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Chapter 1 Directed Numbers Chapter 8 Inequalities Chapter 2 Basic Algebra Chapter 9 Algebraic Fractions and Formulae Chapter 3 Basic Geometry Chapter 10 Areas and Volumes Chapter 4 Linear Equations in One Unknown Chapter 11 Introduction to Trigonometric Ratios Chapter 5 Percentages Chapter 12 Polygons Chapter 6 Statistics in Daily Life Chapter 13 Measures of Central Tendency Chapter 7 Algebraic Expressions and Polynomials Chapter 1 Laws of Integral Indices Chapter 8 Symmetry and Transformation Chapter 2 More about Factorization Chapter 9 Introduction to Coordinates Chapter 3 Study of 3-dimensional Figures Chapter 10 Statistical Graphs Chapter 4 Mensuration Chapter 11 Linear Equations in Two Unknowns Chapter 5 Theorems Related to Triangles Chapter 12 Ratio and Rate Chapter 6 Introduction to Probability Chapter 13 Angles in Rectilinear Figures Chapter 1 Estimation and Approximation Chapter 7 More about Percentages Chapter 2 Measurement and Errors Chapter 8 Properties of Quadrilaterals Chapter 3 Identities and Factorization Chapter 9 Coordinate Geometry Chapter 4 Simultaneous Equations Chapter 10 Applications of Trigonometry Chapter 5 Congruent and Similar Triangles Chapter 11 Use and Misuse of Statistics Chapter 6 Square Roots and Pythagoras’ Theorem Chapter 7 More about Statistical Graphs 2010 Chung Tai Educational Press. All rights reserved. 1. Without using a calculator, find the square roots of the following numbers. (a) 289 (b) 900 (c) 0.000 4 (d) 64 529 2. Is each of the following a surd? Yes No □ □ □ □ (a) 32 (b) 484 (c) 3 .6 □ □ □ (d) 18 50 □ 3. Without using a calculator, find two consecutive numbers between which each of the following lies. (a) 30 30 30 6.1 2009 Chung Tai Educational Press. All rights reserved. i.e. 30 30 lies between and . 180 (b) 180 180 i.e. 180 180 lies between and . 4. Find the values of the following numbers. (Give your answers correct to 3 significant figures if necessary.) 80 (a) 3.62 (c) 4 15 (d) 10 2 32 (e) 1 024 (b) 6.2 2009 Chung Tai Educational Press. All rights reserved. 152 4 2 (f) 1. Find the value of the unknown in each of the following figures. (Give your answers correct to 3 significant figures if necessary.) Q (a) P 24 18 p R p2 ( )2 ( )2 (Pyth. theorem) p A (b) 15 15 B a C 6.3 2009 Chung Tai Educational Press. All rights reserved. C (c) 18 5 c A B P (d) 17 r R 32 Q 6.4 2009 Chung Tai Educational Press. All rights reserved. 2. In the figure, S is the mid-point of QR and PS QR. Find the value of p. P 15 p Q S 18 R 3. In the figure, find the area of rectangle ABCD. A B 17 cm 15 cm D C 6.5 2009 Chung Tai Educational Press. All rights reserved. 4. In the figure, find the area of pentagon ABCDE. (Give your answer correct to 3 significant figures.) A 7 cm E B 4 cm C 12 cm D 6.6 2009 Chung Tai Educational Press. All rights reserved. 5. The figure shows rhombus ABCD. The lengths of the diagonals AC and BD are 10 cm and 8 cm respectively. The diagonals are perpendicular to each other and bisect each other at F. Find the perimeter of rhombus ABCD. (Give your answer correct to 3 significant figures.) A B F D C 6.7 2009 Chung Tai Educational Press. All rights reserved. 