INSTRUCTIONS. F.3 2 nd Maths Examination (1011) P1/14

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1 INSTRUCTIONS 1. The total mark of this paper is This paper consists of THREE sections, A, B and C. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided in this Question-Answer Paper. 4. Unless otherwise specified, all working must be clearly shown. 5. Unless otherwise specified, numerical answers should be either exact or correct to 3 significant figures. 6. The diagrams in this paper are not necessarily drawn to scale. P1/14

2 Section A Multiple Choice (20%) Choose the best answer for each question. Write your answer in the table provided in Pg The depreciation rate of a computer is 12 % per year. What is the percentage decrease in its value after 2 years? A % B. 24 % C. 25 % D % 2. If x is an integer and 2x x, find the smallest value of x. A. 0 B. 1 C. 2 D According to the following front, top and side views of a solid, choose the corresponding 3-D object. front top side top A. B. top front side front side C. D top top front side front side 4. The figure shows two similar solids. Find the value of V. A. 180 B. 237 C. 250 D cm 10 cm Volume = 686 cm 3 Volume = V cm 3 P2/14

3 5. Each of the following cases lists the lengths of three line segments. Which set of the line segments can form a triangle? A. 4.7 cm, 4.7 cm, 9.4 cm B. 5 cm, 6 cm, 12 cm C. 8.5 cm, 9.5 cm, 20 cm D. 10 cm, 15 cm, 18 cm 6. In the figure, AY and BZ are the angle bisectors of BAC and ABC respectively. They intersect at P. CP is extended to meet AB at X. A Which of the following must be true? I. AP = BP = CP II. CX bisects ACB. X III. AXP AZP Z P A. I only B. II only C. I and III only D. I, II and III B Y C 7. In the figure, the slopes of lines l 1, l 2, l 3 and respectively. Which of the following must be true? I. m 1 > m 2 > 0 II. m 3 < m 4 III. m 4 < 0 < m 1 l 4 are m 1, m 2, m 3 and m 4 y l 1 l 2 l 3 A. I only B. II only C. I and III only D. I, II and III O l 4 x 8. In the figure, line segment AB cuts the x-axis at P. Find the x-coordinate of P. A. 3 B. 3.5 C. 4 D. 5 A( 3, 3) O y P x B(5, 1) 9. A( 2, 4) and B(6, 4) are two given points. P(1, 1) is a point on line segment AB. Find AP : PB. A. 5 : 3 B. 5 : 2 C. 3 : 8 D. 3 : Jessica is at point A. She finds a dragonfly at point C which is 5.5 m above the ground. The angle of elevation of C from B A is 25. A bird at point B is 15 m above the dragonfly. Find the angle of elevation of B from A, correct to 15 m 3 significant figures. A B C D P3/ m C D? 25 A

4 Section A Multiple Choice (20%) Section B -- Short Questions (40%) 11. The surface area of a tennis ball is 49π cm 2. Find its diameter. (3 marks) 12. The figure shows a contour map, where XY represents a straight road. If the actual horizontal run between X and Y is 500 m, find the gradient of the straight road. Express your answer as a fraction. Y X 400 m (4 marks) P4/14

5 13. (a) The top and the base of the solid shown in the figure are rectangles. (i) When l is the axis of rotation, find the order of rotational symmetry of the solid. (ii) Find the number of planes of reflection of the solid. (iii) Sketch a net which can be folded into the 3-D object on the right. (4 marks) l (b) The figure shown is a cube. P and Q are the mid-points of EH and FG respectively. (i) Name the projection of the line segment PQ on the plane AFED. D (ii) Name the projection of the line segment AH on the plane ABCD. E (iii) Name the angle between the planes ABCD and AQPD. A C F Q P H (3 marks) B G P5/14

6 14. L is a straight line passing through two points A(3, 2) and B( 4, 6). Find (a) distance between AB, (b) slope of L, (c) inclination of L, correct to the nearest degree. (6 marks) P6/14

7 15. Find x and y in the figure. (7 marks) x A M 40 3y cm N B cm C P7/14

8 16. In the figure, ABC is an isosceles triangle and BAD = CAD. Prove that (a) ABD ACD, A (b) BCD is an isosceles triangle. D B C (7 marks) P8/14

9 17. In the figure, AD = BD, BDE = ADE and AC // ED. Prove that AB is an altitude of ABC. E A B D C (6 marks) P9/14

10 Section C -- Long Quesstion (40%) 18. In the figure, ABCD is a trapezium. E and G are the A D mid-points of BC and DE respectively. (a) Prove that ABED is a parallelogram. G (b) Student A said ABED must be a rhombus. Do you agree with him? Explain your answer. B E C (10 marks) P10/14

11 19. In the figure, AD is the height of ABC. Find (a) the slopes AD in terms of k, (b) the value of k, (c) the area of ABC. (10 marks) y O B( 5, 1) D(2k, 2k 1) A(2, 3) x C(4, 7) P11/14

12 20. (a) Fig. A shows a vessel in the shape of an inverted right pyramid, which is held vertically. Its base is a square of side 6 cm. Fig. B shows an inverted right circular conical vessel which is held vertically. If both vessels are filled up with water of the same volume, find the base diameter (d cm) of the circular conical vessel, correct to 3 significant figures. 6 cm 6 cm d cm 12 cm 10 cm Fig. A Fig. B (5 marks) P12/14

13 (b) Two iron spheres of diameter 3 cm each are put into the inverted right pyramid (Fig. A). They are totally immersed into the water. Some water pour out and is collected in a cylindrical glass which contains some water. Find the rise in the water level. 6 cm 6 cm (5 marks) 12 cm 8 cm P13/14

14 21. In the figure, a ship starts from X and sails along XY and YZ to the pier Z. If XYZ = 90, XY = 21 km and YZ = 28 km, find (a) XZY, (b) the whole circle bearing of X from Z. (c) Find the shortest distance between X and Z. (Give your answers correct to 3 significant figures.) Z Y N 36 X (10 marks) ~End of Paper~ P14/14

QUEEN S COLLEGE. Yearly Examination, Mathematics Paper II. Secondary 5 Date: 23 June, Time: 8:30-9:30 Full Marks: 80

QUEEN S COLLEGE. Yearly Examination, Mathematics Paper II. Secondary 5 Date: 23 June, Time: 8:30-9:30 Full Marks: 80 QUEEN S COLLEGE Yearly Examination, 00-0 Mathematics Paper II Secondary 5 Date: June, 0. Time: 8:0-9:0 Full Marks: 80. Write down the information required in the spaces provided on the Answer Sheet.. When