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1. For Examiner's Use Consider the five numbers stated below. 19 , 8 , , 2 , 5 3 Write down all the (a) prime numbers, (b) irrational number(s). Answer: (a)________________[1] (b)________________[1] 2. Given that A : B 1 1 : and B : C 1 : 2 , find the ratio of A to C as a ratio of two 2 3 integers. Answer:____________________[2] 3. When x is decreased by 15% and then increased by 20%, it becomes y. Express x : y in its simplest form. Answer:____________________[2] 4. 3 (a) Indicate clearly the numbers, ,2.7,3 and 0.5 on a number line. 2 [1] (b) Hence, arrange the numbers in descending order. ______ ; ______ ; ______ ; ______ 1 [1] 5. For Examiner's Use Complete the statements in the answer spaces (a) 8942 correct to 3 significant figures is ___________. (b) 8942 correct to ___________ significant figure is 9000. Answer: (a)________________[1] (b)________________[1] 6. Estimate the value of 82 3 7.9 Answer: __________________[2] 7. Simplify 2 x 2 (3 y) 2 20 x 2 y 2 Answer: __________________[2] 8. (a) (b) Mrs Tan spent 3 of the money in her wallet and had $42 left. How much did 5 she spend? x grams of ham cost 99 cents. Find an algebraic expression for the number of grams of ham that can be bought with y dollars. Answer: (a)________________[1] (b)________________[1] 2 9. It is given that 56 23 7 , 42 2 3 7 and 1225 52 7 2 (a) What is the highest common factor of 56 and 42? (b) What is the smallest positive integer value of n for which 56n is a multiple of 42? (c) Find the value of 1225 Answer: (a)________________[1] (b)________________[2] (c) ________________[1] 10. Evaluate 2 2 1 (a) 2 (1 2 ) 3 3 5 (b) [6 8 (13 7)] 3 Answer: (a)________________[2] (b)________________[2] 3 For Examiner's Use 11. Given that a = 3, b = 4 and c = (a) 5a bc ab 2 (b) c For Examiner's Use 1 , find the value of 2 Answer: (a)________________[2] (b)________________[2] 12. Albert, Ben and Calvin were each given a piece of string of equal length. Albert cut his into equal lengths of 12m, Ben cut his into equal lengths of 16m; and Calvin cut his into equal lengths of 26m. If there was no remainder in each case, find the shortest length of string given to each of them. Answer: __________________[3] 4 13. The temperature inside an igloo is x o C , and the temperature outside it is y o C , where x and y are positive integers. Write down an expression for (a) the difference between the two temperatures, (b) the average of the two temperatures. Answer: (a)________________[1] (b)________________[1] 14. Betty buys 30 apples at x cents each and 20 pears y cents each. She packs them into bags which contain 3 apples and 2 pears each. She later sells the bags of fruits for (10x + 8y) cents each. Write down an algebraic expression, in terms of x and y , for (a) the amount of money she spent on the fruit. (b) the total amount of money for which she sold all the bags of fruits. (c) Use the answers in (a) and (b) to find out how much profit she makes from selling the bags of fruits. Answer: (a)________________[1] (b)________________[1] (c) ________________[2] 5 For Examiner's Use 15. For Examiner's Use Simplify each of the following: (a) 10v 3vv 1 3x y x y (b) 3 4 Answer: (a)________________[2] (b)________________[2] 6 16. Construct on the triangle ABC below, (a) the bisector of angle ACB, [1] (b) the perpendicular bisector of the line BC. [1] (c) These two lines intersect at the point P. Complete the sentence in the answer space. B C A (c) The point P is equidistant from the points ________ and ________ and equidistant from the lines ________ and ________. [2] 7 For Examiner's Use 17. For Examiner's Use Solve the equations 2( x 1) 3x 1 (a) 4x 6 3 12 (b) 2 Answer: (a)________________[2] (b)________________[3] 8 1 (a) (b) 2 3 A:C=3:4 x : y = 50 : 51 3 (b) 2.7,0.5, ,3 2 (a) 8940 (b) 1 -18 2x2 y 2 (a) $63 100xy (b) 99 (a) 14 (b) n = 3 (c) 35 (a) -5 (b) 18 (a) 17 (b) 96 624 (a) x + y x y (b) 2 (a) 30x + 20 y (b) 10 (10 x + 8y) (c) 70x + 60 y (a) 13v 3v 2 15 x y (b) 12 (c) Pt P is equidistant from Pts B and C and equidistant from lines BC and AC (a) 3 (b) -3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2, 5 , 8 9