jawapan : 1. (a) (i) and (b)

Speed (km h-1 )

Frequency Midpoint Upper Boundary

Cumulative Frequency

46 – 50 0 48 50.5 0 51 – 55 2 53 55.5 2 56 – 60 6 58 60.5 8 61 – 65 18 63 65.5 26 66 – 70 15 68 70.5 41 71 – 75 9 73 75.5 50 76 – 80 5 78 80.5 55 81 – 85 1 83 85.5 56


(ii) Mean = 56

)183()578()973()1568()1863()658()253(

= 56

3738

= 66.75 km h-1. (c)

(a) Median = 66.5 km h-1 (b) Interquartile range = 71.0 – 62.5 = 8.5 km h-1 2. (a)

Pocket money(RM) Frequency Midpoint 1 – 3 0 2 4 – 6 3 5 7 – 9 5 8 10 – 12 8 11 13 – 15 7 14 16 – 18 9 17 19 – 21 8 20

(b) (i) Modal class = 16 – 18

(ii) Mean = 8978530

)820()917()714()811()58()35(

= 40

554

= RM 13.85

0

5

10

15

20

25

30

35

40

45

50

55

60

50.5 55.5 60.5 65.5 70.5 75.5 80.5 85.5 90.5

Speed (km/h)

Cu

mu

lati

ve f

req

uen

cy

From the ogive, First quartile = 62.5 Median = 66.5 Third Quartile = 71.0


(iii)

0

1

2

3

4

5

6

7

8

9

10

3.5 6.5 9.5 12.5 15.5 18.5 21.5

Pocket money

Fre

qu

en

cy

3.5 6.5 9.5 12.5 15.5

3. (a) (i) x = ( 4+ 7 +3 ) – ( 5 + 8 ) = 14 – 13 = 1 (ii) Maximum value of x = 7

Mass (kg) Frequency 41 – 44 7 45 – 48 8 49 – 52 5 53 – 56 3 57 – 60 5 61 – 64 8 65 – 68 9

0

1

2

3

4

5

6

7

8

9

10

40.5

44.5

48.5

52.5

56.5

60.5

64.5

68.5

Mass(kg)

Fre

qu

en

cy

40.5 44.5 48.8 52.5 56.5 60.5

64.5 68.5

(iii) The modal class of the data is 65 – 68 kg.

4 (a) Modal class = 9 – 12


(b) Donation (RM) Frequency Cumulative

frequency Upper boundary

0 0 0 0.5 1 – 4 2 2 4.5 5 – 8 5 7 8.5 9 – 12 12 19 12.5 13 – 16 8 27 16.5 17 – 20 5 32 20.5 21 – 24 3 35 24.5 25 – 28 1 36 28.5

(c) (i)

0

5

10

15

20

25

30

35

40

0.5 4.5 8.5 12.5 16.5 20.5 24.5 28.5

Donation (RM)

Cu

mu

lati

ve f

req

uen

cy Third quartile

First

9. 16.5

(ii) Interquartile range = 16.5 – 9.3 = RM 7.20 5 (a) The percentage of students who scored more than 80

= 48

1948 x 100%

= 4829 x 100%

= 60.42 %


(b) Score Cumulative frequency Frequency Midpoint 60 – 64 0 0 62 65 – 69 2 2 67 70 – 74 7 5 72 75 – 79 17 10 77 80 – 84 34 17 82 85 – 89 43 9 87 90 – 94 47 4 92 95 – 99 48 1 97

(c) Mean = 1491710520

)197()492()987()1782()1077()572()267(

= 48

3906

= 81.375 (d)

0

2

4

6

8

10

12

14

16

18

62 67 72 77 82 87 92 97 102

Score

Fre

qu

en

cy

6 (a) (i) Size of class interval = 1.95 – 1.45 = 0.5 kg (ii) Modal class = 3.0 – 3.4

Midpoint of the modal class = 2

4.30.3

= 3.2


(b) (i)

Upper boundary Cumulative frequency

1.45 0 1.95 4 2.45 14 2.95 40 3.45 124 3.95 174 4.45 189 4.95 197 5.45 200

(iii) (a) Median = 3.40 kg

(b) The number of watermelons with the weight less than 3.8 kg = 200 – 164 = 36. 7. (a)

Mark Cumulative frequency

Frequency Midpoint

55 – 59 0 0 57 60 – 64 7 7 62 65 – 69 11 4 67 70 – 74 17 6 72 75 – 79 26 9 77 80 – 84 34 8 82 85 – 89 37 3 87 90 - 94 40 3 92

(b) (i) Size of class interval = 59.5 – 54.5

= 5 marks (ii) Modal class = 75 – 79

(iii) Midpoint of the modal class = 2

7975

= 77

(c) Mean = 33896470

)392()387()882()977()672()467()762(

= 40

3020

= 75.5 marks


(d)

0

1

2

3

4

5

6

7

8

9

10

54.5 59.5 64.5 69.5 74.5 79.5 84.5 89.5 94.5

Mark

Fre

qu

en

cy

54.5 59.5 64.5 69.5 74.5 79.5 84.5 89.5 94.5

8. (a) Range = 51 – 22 = 29 years. (b)

Ages (years) Frequency Midpoint 21 – 25 2 23 26 – 30 6 28 31 – 35 15 33 36 – 40 7 38 41 – 45 5 43 46 – 50 4 48 51 – 55 1 53

(c) (i) Modal class = 31 – 35

(ii) Mean = 14571562

)153()448()543()738()1533()628()223(

= 40

1435

= 35.875 years


(d)

0

2

4

6

8

10

12

14

16

18 23 28 33 38 43 48 53 58

Age (years)

Fre

qu

en

cy

9 (a) Range = 51 – 22 = 29 years. (b)

Ages (years) Frequency Midpoint 21 – 25 2 23 26 – 30 6 28 31 – 35 15 33 36 – 40 7 38 41 – 45 5 43 46 – 50 4 48 51 – 55 1 53

(c) (i) Modal class = 31 – 35

(ii) Mean = 14571562

)153()448()543()738()1533()628()223(

= 40

1435

= 35.875 years


(d)

