1

PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI

MATHEMATICS

FORM 3

MODULE 9

PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMI

LINEAR EQUATIONS II

MINISTRY OF EDUCATION MALAYSIA

2

MODULE 9: LINEAR EQUATIONS II Arahan:

1. Modul ini mengandungi tiga puluh lima soalan. Semua soalan adalah dalam

bahasa Inggeris.

2. Modul merangkumi tujuh konstruk yang diuji

K1 - Memahami soalan dalam bahasa Inggeris K3 - Memahami istilah matematik dalam bahasa Inggeris K5 - Menguasai konstruk pengetahuan K6 - Menguasai konstruk kefahaman K7 - Menguasai konstruk kemahiran K8 - Mengungkapkan idea/informasi dalam bahasa Inggeris K10 - Memahami pengajaran dan pembelajaran dalam bahasa Inggeris

3. Murid hendaklah menulis maklumat diri dalam kertas jawapan objektif disediakan. Murid juga perlu memastikan maklumat konstruk, nombor soalan dan jumlah soalan seperti yang dibaca oleh guru di dalam ruangan disediakan dalam kertas jawapan objektif sebelum ujian.

4. Bagi soalan objektif, anda perlu menandakan jawapan dengan menghitamkan

pilihan jawapan pada pilihan jawapan A , B , C atau D pada kertas jawapan objektif.

Contoh:

Antara berikut, yang manakah haiwan?

A. Pokok B. Kambing C. Kereta D. Pen

5. Untuk soalan subjektif, jawapan hendaklah ditulis pada kertas berasingan

yang disediakan oleh guru.

6. Jawab semua soalan.

Modul ini mengandungi 15 halaman bercetak

D A B C E

3

1 A linear equation in two variables is an equation involving two variables raised to

the power of 1. Which of the following is not a linear equation in two variables?

2 The value of y in the equation 13 += xy can be calculated by substituting a

given value of x in the equation. Example: Which of following is true when 4=x ?

A 97 =+ kh

B 02 =+ yx

C 52 += yx

D yx 635 =+

A ( )143 +=y

B ( ) 143 +=y

C 1)(34 +=y

D ( ) 123 +=y

When 2=x 13(2) +=y

4

3 Simultaneous linear equations in two variables contain the same set of variables.

The variables are raised to the power of 1.

Which of the following is a pair of simultaneous linear equations in two variables?

4 In the linear equation x,yx 732 =+ and y are known as variables. What are the variables in equation 1134 =+ qp ?

5 When writing a linear equation in two variables, we represent the two unknowns

with two suitable letters.

Which of the following is a linear equation in two variables?

A xy

yx325

−=

=+

B 53223=−

=−

mnmnm

C 223

02

=+

=−

qpqp

D 6353

=−

=+

trsr

A x and y

B x and p

C p and q

D p and y

A 112 =p

B 24 =−nm

C xx =+53

D rqp =−4

5

6 An equation involving variables raised to the power of 1 which are connected by

“+” or “─” is known as a

7 The pair of equations shown are known as 8 Quantities which do not have a fixed value are known as

A cubic equation

B linear equation

C quadratic equation

D simultaneous equation

A linear equations

B quadratic equations

C simultaneous equations

D simultaneous linear equations

A coefficents

B constants

C equations

D variables

8343

=+

=−

baba

6

9 The method of solving a pair of simultaneous linear equations shown above is

known as

10 A value that satisfies a linear equation is known as a

A coefficient

B variables

C solution

D factor

A elimation method

B substitution method

C factorisation method

D trial and improvement method

a – b = 3 ----------

2a – 4b = 4 -------

From , a = 3 + b -------

2(3 + b) – 4b = 4

6 + 2b – 4b = 4

6 – 2b = 4

b = 1

Then from , a = 3 + 1

a = 4

1

2

3

1 3

7

11 Which of the following is a linear equation in two variables? 12 Which of the following pairs of equations are simultaneous linear equations?

A

22362−=+

=+

xyx

B

12282

=+

=+

dcba

C 6=+

=

yxxyy

D

1536=+

=+

zxyx

13 Which of the following pairs of simultaneous linear equations is best solved using

the substitution method?

A

14537146

=+

−=

baba

B

155628=+

−=

yxyx

C

1553823

=+

=+

yxyx

D

4361754

=+

=−

baba

A 15=xy

B 85 =+x

C 12=+ yx

D 182 =+xy

8

14 A pair of simultaneous linear equations is shown below:

1335132

=−

=+

yxyx

To eliminate y,

A add the two equations

B multiply the two equations

C divide the second equation by the first equation

D subtract the first equation from the second equation

15 Which of the following is not a linear equation?

A 832 =+x

B 7=+ yx

C 1242 =+xy

D yx =+ 32

16 Sharifah spent RM 55.00 to buy x kg of ciku and y kg of papaya. The ciku costs

RM 5.00 per kg and the papaya costs RM 3.00 per kg. Write a linear equation in two variables for the situation above.

