HCI 2024 Term 3 Class Test Revision Paper 2 Answer

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 ) = (3 x + 1)( x + 5)(2 x – 1). (a) Express h( x ) in the form Ax 3 + Bx 2 + 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 ) = 3 x 3 – 7 x 2 – x – 55 and Q( x ) = 6 x 3 – 5 x 2 – 3 x + 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 x 2 . Express y in terms of x . [3] Question 4: In the figure, x and y are related by 1 2 32 x ex y =− . q=-3 A=6, B=29, C=-6, D=-5 a=37+(1/3) y=-2x^3+7x-1

2 Find (a) the value of  , [3] (b) the coordinates of P and Q . [2] Q uestion 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 log 3 ( x + 6) = 2 – log 3 ( x – 4) + log 9 x 2 , giving your answers in exact values. [5] Question 7 : Given that (log 3 7)(log 7 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] arctan(2)=1.11 rad P(0,-3) Q(1.5,0) x draw ln(y)/3 against x k=9 (x+1)(-3x+1)(x-3) x+1