0

2

4

6

8

10

12

14

16

18 23 28 33 38 43 48 53 58

Age (years)

Fre

qu

en

cy

10. (a)

(b) (i) Modal class = 26 – 30

(ii) Mean = 2481040

)243()438()833()1028()423(

= 28

874

= RM 31.21

Daily income(RM)

Midpoint Upper boundary

Frequency Cumulative frequency

16 – 20 18 20.5 0 0 21 – 25 23 25.5 4 4 26 – 30 28 30.5 10 14 31 – 35 33 35.5 8 22 36 – 40 38 40.5 4 26 41 – 45 43 45.5 2 28


(c ) (i)

0

4

8

12

16

20

24

28

20.5 25.5 30.5 35.5 40.5 45.5

Daily income (RM)

Cu

mu

lati

ve

fr

eq

ue

nc

y

(ii) The number of workers whose daily income is more than RM 38 = 28 – 24 = 4


SULIT NO. KAD PENGENALAN ANGKA GILIRAN

PROJEK JAWAB UNTUK JAYA (JUJ) 2010

PRAKTIS BESTARI 1449/2

MATHEMATICS Kertas 2

221 jam Dua jam tiga puluh minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1 Tulis nombor kad pengenalan dan angka giliran anda pada ruangan yang disediakan . 2 Kertas soalan ini adalah dalam dwibahasa . 3 Soalan dalam bahasa Inggeris mendahului soalan yang sepadan dalam bahasa Melayu . 4 Calon dibenarkan menjawab keseluruhan atau sebahagian soalan sama ada dalam bahasa Inggeris atau bahasa Melayu. 5 Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini . Kertas soalan ini mengandungi 34 halaman bercetak

Untuk Kegunaan Pemeriksa Kod Pemeriksa :

Bahagian Soalan Markah Penuh

Markah Diperoleh

A

Jumlah

1 2

4 3

5 6 7 8 9

10 11 12 13 14 15 16

12 12 12 12 12

3 4 4

7

3 5 4 6 5

6 5

B


MATHEMATICAL FORMULAE RUMUS MATEMATIK

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.

RELATIONS PERKAITAN

1 nmnm aaa 10 Pythagoras Theorem Teorem Pithagoras 2 nmnm aaa 222 bac

3 nmnm aa )( 11 )()()(

SnAnAP

4

acbd

bcadA 11 12 )(1)( ' APAP

5 Distance / Jarak 13 12

12

xxyym

212

212 )()( yyxx

14 m = – 6 Midpoint / Titik tengah

2,

2),( 2121 yyxx

yx m = –

7 Average speed = Purata laju = 8 Mean = Min = 9 Mean = Min = 1449/2 © 2010 Hak Cipta JUJ Pahang SULIT

distance travelled time taken

jarak yang dilalui masa yang diambil

sum of data number of data

hasil tambah nilai data bilangan data

sum of (classmark × frequency ) sum of frequencies

hasil tambah (nilai titik tengah kelas × kekerapan) hasil tambah kekerapan

y - intercept x - intercept

pintasan - y pintasan - x


SULIT 3 1449/2 SHAPES AND SPACE

BENTUK DAN RUANG

1 Area of trapezium = 21 × sum of parallel sides × height

Luas trapezium = 21 × hasil tambah dua sisi selari × tinggi

2 Circumference of circle = d = 2 r Lilitan bulatan = d = 2 j 3 Area of circle = r2

Luas bulatan = j2

4 Curved surface area of cylinder = 2 rh Luas permukaan melengkung silinder = 2 jt 5 Surface area of sphere = 4 r2

Luas permukaan sfera = 4 j2

6 Volume of right prism = cross sectional area × length Isipadu prisma tegak = luas keratan rentas × panjang 7 Volume of cylinder = r2h Isipadu silinder = j2t

8 Volume of cone = 31 r2h

Isipadu kon = 31 j2t

9 Volume of sphere = 34 r3

Isipadu sfera = 34 j3

10 Volume of right pyramid = 31 × base area × height

Isipadu pyramid tegak = 31 × luas tapak × tinggi

11 Sum of interior angles of a polygon Hasil tambah sudut pedalaman poligon = ( n – 2 ) × 180o

1449/2 © 2010 Hak Cipta JUJ Pahang [Lihat halaman sebelah SULIT


SULIT 4 1449/2

12 = = 13 = =

14 Scale factor, PAPAk

'

Faktor skala, PAPAk

'

15 Area of image = k2 × area of object Luas imej = k2 × luas objek 1449/2 © 2010 Hak Cipta JUJ Pahang SULIT

Section A

arc length circumference of circle

angle subtended at centre 360o

panjang lengkuk lilitan bulatan

sudut pusat 360o

area of sector area of circle


luas sektor luas bulatan

sudut pusat 360o


Bahagian A [52 marks]

[52 markah] Answer all questions from this section.

Jawab semua soalan dalam bahagian ini.

1. The Venn diagram in the answer space shows sets P, Q and R, such that the universal set, ξ = P Q R. On the diagrams in the answer space, shade the set Gambar rajah Venn di ruang jawapan menunjukkan set P, set Q dan set R dengan keadaan ξ = P Q R. Pada rajah di ruang jawapan, lorek set (a) 'QP (b) )( RPQ [3 marks] / [3 markah] Answer / Jawapan :

(a) (b)

P

R

Q

R

Q P


2. Solve the quadratic equation : Selesaikan persamaan kuadratik :

)53(212 pp [4 marks] / [4 markah]

Answer / Jawapan: 3. Calculate the value of x and of y that satisfy the following simultaneous linear equations :

Hitungkan nilai x dan nilai y yang memuaskan persamaan linear serentak berikut: 932 yx

231

yx

[4 marks] / [4 markah] Answer / Jawapan :


4. (a) Determine whether the following sentence is a statement or non-statement. Tentukan sama ada ayat berikut adalah pernyataan atau bukan pernyataan. (b) Write two implications based on the following statement: Tulis dua implikasi berdasarkan pernyataan berikut: (c) Make a general conclusion by induction for the sequence of numbers 5, 16, 37, 80, ...