6. In the figure, D is a point on AC such that AD DC . A D 6m 19 m C B (a) Find the length of AB. (Give your answer correct to 3 significant figures.) (b) Find the length of BC. (Give your answer correct to 3 significant figures.) 6.8 2009 Chung Tai Educational Press. All rights reserved. 1. Determine whether each of the following triangles is a right-angled triangle. If yes, indicate the right angle. A (a) 20 39 B 36 C AB 2 BC 2 AC 2 AB 2 BC 2 □ AC 2 ABC (b) P 30 R 16 34 Q PR 2 RQ 2 PQ 2 PR 2 RQ 2 □ PQ 2 PQR 6.9 2009 Chung Tai Educational Press. All rights reserved. 2. (a) Prove that ABC in the figure is a right-angled triangle. B 10.5 A 14 17.5 C (b) Find the area of ABC. 6.10 2009 Chung Tai Educational Press. All rights reserved. 3. (a) Find the area of PQR in the figure. P Q 24 h 25 7 R (b) Express the area of PQR in terms of h. Hence find the value of h. 6.11 2009 Chung Tai Educational Press. All rights reserved. C 4. In the figure, D is a point on AB. (a) Prove that ADC 90. 24 A (b) Find the perimeter of ABC. 6.12 2009 Chung Tai Educational Press. All rights reserved. 32 D 26 10 B 1. At 12:00 noon, aeroplane A is 800 km due west of the airport, while aeroplane B is 1 000 km due north of the airport. If aeroplane A and aeroplane B are on the same horizontal line, what is the distance between these two aeroplanes? (Give your answer correct to the nearest km.) N B 1 000 km A 800 km Airport Let x km be the distance between these two aeroplanes. 6.13 2009 Chung Tai Educational Press. All rights reserved. 2. Given that the perimeter of a square wooden board is 60 cm, find the length of the diagonal of the board. (Give your answer correct to 3 significant figures.) Diagonal Perimeter 60 cm 3. Find the perimeter of OAB in the figure. y A (0, 20) B ( 21, 0) 6.14 2009 Chung Tai Educational Press. All rights reserved. O x 4. A car and a bus travel at the speeds of 80 km/h due east and 70 km/h due south respectively from point A at the same time. What is the distance between the car and the bus after two hours? (Give your answer correct to the nearest km.) A 80 km/h 70 km/h N 6.15 2009 Chung Tai Educational Press. All rights reserved. 5. A pole of 2.5 m long leans against a vertical wall and its upper end is 1.8 m above the ground. If the upper end of the pole slides down by 0.2 m, how far will the lower end of the pole move from its original position? (Give your answer correct to 3 significant figures.) 0.2 m 2.5 m 1.8 m 6.16 2009 Chung Tai Educational Press. All rights reserved. Simplify the following. (1 4) 1. (a) (c) 2. (a) 35 32 ( )( ) 32 ( )( ) (b) )( ) 22 ( )( ) 77 72 ( ) 72 ( ) (d) 58 44 2( ) ( 2( ) ) (b) 135 63 3( ) ( 3( ) ) (c) 26 2 2 ( (d) 252 6.17 2009 Chung Tai Educational Press. All rights reserved. 