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 . In the answer space, shade the sets.

a) b)

[3 marks]

2. Calculate the value of k and m that satisfy the following simultaneous linear equations.

[4 marks]

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SMK TELANG USANSPM SECOND TRIAL

MATHEMATICS PAPER 22 hours 30 minutes

Name : …………….Class : …………….

3. Using factorization, solve the following quadratic equation3x(x – 3) = 4 + 2x

[4 marks]Answer :

4. Diagram shows a right prism with horizontal rectangle base. Right triangle RSW and UTV are the uniform cross section of the prism. Calculate the angle between plane SRV and plane RSTU.

[3 marks]

Answer :

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T

U

V

W

S

R

10 cm12 cm

5 cm

5. (a) State whether each of the following statements is true or false.

(i) 23 = 6 or = 3.5

(ii) ( -4 ) ( -5 ) = 20 and -4 > -2

(b) Complete the premise in the following argument:Premise 1 : If the determinant of a matrix = 0, then the matrix does not have an inverse.

Premise 2 : _______________________________________________Conclusion :Matrix A does not have an inverse.

(c) Write down two implications based on the following sentence.

A B if and only if A B = A’ [5 marks]

Answer :(a) (i)_________________________________________________________

(ii)________________________________________________________

(b) Premise 2 :_________________________________________________

(c) Implication 1 :_______________________________________________

Implication 2 :_______________________________________________

6. In the Diagram, O is the origin, point P lies on the y-axis and point Q lies on the x-axis. The straight line PR is parallel to the straight line QS. The equation of the straight line QS is y + 2x + 4 =0.

a) State the equation of straight line SR.b) Find the equation of the straight line PR

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c) Find the x-intercept for straight line PR [6 marks]Answer :

a)

b)

c)

7. Diagram shows a solid cylinder of height 20cm and diameter 14 cm. A cone with radius 7 cm and height 9 cm is taken out of the solid. Calculate the volume in cm3 of

the remaining solid. (Use π = ).

[4 marks]

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8. a) Given that . Find the value of k and m .

b) Using matrices, find the value of x and y which satisfy the following simultaneous linear equation

4x – 3y = 176x – 5y = 27

[6 marks]

Answer :a) b)

9. In the diagram , JK and PQ are arcs of two circles with centre O. OQRT is a square.

OT = 14 cm and P is the midpoint of OJ.

Using , calculate

(a) the perimeter, in cm, of the whole diagram,(b) the area, in cm2 , of the shaded region.

[6 marks]

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OP

J

T

RQ

K

210

Answer : a)

b)

10. Diagram below shows four cards in box X and three cards in box Y.

Two cards are picked at random, the first card is picked from box X and the second card is picked from box Y.a) List the sample spaceb) By listing all the possible outcomes of the events, find the probability that i) both cards picked are labelled with letters ii) a card labelled with a consonant or the card labelled with an even number are picked.

[5 marks]Answer :

a)

b) i) ii)

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11. The diagram below shows a speed-time graph of the movement of a particle for a period of T seconds

Calculatea) the rate of change of speed in ms-2 , in the first four seconds.b) the distance, in m, travelled at a uniform speed.c) the value of T, if the total distance traveled is 328 m.

[6 marks]

Answer :

a)

b)

c)

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Section B[48 marks]

Answer any four questions from this section

12 a) Complete the table in the answer space for the equation by writing down the values of y when x = -1 and x = 2

[2 marks] b) 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 for

[4 marks]

c) From your graph, find i) the value of y when x = ii) the values of x when y = 8

[2 marks]

d) Draw a suitable straight line on your graph to find the values of x which satisfy the equation for . State the values of x.

[4 marks]

Answer :

b) Refer graph

c) (i) y = __________________________________________________________

(ii) x = __________________________________________________________

d) The equation of the straight line :

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________________________________________________________________

x = _____________________________________________________________

13. Diagram shows quadrilaterals ABCD, PQRS and PTUV drawn on a Cartesian plane.

(a) Transformation M is a translation .

Transformation N is a reflection in the line .State the coordinates of the image of point D under each of the following transformations :

(i) M,(ii) NM.

[3 marks]

(b) (i) PTUV is the image of ABCD under the combined transformation JK. Describe in full, transformation K and transformation J.

[6 marks]

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2 O 2 4 6 8

10

8

6

4

2

C

D

BA

SR

Q

P

V U

T

Diagram 6

y

x

(ii) Given the shaded region QTUVSR represents a region with an area of 78 cm2, calculate the area, in cm2, of the region represented by PQRS. [3 marks]

Answer :

(a) (i)

(ii)

(b) (i) K :

J :

(ii)

14. The diagram below shows the body masses, in kg, of 40 children in a nursery.

a) Based on the data in the diagram, complete the table in the answer space [3 marks]

b) State the modal class [1 marks]

c) Based on the table, calculate the estimated mean of body mass of a child [3 marks]

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

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[4 marks]

e) Based on the histogram drawn in 14(d), state the number of children whose mass are more than 35 kg

[1 marks]

Answer : a)

Body mass (kg) Frequency Midpoint

15 – 19

20 – 24

b) Modal class ________________________________________________________

c)

d) Refer to the graph

e)

15. You are not allowed to use graph paper to answer this question. a) The diagram below shows a solid right prism with rectangular base EFGH on a horizontal ground. The surface FGMKJ is the uniform cross-section of the prism. Rectangle KMNL is an inclined plane and rectangle DJKL is a horizontal

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plane. JF and MG are vertical edges.

Draw to full scale, the elevation of the solid on a vertical plane parallel to FG as viewed from X. [3 marks]

b) A solid right prism with uniform cross-section PSUT is removed from the solid in diagram 15.1. The remaining solid is as shown below. Rectangle PQRS is a horizontal plane. TP and US are vertical edges. RS = 3 cm and RG = 1 cm.

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Draw to full scale

i) the plan of the remaining solid [4 marks]

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ii) the elevation of the remaining solid on a vertical plane parallel to EF as viewed from Y.

[5 marks]

16. P (35ºN, 155ºW), Q (35ºN, 100ºW), R and K are four points on the surface of the earth. PR is the diameter of the parallel of the latitude 35ºN and K is located due south of Q.

a) State the location of R [3 marks]

b) Calculate the distance, in nautical miles, from Q due east to R, measured along the common parallel of latitude. [3 marks]

c) Calculate the shortest distance, in mautical miles from P to R, measured along the surface of the earth. [2 marks]

d) An aeroplane took off from Q and flew due south to K with an average speed of

840 knots. The time taken for the flight is hours. Find

i) the distance, in nautical miles, from Q to K, measured along the meridian.

ii) the latitude of K [4 marks]

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END OF QUESTIONS

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Prepared by : Checked by :

……………………………… ……………………………… (Encik Hazri bin Mohd Hamzah) (Encik Liew Ing Chang)

Verified by : ……………………………… (Pn. Suria Emilda Suzielina bt Othman) Guru Kanan Sains & Matematik