MUNSANG COLLEGE F.3 MATHEMATICS Revision Exercise 2 (M.C.) 1. 8x 3 (x + 2y) 8y 3 (y + 2x) = A. 8(x 2 + y 2 )(x 2 + 2xy y 2 ). B. 8(x 2 + y 2 )(x + y)( x y). C. 8(x + y) 2 (x y) 2. D. 8(x + y) 3 (x y). 2. 4(x 2 + 3x) 2 35(x 2 + 3x) 50 = A. (x + 1)(x + 2)(x 5)(4x + 5). B. (x + 1)(x + 2)(2x 5)(2x + 5). C. (x 2)(x + 5)(2x + 1)(2x + 5). D. (x + 2)(x 5)(2x + 1)(2x + 5). 3. 10 15 3 9 20 100 A. B. C. D. 10 20 2 5 20. 3 20 20 2 5 20. 3 20 3 10 20. 2 5 10 20 3 5 30. 2 4. 70000 1.5 10 2 9 6 3 6 (4 10 ) (5 10 ) A. 5 10-4. B. 5 10-5. C. 5 10-15. D. 5 10-16. 5. Fanny deposits two equal sums of money in two different banks at an interest rate of 2% p.a. for 3 years. Simple interest and compound interest calculated once a year are used to calculate two sums of money respectively. If the compound interest received is $151 more than the simple interest, find the amount of each sum of money correct to the nearest thousand dollars. A. $125 000 B. $135 000 C. $145 000 D. $155 000 1

6. When x is increased by a% and then decreased by 40%, the result is equal to x decreased by a%. Find the value of a. A. 15 B. 20 C. 25 D. 30 7. If a > b > c > d and a, b, c, d are all non-zero numbers, which of the following must be true? I. a + d > b + c II. ab > cd III. a b d c A. II only B. I and II only C. II and III only D. none of the above 8. Henry draws a trapezium which meets two requirements. First, the area of the trapezium is at most 5 times that of the lower base. Second, lower base must be an integer. If the upper base, the lower base and the height of the trapezium are 5 cm, x cm and 4 cm respectively, find the smallest possible value of x. A. 3 B. 4 C. 5 D. 6 9. The pie chart shows the means of transport used by the students in S3A. If a student is chosen at random from S3A, find the probability that he goes to school neither by bus, by MTR nor on foot. A. B. C. D. 1 60 1 36 7 20 13 20 10. There are 4 English books and 3 Chinese books on a bookshelf. How many English books should be added to the bookshelf so that the probability of drawing a Chinese book randomly from the bookshelf is 1 4? A. 3 B. 4 C. 5 D. 6 2

11. The mean height of 24 boys and 26 girls is 165 cm. If the mean height of the girls is 158 cm, what is the mean height of the boys correct to 1 decimal place? A. 161.5 cm B. 171.5 cm C. 172.0 cm D. 172.6 cm 12. There are eight numbers, x, y, 6, 8, 8, 8, 14 and 16. If the mean and median of the eight numbers are 10 and 8 respectively, which of the following cannot be the values of x and y? A. x = 6, y =14 B. x = 7, y =13 C. x = 8, y =12 D. x = 9, y =11 13. In the figure, CE = CF, BA // CF and BC // DF. Which of the following must be true? I. ABC is isosceles. II. AE = EC III. ADE CFE A. I only B. II only C. III only D. I and II only 14. In the figure, if PR is an angle bisector of QPS, QT is an angle bisector of PQS, RPS = 35 and TQS = 24, find PRS. A. 81 B. 83 C. 85 D. 87 15. The lengths of three sides of a triangle are 3x + 1 cm, 2x 5 cm and 11 cm, where x is an integer. What is the value of x? A. 2 B. 3 C. 4 D. 5 16. In the figure, ABDE is a square and BCD is an equilateral triangle. If AB = FB, find DBF. A. 15 B. 22.5 C. 30 D. 40 3