3. (a) 7 169 ( ( ) ) (b) 4. (a) 14 81 (d) ) ) ( ( ) ) 32 225 2 32 (b) ( ( ) ) 6 12 50 216 12 (c) ( ( (c) 27 4 ( ( (d) ) ) 42 8 28 6.18 2009 Chung Tai Educational Press. All rights reserved. ( ( ) ) Rationalize the denominators of the following. (1 2) 1. (a) 1 1 ( 6 6 ( ) ) (b) (c) 2 2 ( 5 5 ( ) ) 9 11 (d) 15 10 2. (a) (c) 5 30 5 ( 30 ( ) ) (b) 2 7 2 7 ( 21 21 ( 81 81 5 5 ( ( (d) ) ) 44 3 ) ) ( ( ) ( ) ( ) ) 6.19 2009 Chung Tai Educational Press. All rights reserved. Simplify the following. (3 4) 3. (a) 5 5 2 5 ( 14 3 14 (b) ) 5 (c) 16 13 9 13 (d) 2 6 8 18 4. (a) 54 5 24 (b) 2 6 5 (c) 4 75 12 (d) 5 28 3 7 6.20 2009 Chung Tai Educational Press. All rights reserved. 5 1. Determine whether each of the following numbers is a perfect square. If yes, find the square roots of the number. (a) 24 (b) 36 (c) 110 (d) 450 (e) 784 (f) 1 089 2. Determine whether each of the following is a surd. (a) 45 (b) 120 (c) 98 200 (d) 55 224 (e) 1.69 (f) 4.8 3. Without using a calculator, find the square roots of the following numbers. (a) 81 (b) 196 (c) 484 (d) 1 144 169 4 (f) 121 100 (e) 4. Find the values of the following numbers. (Give your answers correct to 3 significant figures.) (a) 21 (b) 120 (c) 950 (d) 0.7 (e) 55 6 (f) 227 5 6.21 2009 Chung Tai Educational Press. All rights reserved. 5. Without using a calculator, find two consecutive numbers between which each of the following lies. 35 (a) 22 (b) (c) 60 (d) 140 (e) 380 (f) 480 6. Without using a calculator, find the square roots of the following numbers. (a) 361 400 (b) (c) 625 324 (d) 2.89 (e) 4.84 256 729 (f) 0.002 5 7. Find the values of the following expressions. (Give your answers correct to 3 significant figures.) (a) 9 2 132 (b) 212 17 2 (c) 29 2 10 2 (d) 32 2 182 (f) 352 24 2 13 (e) 8 40 2 252 8. Find the values of the unknowns in the following. (Give your answers correct to 3 significant figures.) B (a) P (b) 8 a 9 A b R 11 A B 6.22 2009 Chung Tai Educational Press. All rights reserved. C 6 3 7 Q C (c) c 9. Find the values of the unknowns in the following. (Give your answers correct to 3 significant figures.) A (a) (b) Q 10 5 p B (c) Q P r 11 14 20 P 14 q R C R A 10. In the figure, BDC is a straight line. Find the value of c. (Give your answer correct to 3 significant figures.) 16 c B D C 5 A 11. In the figure, find the length of each side of square ABCD. (Give your answer correct to 3 significant figures.) D 10 cm B 12. In the figure, the area of ABC is 364 cm 2. Find the length of AB. (Give your answer correct to 3 significant figures.) C A 26 cm B C 6.23 2009 Chung Tai Educational Press. All rights reserved. 13. In the figure, AB 34 cm and AC : BC 8 : 15. Find the length of BC. B 34 cm C A 14. In the figure, find the perimeter of trapezium ABCD. A 12 cm D 12 cm B E 28 cm C 15. The figure shows parallelogram ABCD. E is a point on AB such that AE : EB 1 : 4 . If CD 20 cm and AD 12 cm , find the area of parallelogram ABCD. (Give your answer correct to 3 significant figures.) 20 cm D C 12 cm A E B 16. In the figure, PQ 18 cm, QR 12 cm and PS 10 cm. P 10 cm S 18 cm Q 12 cm R (a) Find the length of QS. (b) Find the length of RS. (Give your answers correct to 3 significant figures.) 