HCI 2024 Term 3 Class Test Revision Paper 2

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Name: _________________________________ ( ) Class: _________ Date: _____________ Term 3 A.Math Class Test (Revision Paper 2) Answer all the questions. Question 1: It is given that h(x) = (3x + 1)(x + 5)(2x – 1). (a) Express h(x) in the form Ax3 + Bx2 + Cx + D, giving the values of the constants A, B, C and D. [2] (b) Find the value of the constant a, given that (x + 3) is a factor of h(x) + ax. [2] Question 2: Given that P(x) = 3x3 – 7x2 – x – 55 and Q(x) = 6x3 – 5x2 – 3x + 2, find the value(s) of q if P(q) = Q(q). [4] Question 3: The figure shows part of a straight line graph obtained by plotting 1y x + against x2. Express y in terms of x. [3] Question 4: In the figure, x and y are related by 1 2 32 x ex y =− .

2 Find (a) the value of , [3] (b) the coordinates of P and Q. [2] Question 5: Given that x and y are known to be related by the equation 3 y st= where s and t are constants. Express the equation in a form suitable for drawing a straight line graph. [3] Question 6: Solve log3 (x + 6) = 2 – log3 (x – 4) + log9 x2, giving your answers in exact values. [5] Question 7 : Given that (log3 7)(log7 k) = 2, find the value of k. [2] Question 8: (a) (i) Solve 323 7 7 3 0x x x− + + − = , showing your working clearly. [4] (ii) Sketch the graph of 323 7 7 3y x x x=− + + − . Indicate clearly, the coordinates of the x- intercept(s) and y-intercept. [3] (b) When a polynomial ()Px is divided by ( 1)x− and ( 2)x− , the remainders are 2 and 3 respectively. Find the remainder when ()Px is divided by ( 1)( 2)xx−− . [4]