17. In the figure, ABQC and PQRS are two squares, BQR and PCQ are straight lines. If AB = 16 cm and PS = 24 cm, find the area of DBR. A. 280 cm 2 B. 300 cm 2 C. 320 cm 2 D. 576 cm 2 18. In the figure, ABCD is a trapezium with AD // BC. E and F are points on AB while G and H are points on DC. DG = GH = HC and AD // EG // FH // BC. Find the length of AB. A. 18 cm B. 24 cm C. 27 cm D. 30 cm 19. If the net is folded into a solid, which of the following statement(s) is / are true? I. Point A coincides with point C. II. HG will be stuck together with IJ. III. Only point D coincides with point J. A. I only B. II only C. I and III only D. II and III only 20. Which of the following statement(s) is / are correct? I. The angle between the line AG and the plane BCGF is AGB. II. The angle between the planes ABG and ABFE is GAF. III. The angle between the planes AGD and ADHE is GDH. A. I only B. III only C. I and III only D. II and III only 21. The front, top and side views of a 3-D object are shown below: Front view Top view Side view How many cubes are there in the 3-D object? A. 10 B. 11 C. 12 D. 13 4

22. The total surface area of a hemisphere is 108 cm 2. Find the volume of the hemisphere correct to 3 significant figures. A. 210 cm 3 B. 294 cm 3 C. 452 cm 3 D. 831 cm 3 23. In the figure, the depth of the water in a cylinder is 4 cm. After a right circular cone of the same base radius as the cylinder is put into the cylinder, the water level rises to a level which is equal to the height of the cone. Find the height of the cone. A. 6 cm B. 7 cm C. 8 cm D. 9 cm 24. A solid wooden sphere is cut into a cube of side x cm. If the radius of the sphere is 4 cm, find the largest possible value of x. A. B. C. D. 8 3 3 8 3 4 3 3 4 3 25. At noon, a typhoon at point A is 600 km from the observatory O. Its compass bearing from observatory O was S48 E. The typhoon keeps moving in the direction of N75 W at a speed of 25 km/h. Find the shortest distance between the track of the typhoon and observatory O correct to 1 decimal place. A. 196.2 km B. 272.4 km C. 326.1 km D. 455.9 km 26. The figure shows a contour map where MN represents a river. If the gradient 1 of the river is 10, find the actual distance between M and N correct to the nearest meter. A. 861 m B. 1 000 m C. 1 500 m D. 1 507 m 5

27. The angle of elevation of the top C of the building CD from the top of the building AB is 30. The angle of depression of the bottom D of the building CD from the top of the building AB is 50. The difference between the heights of the buildings 40 m. Find the height of the building CD correct to 3 significant figures. A. 119 m B. 123 m C. 165 m D. 245 m 28. If the line segment joining A( 4, 3) and B(4, 1) cuts the x-axis at P, find AP : PB. A. 1 : 1 B. 2 : 1 C. 3 : 1 D. 3 : 2 29. Which of the following line segments formed by joining the two given points is parallel to the line segment formed by joining (a, 0) and (0, b)? A. (b, 0), (0, a) B. ( a, 0), (0, b) C. (a, 0), (0, b) D. ( a, 0), (0, b) 30. In the figure, the slopes of straight lines L 1, L 2 and L 3 are m 1, m 2 and m 3 respectively. Which of the following must be correct? I. m 1 < 0 II. m 2 < 0 III. m 3 > 0 IV. m 2 > m 1 L 1 L 2 L 3 A. I and II only B. II and III only C. I, II and III only D. I, II, III and IV END OF PAPER Answers: 1. D 6. C 11. D 16. C 21. B 26. D 2. C 7. D 12. D 17. B 22. C 27. B 3. A 8. B 13. A 18. D 23. A 28. C 4. D 9. A 14. B 19. A 24. A 29. D 5. A 10. C 15. C 20. C 25. B 30. C 6