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SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERTENGAHAN TAHUN TINGKATAN LIMA 2008

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian Soalan MarkahPenuh Markah

Diperoleh

A

1 3

2 4

JANGAN BUKA KERTAS SOALAN INI SEHINGGA DIBERITAHU

1. Kertas soalan ini mengandungi dua bahagian : Bahagian A dan Bahagian B. Jawab semua

soalan daripada Bahagian A dan empat soalan dalam Bahagian B

3 4

4 4

5 5

6 6

7 6

8 5

9 6

10 5

11 4

B

12 12

13 12

14 12

15 12

16 12

Jumlah

Kertas soalan ini mengandungi 23 halaman bercetak dan 1 halaman tidak bercetak

SULIT 1449/2 Matematik Kertas 2 Mei 2008

2 12 jam

1449/2

1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelah SULIT

NAMA :

TINGKATAN :

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For xaminer’s

Use

Section A [52 marks ]

Answer all questions in this section.

1 The Venn diagram in the answer space shows sets P , Q and R such that the universal set, RQ P .

On the diagram in the answer space, shade

(a) the set Q P .

(b) the set ( P Q ) R . [3 marks ]

Answer : (a) (b)

2 Calculate the value of v and of w that satisfy the following simultaneous linear equations:

112 wv

73 3 2

wv

[4 marks ]

Answer :

P Q

R

P Q

R

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For Examiner’s

Only 3 Using factorisation, solve the following quadratic equation:

2 2

13 x

x x

[4 marks ] Answer :

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For xaminer’s

Use 4 Diagram 1 shows a right prism with a horizontal rectangular base PQRS . VUQR is a trapezium.

Identify and calculate the angle between the plane QWR and the base PQRS.

[4 marks ]

Answer :

T

U

W

V

P

Q

R

S

8 cm

6 cm

12 cm

5 cm

DIAGRAM 1

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For Examiner’s

Only 5 In Diagram 2, straight line TU is parallel to straight line VW and O is the origin .

The equation of straight line VW is 02552 y x . Find: (a) the equation of the straight line TU. (b) the x-intercept of the straight line TU.

[5 marks ]

Answer:

(a)

(b)

DIAGRAM 2

y

x

W

U ( 1,5)

V

T O

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For xaminer’s

Use 6 Diagram 3 shows two sectors of circle ORQ and OPS with centre O.

By using = 7

22 , calculate

(a) the perimeter, in cm, of the whole diagram.

(b) the area, in cm 2, of the shaded region.

[ 6 marks ]

Answer :

(a)

(b)

O P

Q

R

S

150° 7 cm

12 cm

DIAGRAM 3

7 cm

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For Examiner’s

Only 7 (a) State whether the following statements are true or false.

(i) 2.0 2 1

and3 aaaa

(ii) Number 5 is an odd number or number 2 is a prime number.

(b) State the antecedent and consequent of the implication:

(c) Complete the following argument.

Premise 1 : If y > 3, then 5 y > 15.

Premise 2 : _________________________________________

Conclusion : 5 y > 15.

[6 marks ] Answer :

(a) (i)

(ii)

(b) Antecedent : ______________________________

Consequent : ______________________________

(c) Premise 2 : ________________________________________________

If y is less than zero, then y is a negative number.

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For xaminer’s

Use 8 (a) Complete the following statement using the quantifier “all” or “ some”, to make it a false statement.

(b) Write down two implications based on the following statement:

(c) Make a general conclusion by induction for the sequence of numbers 2, 14, 34, …

which follows the following pattern.

2 = 4(1) 2 2

14 = 4(2) 2 2

34 = 4(3) 2 2

62 = 4(4) – 2

… = ………..

[ 5 marks ] Answer :

(a) ____________ polygons have six sides.

(b) Implication 1:

____________________________________________________________

Implication 2 :

_____________________________________________________________

(c) _____________________________________________________________

______________________________________________________________

____________ polygons have six sides.

x > y if and only if – x < y

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For Examiner’s

Only9 (a) The inverse matrix of

45

23 is p

35

4 q

Find the value of p and of q. (b) Hence, using matrices, calculate the value of x and of y that satisfy the following

simultaneous linear equations :

3 x – 2 y = 8 5 x – 4 y = 13

[6 marks ]

Answer :

(a)

(b)

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For xaminer’s

Use 10 Diagram 4 shows the speed-time graph of a particle for a period of 50 seconds.

(a) Calculate the rate of change of speed, in ms -2, in the first 10 seconds. (b) Calculate the value of u, if the total distance traveled in the last 40 seconds is 750 m.

[5 marks ] Answer :

(a)

(b)

Speed (ms -1)

Time (s) 0

5

10 30

20

50

DIAGRAM 4

u

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For Examiner’s

Only 11 Diagram 5 shows a solid formed by joining a prism to a right pyramid. Trapezium

ABGF is the uniform cross-section of the prism. FG = GH = 7 cm. The height of the pyramid is 6 cm.

Calculate the volume, in cm 3, of the solid.

[ Use = 722 ]

[4 marks ]

Answer:

DIAGRAM 5

8 cm

11 cm A B

C D

E

F G

H

V

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For xaminer’s

Use Section B

[48 marks ]

Answer four questions from this section.

12 (a) Complete Table 1 in the answer space for the equation y = – 2 x2 + 4 x + 16.

x – 4 – 3 – 2 – 1 0 1 2 3 4 y –32 h 0 10 16 18 k 10 0

Calculate the values of h and of k .

[2 marks ]

(b) For this part of the question, use the graph paper on pag 15 . You may us flexible curve ruler.

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 y = – 2 x2 + 4 x + 16 for – 4 ≤ x ≤ 4.

[4 marks ] (c) From your graph, find

(i) the value of y when x = 2.2

(ii) the value of x when y = 5 [3 marks ]

(d) Draw a suitable straight line on your graph to find all the values of x which satisfy the equation 2 x2 + x – 11 = 0 for – 4 ≤ x ≤ 4. State these values of x.

[3 marks ]

Answer:

(a) h = …………………………

k =…………………………

(b) Refer graph on page 15

(c) (i) y = ………………

(ii ) x = ……………….

(d) x = …………………………

TABLE 1

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For xaminer’s

Use 13 (a) Transformation T is a translation

3

2 and transformation P is an anticlockwise

rotation of 90 o about the centre (5, 0).

State the coordinates of the image of point (9, 4) under each of the following

transformations:

(i) P,

(ii) TP ,

(iii) T 2

[4 marks ]

(b) Diag