2008 F5 Mid Year SBP Math K2

8/17/2019 2008 F5 Mid Year SBP Math K2

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SEKTOR SEKOLAH BERASRAMA PENUHBAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PEPERIKSAAN PERTENGAHAN TAHUNTINGKATAN LIMA 2008

MATEMATIK

Kertas 2

Dua jam tiga puluh minit

Pemeriksa

Bahagian Soalan MarkahPenuhMarkah

Diperoleh

A

1 3

2 4

JANGAN BUKA KERTAS SOALAN INISEHINGGA 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

SULIT1449/2Matematik Kertas 2Mei 2008

212 jam

1449/2

1449/2 2008 Hak Cipta Sektor SBP [Lihat sebelahSULIT

NAMA :

TINGKATAN :


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SULIT 1449/2

1449/2 2008 Hak Cipta Sektor SBP SULIT4

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

7332

wv

[4 marks ]

Answer :

P Q

R

P Q

R


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5

For Examiner’s

Only3 Using factorisation, solve the following quadratic equation:

22

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 atrapezium.

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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7

For Examiner’s

Only5 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

Use6 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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9

For Examiner’s

Only7 (a) State whether the following statements are true or false.

(i) 2.021

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 falsestatement.

(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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11

For Examiner’s

Only9 (a) The inverse matrix of

45

23is 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 = 85 x – 4 y = 13

[6 marks ]

Answer :

(a)

(b)


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For xaminer’s

Use10 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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13

For Examiner’s

Only11 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 theequation 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

Use13 (a) Transformation T is a translation

3

2and 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) Diagram 6 shows three quadrilaterals A, B and C , drawn on a Cartesian plane.

(i) C is the image of A under the combined transformations WV.Descibe in full,:(a) the transformation V(b) the transformation W

[5 marks ](ii) It is given that B represents a region of area 180 cm 2.

Calculate the area, in cm 2, of the region represented by A.[3 marks ]

0 2 4 6 8 10 12 x

2

4

8

y

C A

DIAGRAM 6

B

6


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For xaminer’s

Use

14 The data in Table 2 shows the mass, in kg, of a group of 32 members of Science andMathematics societies.

44 64 59 49 35 40 50 51

60 50 40 43 47 45 57 5354 49 58 54 48 47 53 4551 52 62 59 56 46 51 56

(a) Based on the data in Table 2 and by using a class interval of 5 kg,complete the following table.

[4 marks ] Answer :(a)

Mass (kg) Frequency Midpoint35 – 39

(b) Calculate the estimated mean of the mass of the members.[3 marks ]

(c) Using a scale of 2 cm to 5 kg on the x-axis and 2 cm to 1 member on the y-axis, drawa frequency polygon for the above data.

[5 marks ] Answer:

(b)

(c) Refer graph on page 19

TABLE 2


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For xaminer’s

Use15 (a) Complete Table 3 in the answer space for the equation y =

x2

by writing down the

values of y when x = 0.5 and x = 2. [2 marks ]

(b) For this part of the question, use the graph paper provided on page 21.You may use a flexible curve rule.

By using a scale of 2 cm to 1 unit on both the axes, draw the graph of y = 2 for

4 x 4. [5 marks ]

(c) From your graph, find

(i) the value of x when y = 1.2 ,

(ii) the value of y when x = 2.3. [2 marks ]

(d) Draw a suitable straight line on your graph to find values of x which satisfies the

equation x + 1 = x2

for 4 x 4.

State these values of x.[3 marks ]

Answer:(a)

x 4 3 2 1 0.5 0.5 1 2 3 4 y 0.5 0.67 1 2 4 2 0.67 0.5

TABLE 3

(b) Refer graph on page 21

(c) (i) x = …………………….

(ii) y = …………………….

(d ) x = ………………............................................................................


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For xaminer’s

Use16 (a) Transformation U is a translation

2

1.

Transformation V is a reflection in the straight line y = 1.State the coordinates of the image of point (3, -2) under each of the followingtransformations :(i) U,(ii) UV .

[3 marks ](b) Diagram 7 shows three quadrilaterals ABCD , HGFE and KJIE on a

Cartesian plane.

y

J

K

I

H

G

B

D C

E

F

A

- 2

- 4

6

- 8

4

- 10

2

- 6 - 4 - 2 6420

DIAGRAM 7

HGFE is an image of ABCD under transformation W and KJIE is an image of HGFE under transformation Z .

(i) Describe in full,(a) the transformation W ,(b) the transformation Z.

[6 marks ]

(ii) Given that quadrilateral HGFE represents a region of area 26 cm 2,calculate the area, in cm 2, of the region represented by the shaded region.

[3 marks ]

x

2008 F5 Mid Year SBP Math K2

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