6.24 2009 Chung Tai Educational Press. All rights reserved. 17. In the figure, find the perimeter of quadrilateral ABCD. (Give your answer correct to 3 significant figures.) B 7 cm A 5 cm C 13 cm D 18. In the figure, WX 47, XY 40 and YZ 32. Z 32 Y q p W 40 47 X (a) Find the value of p. (b) Find the value of q. (c) Find the area of quadrilateral WXYZ. (Give your answers correct to 3 significant figures.) 19. In the figure, find the perimeter of pentagon PQRST. (Give your answer correct to 3 significant figures.) T P S 25 cm 30 cm Q R 7 cm 6.25 2009 Chung Tai Educational Press. All rights reserved. 20. Determine whether each of the following triangles is a right-angled triangle. If yes, indicate the right angle. A (a) (b) A 15 B 7.5 C 40 24 A (c) 9 18 B 19.5 C C 32 18 B 21. In the figure, the areas of squares ABCD, DPQR and ARST are 65 cm2 , 90 cm 2 and 155 cm 2 respectively. Determine whether ADR is a right angle. Q Area 90 cm 2 R S P Area 155 cm2 D C Area 65 cm2 A T B 22. (a) Prove that PQR in the figure is a right angle. P (b) Find the area of PQR. 34 3 Q 6.26 2009 Chung Tai Educational Press. All rights reserved. 5 R 23. In the figure, D is a point on BC and BD DC. A (a) Prove that ABC is a right-angled triangle. 39 (b) Find the value of h. (Give your answer correct to 3 significant figures.) 15 h B 24. (a) Prove that ABC in the figure is a right-angled triangle. A 1.5 2 B C 2.5 25. In the figure, ADB DCB. (b) Find the perimeter of quadrilateral ABCD. (Give your answer correct to 3 significant figures.) C P (b) If 3PQ 4 PR , prove that ABC ~ PQR. (a) Prove that ABD ~ DBC . D 36 A 5 Q R D 7 74 B C 26. In the figure, AC and BD intersect at E. D (a) Prove that AC BD. 30 (b) Find the lengths of BC and DC. (c) Is BCD a right-angled triangle? Explain briefly. A 9 E 15 16 12 B C 6.27 2009 Chung Tai Educational Press. All rights reserved. 27. The lengths of the hour hand and minute hand of a watch are 8 mm and 15 mm respectively. What is the distance between the tips of these two hands when it is 9 o’clock? 12 15 mm 9 8 mm 3 6 28. A ladder of 5 m long leans against a vertical wall. If the upper end of the ladder is 3.5 m above the ground, what is the distance between the lower end of the ladder and the wall? (Give your answer correct to 3 significant figures.) 5m 3.5 m 29. In each of the following figures, find the coordinates of B and the length of OA. y (a) y (b) A (12, 16) x O B O B x 6.28 2009 Chung Tai Educational Press. All rights reserved. A (12, 9) 30. One end of a rope of 6.4 m long is fixed at point D on the ground, while the other end is at point B on a lamp post. The distances from point B to top A and to bottom C of the lamp post are the same. If DC 3.6 m , find the height of the lamp post. (Give your answer correct to 1 decimal place.) A B 6.4 m D 3.6 m C 31. In the figure, two vertical poles are 5 m apart and the height of the shorter pole is 3 m. If the distance between the tops of the poles is 7 m, what is the height of the longer pole? (Give your answer correct to 3 significant figures.) 