which follows the following pattern: Buat satu kesimpulan umum secara aruhan untuk urutan nombor 5, 16, 37, 80, ... yang

mengikut pola berikut: 5 = 4(1) + 13 16 = 4(2) + 23 37 = 4(3) + 33 80 = 4(4) + 43

……………… [5 marks] / [5 markah]

Answer / Jawapan : (a) …………………………………………………………………………………………. (b) Implication 1 / Implikasi 1 : ………………………………………………………………………………………….. Implication 2 / Implikasi 2 : ………………………………………………………………………………………… (c) ………………………………………………………………………………………… …………………………………………………………………………………………

”7 is a factor of 30” “7 ialah faktor bagi 30”

”x is an even number if and only if x is divisible by 2” “x ialah nombor genap jika dan hanya jika x boleh dibahagi tepat dengan 2”


5. Diagram 5 shows a right prism LMNOPQ with horizontal base LMNO and POL as its

cross-section. Rajah 5 menunjukkan sebuah prisma tegak LMNOPQ dengan tapak mengufuk dan POL sebagai keratan rentasnya.

(a) Name the angle between the plane POM and the plane PONQ. Namakan sudut antara satah POM dengan satah PONQ

(b) Calculate the angle between the plane POM and the plane PONQ

Hitung sudut antara satah POM dengan satah PONQ. [3 marks] / [3 markah]

Answer / Jawapan :

(a)

(b)

P Q

N

O

L M

16 cm

Diagram 5 Rajah 5

12 cm


6. It is given that matrix A =

k234

Diberi bahawa matriks A =

k234

(a) Find the value of k if the inverse of matrix A does not exist.

Cari nilai k jika songsangan matriks A tidak wujud. (b) Write the following simultaneous linear equations as matrix equation :

Tuliskan persamaan linear serentak berikut dalam bentuk persamaan matriks: 4m + 3n = 5 2m - n = 5

Hence, by using matrix method, calculate the value of m and of n.

Seterusnya dengan menggunakan kaedah matriks, hitungkan nilai m dan nilai n. [6 marks] / [6 markah]

Answer / Jawapan :

(a)

(b)


7. Diagram 7 shows a circle PQR with centre O, and three semi circles. Given that POQ = QOR = ROP and OP = OQ = OR = 28 cm.

Rajah 7 menunjukkan sebuah bulatan PQR berpusat O dan tiga buah separuh bulatan. Diberi bahawa POQ = QOR = ROP dan OP = OQ = OR = 28 cm.

Using 722

, calculate

Menggunakan 722

, hitung

a) the perimeter, in cm, of the shaded region

perimeter, dalam cm, kawasan berlorek

b) the area, in cm2, the shaded region

luas, dalam cm2, kawasan berlorek

[6 marks] / [6 markah] Answer / Jawapan : (a) (b)

R

P

Q Diagram 7 / Rajah 7

O


8. Diagram 8 shows a composite solid. PQRSTU is a right prism with PQ = QR. SUV is a half circular cylinder. They are joined at the rectangular plane PRSU. STUV is its cross-section.

Rajah 8 menunjukkan sebuah gabungan pepejal. PQRSTU ialah sebuah prisma tegak dengan PQ = QR. SUV ialah sebuah separuh silinder. Kedua-dua pepejal ini dicantum pada satah PRSU. STUV ialah keratan rentasnya.

Using 722

, calculate the volume, in cm3, of the composite solid.

Menggunakan 722

, hitung isipadu, dalam cm3 , gabungan pepejal itu.

[4 marks] / [4 markah]

Answer / Jawapan :

U

V

S

R

Q

T P

W Diagram 8 Rajah 8

13 cm

10 cm

10 cm


9. Diagram 9 shows three cards labelled with letters in box A and four numbered cards in box B. Rajah 9 menunjukkan tiga kad huruf di dalam kotak A dan empat kad nombor di dalam kotak B.

A B

A code is form by a letter selected from box A and a number from box B.

Satu kod dibina menggunakan huruf yang dipilih daripada kotak A dan satu nombor yang dipilih daripada kotak B.

(a) Listing the sample space of the possible outcomes of the event. Senaraikan ruang sample bagi kesudahan peristiwa.

(b) Hence, find the probability of Seterusnya, cari kebarangkalian bahawa

(i) choosing a code that contain number 2 memilih kod yang mengandungi nombor 2

(ii) choosing a code that contain a vowel or number 3 memilih kod yang mengandungi huruf vokal atau nombor 3


Answer / Jawapan : (a) (b)(i) (ii)

E R K 1 2 3 4


10. In diagram 10, PQ is parallel to SR and O is the origin.

Dalam rajah 10, PQ adalah selari dengan SR dan O ialah titik asalan.

Find Cari (a) the gradient of PQ. Kecerunan PQ. (b) the equation of straight line SR. persamaan garis lurus SR. (c) the y-intercept of SR. pintasan-y bagi garis lurus SR.

[5 marks] / [5 markah] Answer / Jawapan :

(a) (b) (c)

y

x

Q(1, 7)

R(6, 2) P(-2, 1)

S

Diagram 10 Rajah 10


11. Diagram 11 shows a speed-time graph for the movement of a particle for a period of

18 seconds. Rajah 11 menunjukkan graf laju-masa bagi pergerakan satu zarah dalam tempoh 18 saat.

Speed (ms-1)

(a) How long does the particle move in uniform speed ? Berapa lamakah zarah itu bergerak dengan laju malar ?

(b) Calculate the rate of change of speed, in ms-1, in the first 8 seconds. Hitung kadar perubahan laju, dalam ms-1, dalam tempoh 8 saat yang pertama.

(c) Calculate the value of u, if the distance travelled in the last 10 seconds is 172 m. Hitung nilai u, jika jumlah jarak yang dilalui dalam tempoh 10 saat terakhir ialah 172m.


Answer / Jawapan : (a) (b) (c)

Diagram 11 Rajah 11

32

18 12

u

Time (s) Masa(s)

16

8 0

Laju(ms-1)


Section B Bahagian B [48 marks]

[48 markah] Answer any four questions from this section.

