PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPP

MATHEMATIC

FORM 5

MODUL 2

PPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPPSMIPP

GRAPH OF FUNCTION II

KEMENTERIAN PELAJARAN MALAYSIA

2

GRAPH OF FUNCTION II Arahan :

1. Modul ini mengandungi tiga puluh enam soalan. 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 mengisikan 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. Soalan 31 hingga 36 akan dibaca oleh guru. Murid perlu mendengar dengan teliti dan

menjawab di dalam kertas jawapan objektif.

7. Jawab semua soalan.

Modul ini mengandungi 21 halaman bercetak

D A B C E

3

Answer all question given. 1. Which of the following represents a straight line graph? 2. ‘y > 2x ’ means ‘ y is greater than two times x’. Which of the following represents ‘y is

greater than three times x’?

A y ≤3x

B y < 3x

C y >3x

D y ≥3x

3. For a quadratic function in the form of y = ax2+bx+c, the value of c is always the y-

intercept of the graph. What is the y-intercept of the graph y = 2x2+3x+5?

A 2

B 3

C 5

D -5

O O

O O

y y

y y

x x

x x

A C

B D

4

4. Diagram shows a graph with a maximum point.

Which of the following graphs has a maximum point?

O

y

x

O O

O O

y y

y y

A C

B D

x x

x x

5

5. Diagram shows the graph y = x2. Which of the following shows the graph of y = 3x2?

O

y

x

A y

Ox

C

O x

y B

O

y

x

6

6. Diagram shows a straight line graph. What is P?

A x-intercept

B y-intercept

C gradient

D origin

7. In the equation ax + by = c, a and b are known as ……

A unknowns

B constants

C variables

D coefficients

8. Which of the following is a cubic function?

A y = x

B y = x2

C y = 3x3

D y = x1

O x

y

P

7

9. What is the type of graph shown in the diagram?

A Cubic graph

B Linear graph

C Quadratic graph

D Reciprocal graph

10. Diagram shows the graph xay = and the line PQ.

Which of the points A, B or C is the intersection point of the line PQ and the

graphxay = ?

x

y

Q

P

A

B

C

·· ·

O

y =xa

O

y

x

8

11. Which of the following is a reciprocal function?

A y = 2x2

B 2xy =

C x

y 2−=

D y = x3 12. 3−= nxy is a quadratic function. What is the value of n?

A 1

B 2

C 3

D -3

13. Which of the following represents the graph of y = ax3 + b?

O

O

O

y

yy

y

O

A C

B D

x

x

x

x

9

14. What is the inequality which represents the shaded region?

A y > x

B y ≥ x

C y < x

D y ≤ x

15. Diagram shows a graph of a function.

Which of the following is the equation of the graph?

A y = x2

B y = 2x3 + 3

C y = x2 + x + 12

D y = -x2 + x + 12

x

y

O

y

x O

y = x

10

16. Diagram shows the graph of 62 −+= xxy . What is the value of y when x = 0?

A -6

B -3

C 2

D 6

17. Diagram shows the graph nxy 2−= . State the value of n.

A 2

B 1

C -1

D -2

-3

-6

2 O x

y

y

x O

11

18. Which of the following is true for the function y = 2x2 + 5 when x = - 3?

A y = 2(9) + 5

B y = 2(6) + 5

C y = 2(-6) + 5

D y = 2(-9) + 5

19. Which of the following graphs shows the function of y = (x+4)(x-1) ?

-1 O 4 x

y

y

-1 O 4 xx

-4 O 1

y B

x

y

- 4 O 1

A C

D

12

20. Which of the following shaded regions satisfies the inequalities y ≤ 4, x ≤ 4 and x + y > 4?

21. Table shows the value of x and y for the graph y = x2 + 2x -1.

X 2 3 4 Y 7 n 23

Calculate the value of n.

A 11

B 14

C 15

D 28

A

O

x = 4 y = 4

x + y = 4

y

x O

x = 4 y = 4

x + y = 4

y C

x

O

x=4 y = 4

x + y=4

y D

x O

x=4 y = 4

x + y = 4

y B

x

13

0

22. Diagram shows the graph y = (x – 2)(x + 3).

Find the value of k.

A 3

B 2

C -2

D -3

23. Diagram shows the graph y = - xm, where m is an integer.

Find the value of q.

A -9

B -6

C 6

D 9

x ●

y

k O

P (3,q) .

y

x

14

●

24. Diagram shows the graph y = -2x3 – 12.

Find the value of k.

A -18

B -14

C -12

D -10

25. Diagram shows the graph of y = x2 – 5x – 3.

Find the equation of a straight line to be drawn on the graph to solve the equation x2 – 7x – 2 = 0.

A y = 2x – 1

B y = 2x + 1

C y = -2x + 1

D y = -2x – 1

y

x O

y

(-1,k)

x O

15

26. Statements below describe the steps to draw a graph.

I Construct a table of values for a chosen range.

II Draw a smooth curve to join the points.

III Draw the x-axis and y-axis with suitable scales.

IV Plot the x and y values as coordinate pairs on the Cartesian plane.

Explain the steps to draw the graph. A I, II, III and IV

B III, I, IV and II

C I, III, IV and II

D III, I, II and IV

27 Diagram shows a shaded region for an inequality.

Describe the shaded region.

A x is greater than -2

B x is less than -2

C y is greater than -2

D y is less than -2

-2

y

x

4

2

O

16

28. Describe a quadratic function.

A The highest power of the independent variable is 1 and the shape of the graph is

parabolic.

B The highest power of the independent variable is 2 and the shape of the graph is

parabolic.

C The highest power of the independent variable is 2 and the shape of the graph is

hyperbolic.

D The highest power of the independent variable is -1 and the shape of the graph is

hyperbolic.

29. Describe the steps to shade the region that satisfies y > x + 1.

I Draw a solid line for the equation y = x + 1.

II Draw a dashed line for the equation y = x + 1.

III Shade the region below the line y = x + 1.

IV Shade the region above the line y = x + 1.

A I and III

B I and IV

C II and III

D II and IV

17

30. Diagram shows a shaded region.

Describe the steps to obtain the shaded region.

I Shade the region below the line y = x + 4

II Shade the region above the line y = x + 4

III Shade the region on the left side of the line x = 2

IV Shade the region on the right side of the line x = 2

V Shade the region above the line y = 4

A I, III and V

B I, IV and V

C II, III and V

D II, IV and V

y

x

y = x + 4

y = 4

x = 2 - 4 O

18

From Question 31 – 35, the teacher reads the questions to the students. Students choose the correct answer

31. 32.

A x + y ≤ 20

B x + y < 20

C x + y ≥ 20

D x + y > 20

y

x

y

x

x

x

y

y

O

O O

O

A C

B D

19

33.

A y = 3x – 4

B y = 3x + 4

C y = 3(x + 4)

D y = 43+

x

34.

A 2 B 4 C 6 D 8

35.

A 60 + 9x2

B 60 + 6x2

C 60 - 9x2

D 60 - 6x2

3x cm

10 cm

6 cm

20

36.

END OF QUESTION PAPER

A y

xO

7

7

y

xO

7

7

C

y

xO

7

7

B y

xO

7

7

D

Tahun/ Tingkatan : 5 Mata Pelajaran: MATHEMATIC

Nama Pelajar:

Nama Sekolah: Modul:

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

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

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 - 36

5

5

5

5

5

5

6

1

9

2

3

10

4

5

6

7

8