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1 SECTION A ( 38 marks) Answer all the questions 1 The following information refer to the set A and set B. Set A = { -3, -2, 2, 3 } Set B = { 4, 9 } The relations between set A and set B is defined by the set of ordered pairs {(-3, 9) (-2, 4) (2, 4) (3, 9)}. (a) State the type of relations. (b) Using function notation, write a relation between set A and set B. [ 2 marks ] Answer ( a ) ( b ) Given that the functions f : x 2x + 6 and f -1 : x kx + p, where k and p are constants, find the value of k and of p. [ 3 marks ] Answer : (a)... (b)... 1
2 3. Given the functions f : x x + 4 and fg : x 2x 3, find (a) g(x) (b) the value of x when gf(x) = 5. [ 3 marks] Answer : (a)... (b) Form the quadratic equation which has roots - 4 and Give your answer in the form ax + bx + c = 0, where a, b and c are constants. [ 2 marks ] 5. Given that p 1 is one of the roots of the quadratic equation px 2 + 7x 2p = 0, find the values of p. [ 2 marks ] 2
3 6. Diagram 1 shows the graph of a quadratic function f(x) = 3(x + p) 2 + 2, where p is a constant. The curve y = f(x) has a minimum point (4, q), where q is a constant ( 4, q ) Diagram 1 State, (a) the value of p, (b) the value of q, (c) the equation of the axis of symmetry. [ 3 marks ] Answer: (a)... (b)... (c) Find the range of values of x for which x ( x 6) 27. 3
4 x+ 1 2x 3 8. Solve the equation = 0. [ 3 marks ] 9. Solve log3 (4x) log 3 ( x + 1) = 1 [ 3 marks ] 4
5 10. The first three terms of an arithmetic progression are 6, t 2, 14,.... find, (a) the value of t, (b) the sum of the first ten term. [ 4 marks ] Answer(a)... (b) The sum of the first n terms of the geometric progression, 64, 32, 16,.. is 126. Find, (a) the value of n, (b) the sum to infinity of the geometric progression. [ 3 marks] Answer(a)... (b)... 5
6 12. The radius of a circle decreases at the rate of 1 0.5cms. Find the rate of change of the area of the circle when the radius is 4 cm..[ Given the area of a circle is A = πr 2 ] [ 3 marks] Answer Diagram 2 shows a sector POQ with centre O. It is given PA=AO=OB=BQ = 6 cm. (a) (b) Find the length, in cm of arc PQ. Find the area, in, of the shaded region. [4 marks] Answer... 6
7 SECTION B ( 42 marks) Answer all the questions 1. Solve the following simultaneous equations. 3x + y = 2 xy - 4y + 3 = 0 [ 5 marks] 2. The quadratic functions = has a minimum value of +12, where k is constant. a) By using a method of completing the square, find the values of k. [5 marks] b) Hence, determine the axis of symmetry. [ 1 marks] 3. Diagram 3, shows a straight line AB. (a) Write the equations of the straight line AB. (b) Find the coordinates of point C. (c) Point C divides AB in ratio m:n. Find the ratio m:n [2 marks] [1 mark] Diagram 3 7
8 4. A pump is used to extract a type of gas from tank. The first extraction draws out 96 of the gas and the subsequent extraction follow a geometric progression. The third extraction draws out of the gas. (a) Determine the common ratio of the geometric progression [ 2 marks] (b) Calculate the volume of gas extracted in the eighth extraction. [2 marks ] (c) If the tank contains 530 of the gas, find the number of extractions needed to empty the tank. 5. A curve with gradient function 2 has turning point at ( k, 8 ) (a) Find the value of k. (b) Determine whether the turning point is a maximum or minimum point. [ 2 marks] (c) Find the equations of the curve. 6. A particular kind of cake is made by using four ingredients, P, Q,R and S. Table 1 shows the price of the ingredients. Price per kilogram (RM) Ingredient Year 2004 Year 2005 P 5.00 w Q R x y S Table 1 (a) The index number of ingredient P in the year 2005 based on the year 2004 is 120. Calculate the value of w. [2 marks] (b) The index number of ingredient R in the year 2005 based on the year 2004 is 125. The price per kilogram of ingredient R in the year 2005 is RM2.00 more than its corresponding price in the year Calculate the value of x and y. (c) The composite index for the cost of making the cake in the year 2005 based on the year 2004 is Calculate (i) The price of a cake in the year 2004 if its corresponding price in the year 2005 is RM30.60 (ii) The value of m if the quantities of ingredients P, Q, R and S used are in the ratio of 7:3:m:2. [5 marks] END OF QUESTIONS Prepared by, Checked by, 8
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