Jawab mana-mana empat soalan dalam bahagian ini. 12.(a) Table 12 in the answer space shows the values of x and of y for the equation

432 2 xxy . Find the value of m and of p. [2 marks]

Jadual 12 di ruang jawapan menunjukkan nilai-nilai x dan y bagi persamaan 432 2 xxy .

Cari nilai bagi m dan p. [2 markah]

(b) For this part of the question, use graph paper. You may use a flexible curve ruler. Untuk ceraian soalan ini, gunakan kertas graf. Anda boleh menggunakan pembaris fleksibel.

By using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw

the graph of 432 2 xxy for 52 x . [4 marks] Dengan menggunakan skala 2 cm kepada 1 unit pada paksi-x dan 2 cm kepada 5 unit

pada paksi-y, lukis graf 432 2 xxy untuk 52 x . [4 markah] (c) Using the graph drawn in 12(b), find

Menggunakan graf yang dilukis di 12(b), cari (i) the value of y when x = -1.5.

nilai y apabila x = -1.5 (ii) the values of x when y = 0. [3 marks]

Nilai-nilai x apabila y = 0 [3 markah]

(d) Draw a suitable straight line on your graph to find the value of x that satisfies the equation 1822 2 xx for 52 x . State the value of x. [3 marks] Lukis garis lurus yang sesuai pada graf anda untuk mencari nilai x yang memuaskan persamaan 1822 2 xx untuk 52 x . Nyatakan nilai x itu. [3 markah]


Answer / Jawapan : (a)

x -2 -1 0 1 2 3 4 4.5 5 y m 1 -4 -5 -2 p 16 23 31

Table 12 / Jadual 12

m = ..............................................

p = .............................................. (b) Refer graph / rujuk graf . (c) (i) y = ........................................... (ii) x = ............................................ , ............................................... (d) ...................................................................


13. (a) Transformation R is a reflection in the line x = 6 and transformation P is a clockwise

rotation of 90° about the centre (4, 2). Penjelmaan R ialah pantulan pada garis x = 6 dan penjelmaan P ialah putaran 90° arah jam pada pusat (4,2).

State the coordinates of the image of point (9, 4) under each of the following transformations: Nyatakan koordinat imej bagi titik (9, 4) di bawah setiap penjelmaan berikut: (i) R (ii) P (iii) PR [4 marks] / [4 markah]

(b) Diagram 13 shows three pentagons, ABCDE, HJKLM and PQRST, drawn on a Cartesian

plane. Rajah 13 menunjukkan tiga pentagon, ABCDE, HJKLM dan PQRST dilukis di atas satah Cartesan.

Diagram 13 Rajah 13

6

4

2

0 10 8 6 4 2 x

y

10

8

T

P Q

S

M L

R

J

K

D

E A

B

C

H


(i) HJKLM is the image of ABCDE under the combined transformation TU. Describe in full the transformation :

HJKLM ialah imej bagi ABCDE di bawah gabungan penjelmaan TU. Huraikan selengkapnya penjelmaan : (a) U (b) T [5 marks] / [5 markah]

(ii) It is given that pentagon ABCDE represents a region of area 12 m2. Calculate the

area , in m2 , of the region represented by the shaded region. Di beri bahawa pentagon ABCDE mewakili suatu kawasan yang mempunyai luas 12 m2. Hitungkan luas, dalam m2, kawasan yang diwakili oleh rantau berlorek.

[3 marks]

Answer / Jawapan : (a) (i) (ii)

(iii) (b)(i) U : …………………………………………………………………………………… ……………………………………………………………………………………. T : ……………………………………………………………………………………. ……………………………………………………………………………………..

(ii)


14. Table 14.1 shows the frequency distribution of the number of books read by 40 students in a

reading programme in a school. Jadual 14.1 menunjukkan taburan kekerapan bagi bilangan buku yang dibaca oleh 40 orang pelajar dalam suatu program membaca di sebuah sekolah.

Class interval Selang Kelas

Frequency Kekerapan

5 – 7 3 8 – 10 5 11 – 13 9 14 – 16 10 17 – 19 8 20 – 22 4 23 – 25 1

(a) Based on the data in Table 14.1 complete Table 14.2 in the answer space. [4 marks] Berdasarkan Jadual 14.1, lengkapkan Jadual 14.2 di ruang jawapan. [4 markah]

(b) Calculate the estimated mean of books read by a student. [3 marks]

Hitung min anggaran buku yang dibaca oleh seorang pelajar. [3 markah]

(c) For this part of the question, use the graph paper Untuk ceraian soalan ini gunakan kertas graf By using a scale of 2 cm to 3 books on the horizontal axis and 2 cm to 5 students on the vertical axis, draw an ogive for the data. [4 marks]

Dengan menggunakan skaia 2 cm kepada 3 buah buku pada paksi mengufuk dan 2 cm kepada 5 orang pelajar pada paksi mencancang , lukiskan satu ogif bagi data di atas. [4 markah]

(d) Based on the ogive in 14(c), give one information about the marks obtained. [1 marks]

Berdasarkan ogif (b), beri satu maklumat tentang markah yang diperoleh. [1 markah]

Table 14.1 Jadual 14.1


Answer / Jawapan : (a)

Class interval Selang Kelas

Frequency Kekerapan

Mid point

Titik tengah

Upper Boundary Sempadan Atas

Cumulative Frequency Kekerapan Longgokan

5 – 7

3

8 – 10

5

11 – 13

9

14 – 16

10

17 – 19

8

20 – 22

4

23 – 25

1

(b) (c) Refer graph. Rujuk graf. (d)

Table 14.2 Jadual 14.2


15. You are not allow to use graph paper to answer this question.

(a) Diagram 15.1 shows a right prism with rectangular base ABCD on a horizontal table. The surface AEHILD is its uniform cross-section. The rectangle IJKL is an inclined plane. The rectangle EFGH is a horizontal plane. The edges AE, BF, CK, DL, GJ and HI are vertical edges. Given EH = FG = 3 cm. Rajah 15.1 menunjukkan sebuah prisma tegak dengan tapak ABCD di atas meja mengufuk. Permukaan AEHILD ialah keratan rentasnya. Sisiempat IJKL adalah satah condong. Sisiempat EFGH adalah satah mengufuk. Sisi AE, BF, CK, DL, GJ dan HI adalah tegak. Diberi EH = FG = 3 cm.