7m 3m 5m 32. In the figure, find the perimeter of ABC. y A (9, 6) B (3, 6) x O C (3, 3) 6.29 2009 Chung Tai Educational Press. All rights reserved. 33. In the figure, the lighthouse is 20 m high. The top A of the lighthouse is connected to points C and D on the ground by two wires, where CBD is a straight line. If AC AD 30 m, find the distance between C and D. (Give your answer correct to 3 significant figures.) A 30 m C 30 m 20 m D B 34. The figure shows a rectangular top ABCD of a desk. If the area of ABCD is 0.98 m 2 and AB 2 BC, find the length of diagonal AC. (Give your answer correct to 3 significant figures.) A B D C 35. The length and width of a field are 130 m and 74 m respectively. A 74 m D Field B C 130 m The following are two routes to walk from point A to point C. Route 1: Walking along the sides of the field (i.e. A B C). Route 2: Walking diagonally across the field (i.e. A C). What is the difference in length between the above two routes? (Give your answer correct to 3 significant figures.) 36. Given that the area of a square wooden board is 125 cm 2, find the length of the diagonal of the board. (Give your answer correct to 3 significant figures.) Diagonal Area 125 cm2 6.30 2009 Chung Tai Educational Press. All rights reserved. 37. Oscar walked due west from point A at a speed of 60 m / min. After 3 minutes, he reached point B. A tree is 425 m and 385 m away from points A and B respectively. B A N 425 m 385 m (a) Prove that point B is due north of the tree. (b) If Oscar continued to walk due west from point B at the same speed for 5 minutes, he reached point C finally. Find the distance between point C and the tree. (Give your answer correct to 3 significant figures.) 38. In the figure, find the length of PR. (Give your answer correct to 3 significant figures.) y Q (4, 4) P (2, 4) x O S (4, 2) R (2, 2) 39. Find the area of the polygon in the figure. (Give your answer correct to 3 significant figures.) 4 cm 3 cm 1 cm 2 cm 6.31 2009 Chung Tai Educational Press. All rights reserved. 40. Simplify the following. (a) 27 (b) 54 (c) 173 (d) 105 (e) 114 (f) 69 41. Simplify the following. (a) 28 (b) 99 (c) 104 (d) 140 (e) 264 (f) 756 42. Simplify the following. (a) 3 64 (b) 27 100 (c) 80 49 (d) 32 144 (e) 216 50 (f) 135 784 43. Simplify the following. (a) 6 54 (b) 10 45 (c) 60 42 (d) 125 5 (e) 180 15 (f) 243 3 3 6.32 2009 Chung Tai Educational Press. All rights reserved. 44. Simplify the following. (a) 15 20 75 (b) 40 125 18 (c) 21 70 54 (d) 315 12 105 (b) 6 13 45. Rationalize the denominators of the following. (a) 3 10 (c) 27 6 (d) 70 21 (e) 18 42 (f) 36 8 46. Rationalize the denominators of the following. (a) 15 2 (b) 6 120 (c) 147 45 (d) 2 108 5 (f) 4 15 18 (e) 3 3 54 6.33 2009 Chung Tai Educational Press. All rights reserved. 47. Rationalize the denominators of the following. (a) 64 7 (b) 32 15 (c) 11 48 (d) 25 128 (e) 135 72 (f) 168 30 48. Simplify the following. (a) 4 3 13 3 (b) 8 7 2 7 3 10 2 (d) 12 5 5 (c) 10 (e) 9 11 6 11 (f) 14 15 2 15 3 3 49. Simplify the following. (a) 3 12 2 27 (b) 4 15 60 (c) 5 28 9 63 (d) (e) 8 45 3 20 (f) 2 150 3 54 6.34 2009 Chung Tai Educational Press. All rights reserved. 