F.2 Mathematics Final Revision Exercise (2009-06-04) Part A : True or False 1. 2m 7n = 14m + n True / False 2. 2 2n = 4n True / False 3. 2m 2n = 4mn True / False 4. m m m 3m True / False 5. 11103 is a scientific notation. True / False 6. 2(x + 1)(2x + 3) = (2x + 2)(4x + 6) True / False 7. (a)10 = a10 True / False 8. (a)9 = a9 True / False 9. The place value of B is ABCD(16) is 11. True / False 1 10. 2x + is a polynomial. True / False x 11. sin(10 + 10) = 2sin10 True / False 12. If x2 = 10, then x = 10 True / False 13. a3 b3 = (a b)3 True / False 14. If x > 2, then x > 2. True / False 15. ( 3 2 )2 = 3 2 = 1 True / False 16. 64 is a surd. True / False 17. 1.21 is a surd. True / False 18. 4 is not a polynomial. True / False 19. The degree of 3x2y4 is 4. True / False h h 2h 20. True / False tan 10 tan 20 tan 10 tan 20 Part B: Short and Long Questions 21. Which of the following is/ are irrational numbers, 4 ,, 5 , 1. 2 ? 22. (a) Solve 8x2 22x = 5 (b) Solve (x + 1)(x 2) = (x 2)(3x 9) 1 x 2 ax a 2 x 2 ax a 2 23. Simplify 2a x 3 a 3 x3 a3 1 2 24. (a) Make v as the subject in the formula E mv 2 2z 3 (b) Make z as the subject of the formula 1 y. z2 25. Factorize 507(a + b)2 147c4 . 26. A circular region with diameter 60 cm is enclosed by a wire. A portion of the wire is now rusted and useless, the remaining portion is bent again to form a smaller circular region, find the decrease in the area of the new region compared with the original one. (The length of the useless portion is given to be 30 cm.) (Give 3 significance figures if necessary) 2 27. Suppose tan = , without finding the value of , find the value of cos. 5 28. The following figure shows the original position of a 3 metres long rod leaning against a vertical wall. Suppose the end point A of the rod is 1.5 metres from the wall. (a) Find the acute angle between the rod and the ground. (b) The rod slides down to a position that the point A is now 1 metre further away from the wall. What is the decrease in the acute angle between the rod and the ground? (Give 3 significance figures if necessary) A 29. In the figure, PQR is a straight line and RQ = QP = PS = SQ. Find the size of PSR. 30. Refer to the figure, AB = 20 cm, BC = 15 cm, CA = x cm, the length of altitude from C to AB is 10 cm (as shown). C (a) Find the value of x. x cm D 15 cm (b) Find the shortest distance from B to AC. 10 cm A B E 20 cm 31. The cumulative frequency curve shows the money donated by different people in a fund-raising campaign. Find (a) the median, (b) the number of people donating more than $70, (c) the percentage of people donating less than $30. 32. 3 7 Form a quadratic equation with integral coefficients and roots and . 5 9 33. In △ABC, B = 90, AB = x cm, BC = (3x 3) cm and CA = (2x + 3) cm. Find the area of △ABC. 34. 9 10 x 8 y (a) Solve the simultaneous equation 5. 6 x 5 y 5 10 8 9 x y5 (b) Solve the simultaneous equation . 6 5 5 x y 35 Suppose Ax 2 Bx 2 x 3B A 5C ( B 1) x 2 4 x where A, B and C are constants. Find the values of A, B and C. 36. Refer to the figure above. Given that △ABC is equilateral and the radius of the sector AFDE is 3 cm. Find the area of △ABC. (Hint: AD BC) 37. 3 8 27 Simplify . 6 24 54 38. Refer to the figure above. △ABC and △ABE are right-angled triangles such that AC = CD = 2 cm, AB = 3 cm and BE = 1 cm. Suppose C, A and B are collinear (i.e. lying on the same straight line), find (a) the length of line segment DE and (b) the size of ADE.