Draw in full scale, the plan of the solid. Lukis dengan skala penuh pelan pepejal itu. [3 marks] / [3 markah]

Answer / Jawapan :

3 cm H

L

8 cm

4 cm

6 cm

5 cm

A

E

D

C

B

J

K

I

G

F

Diagram 15.1 Rajah 15.1


(b) A half cylinder is joined to the solid in diagram 15.1 at plane CDLK to form a combined solid as diagram 15.2. Separuh silinder digabungkan kepada rajah 15.1 pada satah CDLK untuk membentuk

gabungan pepejal seperti dalam rajah 15.2.

Draw in full scale,

Lukis dengan skala penuh, (i) the elevation of the combined solid on a vertical plane parallel to AD as viewed from P

Dongakan gabungan pepejal pada satah tegak yang selari dengan AD sebagaimana dilihat pada arah P.

[4 marks] / [4 markah] (ii) the elevation of the combined solid on a vertical plane parallel to AD as viewed from Q

Dongakan gabungan pepejal pada satah tegak yang selari dengan DC sebagaimana dilihat pada arah Q.


Answer / Jawapan :

Diagram 15.2 Rajah 15.2

8 cm

4 cm

6 cm

5 cm

A

E

D

C

B

J

K

I

G

F

H

L

3 cm

P Q


16. P (38oS, 80oE), Q (38oS, 30oE), and H are three points on the surface of the earth and PH

is the diameter of the earth. P (38oS, 80oE), Q (38oS, 30oE), dan H adalah tiga titik di atas permukaan bumi dan PH ialah diameter bumi.

(a) State the longitude of H [2 marks] Nyatakan longitud bagi H [2 markah]

(b) Calculate the distance, in nautical miles, of P due west to Q measured along the common

parallel of latitude. [3 marks] Hitung jarak, dalam batu nautikal, dari P ke arah barat ke Q di ukur sepanjang selarian latitud sepunya. [3 markah]

(c) Given that F is situated 4380 nautical miles due north of P. Find the latitude of F.

Diberi F terletak 4380 batu nautikal ke arah utara P. Cari latitud F. [3 markah] (d) An aeroplane took off from P and flew to H via the South Pole with an average speed of 900 knots. Calculate the shortest time taken for the flight. [4 marks]

Sebuah kapal terbang berlepas dari P dan terbang ke arah H melalui Kutub Selatan dengan purata laju 900 knot. Hitung masa terpantas yang diambil oleh kapal terbang itu. [4 markah]

Answer / Jawapan :


JAWAB UNTUK JAYA JAWAB UNTUK JAYA 2010 1449/1 SIJIL PELAJARAN MALAYSIA MATHEMATICS Kertas 1 1¼ jam Satu jam lima belas minit

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini adalah dalam dwibahasa .

2. Calon dikehendaki membaca maklumat di halaman belakang kertas soalan ini.

Kertas soalan ini mengandungi 23 halaman bercetak.


MATHEMATICAL FORMULAE RUMUS MATEMATIK

The following formulae may be helpful in answering the questions. The symbols given are the ones commonly used. Rumus-rumus berikut boleh membantu anda menjawab soalan. Simbol-simbol yang diberi adalah yang biasa digunakan.

RELATIONS PERKAITAN

1 nmnm aaa 10 Pythagoras Theorem Teorem Pithagoras 2 nmnm aaa 222 bac

3 nmnm aa )( 11 )()()(

SnAnAP

4

acbd

bcadA 11 12 )(1)( ' APAP

5 Distance / Jarak 13 12

12

xxyym

212

212 )()( yyxx

14 m = – 7 Midpoint / Titik tengah

2,

2),( 2121 yyxx

yx m = –

7 Average speed = Purata laju = 8 Mean = Min = 9 Mean = Min =

distance travelled time taken

jarak yang dilalui masa yang diambil

sum of data number of data

hasil tambah nilai data bilangan data

sum of (classmark × frequency ) sum of frequencies

hasil tambah (nilai titik tengah kelas × kekerapan hasil tambah kekerapan

y - intercept x - intercept

pintasan - y pintasan - x


SHAPES AND SPACE BENTUK DAN RUANG

1 Area of trapezium = 21 × sum of parallel sides × height

Luas trapezium = 21 × hasil tambah dua sisi selari × tinggi

2 Circumference of circle = d = 2 r Lilitan bulatan = d = 2 j 3 Area of circle = r2

Luas bulatan = j2

4 Curved surface area of cylinder = 2 rh Luas permukaan melengkung silinder = 2 jt 5 Surface area of sphere = 4 r2

Luas permukaan sfera = 4 j2

6 Volume of right prism = cross sectional area × length Isipadu prisma tegak = luas keratan rentas × panjang 7 Volume of cylinder = r2h Isipadu silinder = j2t

8 Volume of cone = 31 r2h

Isipadu kon = 31 j2t

9 Volume of sphere = 34 r3

Isipadu sfera = 34 j3

10 Volume of right pyramid = 31 × base area × height

Isipadu pyramid tegak = 31 × luas tapak × tinggi

11 Sum of interior angles of a polygon Hasil tambah sudut pedalaman polygon = ( n – 2 ) × 180o


12 = = 13 = =

14 Scale factor, PAPAk

'

Faktor skala, PAPAk

'

15 Area of image = k2 × area of object Luas imej = k2 × luas objek

arc length circumference of circle


panjang lengkuk lilitan bulatan

sudut pusat 360o

area of sector area of circle


luas sektor luas bulatan

sudut pusat 360o


1. Find the value of and round off the answer correct to three significant figures. Cari nilai , dan bundarkan jawapan betul kepada tiga angka bererti.

A. 9.01

B. 9.02 C. 9.018

D. 9.020

2. Express as a single number Ungkapkan sebagai satu nombor tunggal.

A. 0.00000707

B. 0.0000707

C. 7067000 D. 706700

3.