128 50 Worksheet 6A (page 6.1) 1. (a) 17 or 17 (c) 0.02 or 0.02 Worksheet 6F (b) 30 or 30 8 8 (d) or 23 23 (page 6.19) 1. (a) 6 6 (b) 2 5 5 (c) 9 11 11 (d) 3 10 2 6 6 (b) 2 3 3 (c) 9 5 5 (d) 2 33 3 8 6 5 2. (a) Yes (c) Yes (b) No (d) No 2. (a) 3. (a) Between 5 and 6 (b) Between 13 and 14 3. (a) 7 5 (b) 4 14 (c) 7 13 (d) 4. (a) 8.94 (c) 1.90 (e) 10.4 (b) 32 (d) 0.516 (f) 14.5 4. (a) 5 2 (b) 13 6 (c) 18 3 (d) 7 7 Worksheet 6B Build-up Exercise 6A (page 6.21) (page 6.3) 1. (a) 30 (c) 17.3 (b) 21.2 (d) 27.1 2. 12 3. 120 cm 2 4. 82.1 cm 2 5. 25.6 cm 6. (a) 18.0 m 1. (a) No (c) No (e) Yes, 28 or 28 (b) Yes, 6 or 6 (d) No (f) Yes, 33 or 33 2. (a) Yes (c) No (e) No (b) Yes (d) Yes (f) Yes 3. (a) 9 or 9 (b) 14 or 14 1 1 (d) or 12 12 11 11 (f) or 10 10 (c) 22 or 22 (b) 21.7 m (e) Worksheet 6C (page 6.9) (b) Yes, PRQ 1. (a) No 2. (b) 73.5 (b) Area 3. (a) 84 25h ; h 6.72 2 4. (b) 108 13 13 or 2 2 4. (a) 4.58 (c) 30.8 (e) 3.03 (b) 11.0 (d) 0.837 (f) 6.74 5. (a) Between 4 and 5 (c) Between 7 and 8 (e) Between 19 and 20 (b) Between 5 and 6 (d) Between 11 and 12 (f) Between 21 and 22 19 19 or 20 20 25 25 (c) or 18 18 (e) 2.2 or 2.2 6. (a) Worksheet 6D (page 6.13) 1. 1 281 km 2. 21.2 cm 7. (a) 15.8 (c) 27.2 (e) 39.2 3. 70 units 4. 213 km (b) 16 16 or 27 27 (d) 1.7 or 1.7 (f) 0.05 or 0.05 (b) 27.0 (d) 26.5 (f) 12.5 5. 0.186 m Build-up Exercise 6B Worksheet 6E (page 6.17) 1. (a) 9 3 (b) 8 (c) 343 7 (d) 625 2. (a) 2 11 (b) 3 7 (c) 3 15 (d) 6 7 7 3. (a) 13 3 3 (b) 2 (c) 4. (a) 8 (b) 3 2 (c) (page 6.22) 8. (a) 11.4 (c) 12.5 (b) 8.54 9. (a) 9.80 (c) 14.3 (b) 9.80 10. 12.5 14 9 6 5 4 2 (d) 15 (d) 3 4 11. 7.07 cm 12. 38.2 cm 13. 30 cm 6.35 2009 Chung Tai Educational Press. All rights reserved. 35 14. 72 cm 44. (a) 150 15. 226 cm 2 16. (a) 15.0 cm (b) 19.2 cm (d) (b) 50 3 (c) 7 5 3 1 2 17. 35.0 cm 18. (a) 51.2 (c) 1 120 (b) 20.4 Build-up Exercise 6F 19. 87.5 cm 3 10 10 (b) 6 13 13 (c) 10 21 3 (e) 3 42 7 (f) 9 2 30 2 (b) 5 10 (c) 7 15 15 12 15 5 (e) 2 2 (f) 2 30 3 47. (a) 8 7 7 (b) 4 30 15 (c) 33 12 (d) 5 2 16 (e) 30 4 (f) 2 35 5 5 10 2 45. (a) Build-up Exercise 6C (page 6.26) 20. (a) Yes, ABC (c) Yes, BAC (d) (b) No 46. (a) 21. Yes (d) 22. (b) 7.5 (page 6.33) 9 6 2 23. (b) 23.4 25. (b) 38.8 26. (b) BC 20, DC 34 (c) No 48. (a) 17 3 (b) 10 7 (c) 27. 17 mm (d) 11 5 (e) 3 11 (f) 4 15 28. 3.57 m 49. (a) 12 3 (b) 6 15 (c) 37 7 (e) 18 5 (f) Build-up Exercise 6D (page 6.28) 29. (a) B (12, 0), OA 20 units (b) B (0, 9), OA 15 units (d) 3 2 30. 10.6 m 31. 7.90 m 32. 36 units 33. 44.7 m 34. 1.57 m 35. 54.4 m 36. 15.8 cm 37. (b) 488 m 38. 7.21 units 39. 6.41 cm 2 Build-up Exercise 6E 40. (a) 8 2 (d) 100 10 41. (a) 2 7 (d) 2 35 (page 6.32) (b) 25 (c) 17 17 (e) 121 (f) 1 296 6 (b) 3 11 (c) 2 26 (e) 2 66 (f) 6 21 42. (a) 3 8 (b) 3 3 10 (c) 4 5 7 (d) 2 3 (e) 6 3 5 (f) 3 15 28 43. (a) 18 (d) 5 (b) 15 2 (c) 6 70 (e) 2 3 (f) 3 6.36 2009 Chung Tai Educational Press. All rights reserved. 6