A 55=+ yx

B 5553 =+ yx

C 5535 =+ yx

D 55)8( =+ yx

9

17 Given that 102 =− kh , and 8=h , then 18 723 =+ yx and xy 23 −= are a pair of simultaneous linear equations. Which of the following is true? 19 During the Chinese New Year season, Mr. Choo bought x boxes of L-sized

oranges at RM 30 per box and y boxes of M-sized oranges at RM 25 per box for RM 120.00.

If he bought a total of 5 boxes of oranges, write a pair of simultaneous equations for the situation above.

A ( ) 1082 −=k

B ( )8210 −=k

C ( )8210 +=k

D ( )8210 −−=k

A 7)2(33 =−+ xx

B 7)2(33 =++ xx

C 72x)2(33 =++x

D 7)22(33 =−+ xx

A 1203025

5=+

=+

yxyx

B 1202530

5=+

=+

yxyx

C

52530120

=+

=+

yxyx

D

53025120

=+

=+

yxyx

10

20 Equations and are simultaneous linear equations Which of the following is an incorrect step in solving the equations? 21 Given that 22 =− yx , find the value of x when 12=y

22 Part of the solution of the simultaneous linear equations 65 −=+ nm and

223 =+ nm is as follows: What is the number in the box?

A -14

B -10

C 10

D 14

A Subtract equation from equation

B Add equation to equation

C Multiply equation by two

D Divide equation by two

A 12

B 7

C - 5

D - 10

10m + 2n = -12 3m + 2n = 2 7m =

2x + y = 4 -------------- 4x – y = 16 -------------

1

2

1 2

2

2

1

1

1 2

11

23 An equilateral triangle PQR is shown below.

Calculate the value of x.

24 Given xy 35 −= and 102 −= xy , find the value of y . 25 Given 213 =−mf and 246 =+mf , find the value of mf − .

A 8

B 16

C 32

D 64

A -4

B -1

C 1

D 3

A -11

B -6

C 5

D 11

3y

48

4x + y

P

QR

12

All questions from number 26 to number 30 must be answered in words. 26 Why is the equation rpr 783 =− not a linear equation? Answer: 27 State two characteristics of linear equations in two variables. Answer: 28 Give two characteristics of simultaneous linear equations. Answer: 29 Explain how to use the elimination method to eliminate x from the given pair of

simultaneous linear equations. 73 =+ yx ---------- 192 =+ yx ---------- Answer:

1

2

13

30 Explain the meaning of “solution” of a pair of simultaneous linear equations. Answer: From Question 31 – 35, the teacher reads the questions to the students. Students choose the correct answer. 31

32

A

423645

=+

=+

yxyx

B

423645

=+

=+

yxxy

C

43645

=+

=+

yxzx

D

43645

=

=+

xyyx

A 3

B 5

C 10

D 15

14

33 x – 3y = 1 ------------ 1

2x – y = -1 ----------- 2

A yx 31+=

B 136 =−− xx

C 132(1 −=−+ yy)

D 11)32( −=−+− yy

34 35

END OF QUESTION PAPER

A 8

B _ 8

C 47

D _ 47

A 1

B 2

C 4

D unlimited

16 17

18

19

20

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

21 22

23

24

25

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

26 27

28

29

30

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

Tahun/ Tingkatan : 3 Mata Pelajaran: MATEMATIK

GUNAKAN PENSIL 2B ATAU BB SAHAJA. TENTUKAN TIAP-TIAP TANDA ITU HITAM DAN MEMENUHI KESELURUHAN RUANG. PADAMKAN HINGGA HABIS MANA-MANA TANDA YANG ANDA UBAH

SILA HITAMKAN JAWAPAN DI BAWAH MENGIKUT HURUF JAWAPAN YANG ANDA PILIH

KEMENTERIAN PELAJARAN MALAYSIAKERTAS JAWAPAN OBJEKTIF

Ujian Diagnostik

5152

53

54

55

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

5657

58

59

60

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

4647

48

49

50

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

4142

43

44

45

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

31 32

33

34

35

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

36 37

38

39

40

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

1 2

3

4

5

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

6 7

8

9

10

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

11 12

13

14

15

A B C D E

A B C D E

A B C D E

A B C D E

A B C D E

Konstruk No. Soalan Jumlah Soalan

Bilangan Soalan Gagal Dijawab

Kegunaan Guru

K1

K3

K5

K6

K7

K8

K10

1-5

6-10

11-15

16-20

21-25

26-30

31-35

5

5

5

5

5

5

5

1

9

2

3

10

4

5

6

7

8

Nama Pelajar:

Nama Sekolah: Modul: 9