A. 5.58 × 10-8

B. 4.38 × 10-8 C. 5.58 × 10-7

D. 4.38 × 10-7

4. Given that the diameter of red blood cell of a human is about and

a diameter of one molecul protein is .The difference between the two diameter is Diberi bahawa diameter satu sel darah merah manusia ialah dan diameter satu molekul protein ialah . beza antara dua ukuran diameter itu ialah A. 5.75 710 B. 7.73 710

C. 5.75 210 D. 7.73 210


5. 101012 - 10012

A. 10102 B. 11002 C. 101002 D. 111102

6. State the value of the digit 4 in the number 14325, in base ten Nyatakan nilai bagi digit 4 dalam nombor 14325, dalam asas sepuluh.

A. 25 B. 100 C. 125 D. 500

7. In Diagram 1, PQRST is a regular pentagon and PSUV is a parallelogram. STU is a straight line.

Dalam Rajah 1, PQRST ialah pentagon sekata dan PSUV ialah sisiempat selari. STU ialah garis lurus

Find the value of x.+ y Cari nilai bagi x+ y

A. 144

B. 212

C. 252

D. 288

Diagram 1

S

x

R Q

T

U

V

P

y


8. In Diagram 2, PQRSTU is a regular hexagon. Dalan Rajah 2, PQRSTU ialah sebuah heksagon sekata.

The value of x is Nilai x ialah A. 30 B. 40

C. 50

D. 60

9. In Diagram 3, PTU is a tangent to a circle with centre O at T. Dalam Rajah 3, PTU ialah tangen kepada bulatan berpusat O di titik T. Find the value of y. Cari nilai y.

A. 60 B. 80°

C. 120° D. 140°

Diagram 2

xo

o P

Q R

S

T U

Diagram 3

yo

T U

40o yo P O

110O


10. In Diagram 4, J is the image of K under a certain transformation. Which of the points A,B C or D is the image of P under the same transformation.

Which of the point A,B,C and D is the centre of rotation. Dalam Rajah 4, N ialah imej bagi M di bawah satu penjelmaan. Diantara titik A, B, C dan D yang manakah imej bagi titik P di bawah penjelmaan yang sama.

11. Diagram 5 shows two triangles P and Q drawn on a square grid. Q is the image of M under rotation of 90o

Rajah 5 menunjukkan dua segitiga P dan Q yang dilukis pada grid segiempat sama. Q ialah imej bagi P di bawah putaran 90o

8

Q

P

4

2

6

0 2 4 6 8 x

•

•

B •

• K

•J

C

A •P

•

• D

Diagram 4

Diagram 5

y


State the centre of rotation. Nyatakan pusat putaran

A. ( 5, 3 )

B. ( 6, 4 ) C. ( 5, 5 ) D. (3, 5 )

12 In Diagram 7, given that JK = JM. Find the value of cos yo Dalam Rajah 7, diberi bahawa JK = JM. Cari nilai kos yo

A -0.5299

B 0.5299

C 58o D 122o

J

K

L

M

64o

yo

Diagram 7


13. Which of the following represent the graph of y = sin x for 0o < x < 180o Antara yang berikut, yang manakah mewakili graf y = sin x for 0o < x < 180o A. B.

C.

D.

90o 180o O

1

x

-1

y

90o 180o O

1

x

-1

y

90o 180o O

1

x

-1

y

90o 180o O

1

x

-1


14. Diagram 8 shows a cuboid with a horizontal base ABCD Rajah 8 menunjukkan sebuah kuboid dengan tapak ABCD What is the angle between the line DF and plane EFGH? Apakah sudut di antara garis DF dengan tapak EFGH?

A. FDB B. FHD

C. FDH D. HFD

15. Diagram 9 shows a flag pole DC. The points A, B, and C lie on a horizontal plane. The angle of depression of A from D is 40o. Rajah 9 menunjukkan tiang bendera DC. Titik A, B, dan C terletak di atas satah Mengufuk. Sudut tunduk titik A dari D ialah 40o Find the angle of elevation of D from B

Hitungkan sudut dongakan D dari B

Diagram 8 A B

D C

E F

H G

A •

• B C

10 m

4.4 m

•

Diagram 9

D


A 37.0o B 36.95o C 53.3o D 53.07o

16. In Diagram 10, A,B and C are three points on horizontal ground. BE and CD are two

pine trees. Given that the angle of elevation of point D from A and from B are 30o and 62o respectively. Dalam Rajah 10 A,B dan C adalah tiga titik terlelak atas satah mengufuk. BE dan CD adalah dua batang pokok. Diberi sudut dongakan titik D dari A dan dari B ialah 30o

dan 62o

Calculate the height of pjne tree, BE

Kirakan tinggi pokok pine, BE A. 4.16

B. 7.2

C. 8.09

E. 11.

B C

D

E 6 m

A Diagram 10


17. In Diagram 11 P, Q and R are three points on horizontal ground, and P lies to the North of R. Given that the distance of PR = PQ.

Dalam Rajah 11, P,Q dan R adalah tiga titik terletak pada satu satah ufuk.P terletak di utara R. Diberi jarak PR =PQ.

Find the bearing of R from Q. Cari bearing R dari Q

A. 205O

B. 215O

C. 270O D. 285O

18. In Diagram 12, N is North Pole, S is the South Pole and O is the centre of the earth. R is the centre of the circle of latitude 300N. The longitude of Q is 500 E.

Dalam Rajah 12, N ialah Kutub Utara,S ialah Kutub Selatan dan O ialah pusat bumi. R ialah pusat bulatan latitude 30oU. Longitud Q ialah 50o T

Find the position of P. Cari kedudukan P

N

S

O P

R

Q

700

Diagram 12

130O

P

Q

R

Diagram 11


A.

B.

C.

D.

19 Express as a single fraction in its simplest form.

Ungkapkan sebagai pecahan tunggal dalam sebutan teringkas. A. B. C. D.

20.

A.

B. C. D.


21. Given that . The value of m is Diberi . Nilai m ialah

A.

B.

C. E. 1

22. Given fd

d 33

, express d in term of f

Diberi fd

d 33

nyatakan d dalam sebutan f

A. 3

9

f

d

B. 33

fd

C. f

d

3

3

fd

39

23. = A -8 B -6

C

D

D


24. ( =

A. 4p2

B. 16p2 C. 4p4

D. 16p4 25 List all the integers x which satisfy both the inequalities Senaraikan semua integer x yang memuaskan kedua-dua ketaksamaan

A. -1, 0, 1, 2 B. -1, 0, 1, 2, 3

C. -2, -1, 0, 1, 2 D. -2, -1, 0, 1, 2, 3

26. Which number line represents the solution of the simultaneous linear

inequalities )2(2109 pp and 12

2 p ?

Garis nombor manakah yang mewakili penyelesaian bagi ketaksamaan

)2(2109 pp dan 12

2 p ?

A.

B. C. D.

• •

0 1 -1 -2 2 3 -3

0 1 -1 -2 3

•

2 -3

°

0 1 -1 -2 2 3 -3

• •

0 1 -1 -2 2 3 -3

° °


27. Diagram 13 shows a set of six pieces of data where m represents an integer Rajah 13 menun jukkan sekumpulan enam data dimana m mewakili integer. The mode of the data is 2 and the median is 3. Two new pieces of data 5 and 7 were

put into the set. Calculate the mean for those eight pieces of data Mod bagi data tersebut ialah 2 dan median ialah 3. Dua data baru bernilai 5 dan 7

dimasukkan ke dalam kumpulan data itu. Kirakan min bagi lapan data itu

A. 3.50

B. 3.80 C. 3.87

D. 3.88

28. Table 1 shows a frequency of the score obtained by 20 students in a mathematics game

competition Jadual menunjukkan kekerapan skor yang diperolehi oleh 20 orang pelajar dalam satu

pertandingan permainan matematik

Score 0 1 2 3 4 5 6

Number of students 3 4 7 1 3 1 1

From the table, find mode. Dari jadual itu , cari mod.

A. 1

B. 2

C. 3

D. 7

Diagram 13

2, 2, 5, m, m, 2

Table 1


29. Table 2 shows a weight of a group of tourist from Midle East. Jadual 2 menunjukkan berat sekumpulan pelancong dari Timur Tengah.

Weight(kg) Frequency 15 – 17 3 18 – 20 2 21 – 23 5 24 – 26 7 27 - 29 4

Midpoint of modal class is Titik Tengah bagi kelas Mod ialah

A. 11.5 B. 19

C. 22 D. 25

30. Diagram 14 shows . State the value of n and k.

Rajah 14 menunjukkan Nyatakan nilai n dan nilai k.

A. n = 3, k = 2

B. n =3, k = -2 C. n = 2, k = - 2 D. n = - 2, k = 2

x

y

0

(0,4)

(k ,0)

•

•

Table 2

Diagram 14


31. Which of the following Venn diagrams represent such that the universal set ?

Antara berikut gambarajah Venn yang manakah mewakili dengan keadaan Set semesta ?

A.

B. C.

D. 32. Diagram 15 shows a Venn diagram showing the element of universal set , ξ, set M and set N

Rajah 15 menunjukkan gambarajah Venn dengan bilangan unsur dalam set,ξ, Set M dam set N

Find Cari

Diagram 15

ξ M N

2

3

5 1

M N

N M

M N

M N


A. 3

B. 8 C. 9 D. 10

33. Diagram 16, shows a straight line PQ

Rajah 6, menunjukkan garis lurus PQ The coordinate Q is Koordinat Q ialah A. B. C. (-3,0) D. (0, -3)

34. Which of the following equation has the same gradient with straight line y = 2x + 5 Di antara persamaan berikut yang manakah mempunyai kecerunan yang sama dengan Garis lurus y = 2x +5 A. 2x + y = 5 B. x + 2y = 5 C. y = 7 -2x

D. y – 2x = 7

Diagram 16

x

y

Q • O

P


35. Diagram 17 shows a collection of letter cards. Rajah 17 menunjukkan suatu koleksi kad huruf.

A card is chosen at random from this collection. State the probability that the card chosen is a card with letter H. Sekeping kad dipilih secara rawak daipada koleksi ini. Nyatakan kebarangkalian bahawa kad yang dipilih ialah kad huruf H

A.

B.

C. D.

36. Given that Sets . If one integer is chosen at random from sets S,

the probability that the integer has a number that less than 6 is . Diberi bahawa sets . Jika satu integer dipilih secara rawak

daripada set S, kebarangkalian bahawa integer itu mempunyai nilai yang lebih kecil daripada 6 ialah

The value of n is, Nilai n ialah,

A. 10

B. 12

C. 15 D. 18

E A R T H H O U R

Diagram 17


37. Given that p varies directly as the square of q and the cube root of r , and p = 32 when q = 2 and r = 8. Find the relation between p,q and r. Diberi bahawa p berubah langsung dengan kuasa dua q dan dan punca kuasa tiga r, dan p =32 apabila q = 2 dan r = 8. Cari hubungan antara p, q, dan r

A.

B. C. D. 38. Table 3 shows the values of variables x and y. If x is varies inversely as y and

pq = 3, calculate the value of m Jadual 3 menunjukkan nilai-nilai pembolehubah x dan y. Jika x berubah songsang

dengan y dan pq = 3, kirakan nilai m

x p 12 y q m

A. -9

B.

B. 4

C. 9

39. Given that ( 1 6 )

113 n

= (-3 4). Find n

Diberi bahawa ( 1 6 )

113 n

= (-3 4). Cari n

A. -2 B. 2

C. 4

D. 10

Table 3


40 Given that

3012

23

= k

34

Diberi bahawa

3012

23

= k

34

Find k. Cari k

A. 1

B. 2

D. 4 C. 8

END OF QUESTION PAPER KERTAS SOALAN TAMAT


INFORMATION FOR CANDIDATES MAKLUMAT UNTUK CALON

1. This question paper consist of 40 questions

Kertas soalan ini mengandungi 40 soalan

2. Answer all questions Jawab semua soalan

3. Each question is followed by four alternative answers, A, B, C and D. For each

question ,shoose one answer only. Blacken your answer on the objective answer sheet provided. Tiap-tiap soalan diikuti dengan EMPAT pilihan jawapan ,iaitu A,B,C dan D. Bagi setiap soalan, pilih satu jawapan sahaja. Hitamkan jawapan anda pada kertas jawapan objektif yang disediakan

4. If you wish to change your answer, erase the blackened mark that you have made.

Then blacken the new answer. Jika anda hendak menukar jawapan, padamkan tanda yang telah dibuat. Kemudian Hitamkan jawapan yang baru

5. The diagrams in the questions provided are not drawn to scale unless stated.

Rajah yang mengiringi soalan tidak dilukis mengikut skala kecuali dinyatakan.

6. A list of formulae is provided on pages 2 to 4. Satu senarai rumus disediakan di halaman 2 hingga 4

7. A booklet of four- figure mathematical tables is provided

Sebuah buku sifir matematik empat angka disediakan .

8. You may use a non-programmable scientific calculator. Anda dibenarkan menggunakan kalk


JUJ 2010

SCHEME OF MARKING PAPER 1 AND 2 Modul

NO. OF QUESTI

ON ANSWER

NO. OF QUESTIO

N ANSWER

1 B 21 C

2 C 22 D

3 C 23 D

4 B 24 A

5 B 25 C

6 B 26 D

7 C 27 D

8 D 28 B

9 B 29 D

10 C 30 A

11 B 31 D

12 A 32 C

13 B 33 A

14 D 34 D

15 D 35 B

16 A 36 C

17 A 37 B

18 B 38 B

19 B 39 A


20 B 40 B

No. Scheme Mark Total

Marks 1. (a)

(b)

1 2

3

2. 0352 2 pp 0312 pp

21 , -3

1 1

1, 1

4

3. 63 yx or equivalent 3x = 15 OR

29

231

31

313)1(2

1yx

(2)

5x

1 1 1 1

4

P

R

Q

R

Q P


31

y

4. (a) statement

(b) Implication 1 : If x is an even number then x is divisible by 2 Implication 2 : If x is divisible by 2 then x is an even number (c) 34 nn , n = 1, 2, 3, 4, . . .

1 1 1 2

5

5. (a) MON

(b) 1612tan 1

087.36 or '5236o

1 1 1

3

6. (a) 4k -3(2) = 0

23

k

(b)

55

1234

nm

55

4231

)2(3)1(41

m = 2, n = -1

1 1 1 1 1 1

6

7. (a) 28

7222 or 14

7222

21

287222 + 3( 14

7222

21

) + 28 + 28 + 28

392

(b) 228722

or 214722

21

228722

- 3( 214722

21

)

1540

1 1 1 1 1 1

6


8.

10121021

105722

21 2

10121021

+ 105722

21 2

992.86 or 7

6950 or 76992

1 1 1 1

4

9. (a) {(E,1), (E,2), (E,3), (E,4), {(R,1), (R,2), (R,3), (R,4), {(K,1), (K,2), (K,3), (K,4)} (b) (i) {{(E,2), (R,2), (K,2)}

123

(ii) {{(E,1), (E,2), (E,3), (E,4), (R,3), (K,3)}

126

2 1 1 1 1

6

10. (a) 2 (b) mSR = 2 2 = 2(6) + c or c = -10 y = 2x - 10 (c) y-intercept = -10

1 1 1 1 1

5

11. (a) 4

(b) 083216

-2

(c) 1726162181216 u

u = 20

1 1 1 2 1

6

12. (a) m = 10 1 http://edu.joshuatly.com/ http://exammy.com/

p = 5 (b) uniform scale and in correct direction All points correctly plotted *if only 7 or 8 points correctly plotted, give 1 mark Smooth and continuous curve (c) (i) 4.5 ≤ y ≤ 5.5 (ii) 2.30 ≤ x ≤ 2.40 , -0.80 ≤ x ≤ -0.90 (d) y = -5x + 14 Straight line y = -5x + 14 drawn on the graph 2.45 ≤ x ≤ 2.55

1 1 2 1 1

1, 1 1 1 1

12

13. (a) (i) (3, 4) (ii) (6, -3)

(iii) (6, 3) (b) (i) U : rotation 90o clockwise about (1, 5) T : enlargement of scale factor 2 at (4, 3) (ii) 22 x 12 22 x 12 – 12 36

1 1 1 3 3 1 1 1

12

14. (a) Class

interval Selang Kelas

Frequency Kekerapan

Mid point Titik

tengah

Upper Boundary Sempadan

Atas

Cumulative Frequency Kekerapan Longgokan

5 – 7

3

6

7.5

3

8 – 10

5

9

10.5

8

11 – 13

9

12

13.5

17

14 – 16

10

15

16.5

27

17 – 19

8

18

19.5

35

20 – 22

4

21

22.5

39

23 – 25

1

24

25.5

40

All midpoints are correct All upper boundaries are correct All cumulative frequencies correct

1 1


*allow 2 mistakes for 1 mark (b)

14810953)124()421()818()1015()912()59()36(

14.33 (c) uniform scale and in correct direction All points correctly plotted *if only 7 or 8 points correctly, give 1 mark Smooth and continuous curve (d) accept any correct information.

2 2 1 1 2 1 1

12

15. (a) The shape seem correct with rectangle EFGH and IJKL EH < IL < EF Measurement 0.2 cm and all angles at vertices of rectangles = 90o 1 (b) (i) The shape seem correct AE = EH < DL < IH Measurement 0.2 cm and all angles at vertices of rectangles = 90o 1

1 1 1 1 1 2


(ii) The shape seem correct with rectangles CDLK, ABFE, IJKL EF is joined by dotted line. AE < DL Measurement 0.2 cm and all angles at vertices of rectangles = 90o 1

1 1 1 2

12

16. (a) 100 W (b) 38cos60)3080( 2364

(c) 60

4380 or 73

60

4380 38

35oN (d) 90 – 38 or 52 60)3890(2

90060)3890(2

6 hours 56 minutes or 6.933 hours

2 2 1 1 1 1 1 1 1 1

12


14 (c). 12(b)

7.5 13.5 16.5 19.5 25.5 22.5 10.5

5

15

10

20

25

30

35

40


10

25

20

15

5

30

35

y

-2 -1 5 4 3 2 1

-5


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Modul JUJ Tahun 2010