HCI 2024 Term 3 Class Test Revision Paper 1

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Name: _________________________________ ( ) Class: _________ Date: _____________ Term 3 A.Math Class Test (Revision Paper 1) Answer all the questions. Question 1: (a) Given that ( )3log b x y p = and 2log b y q x  = , express log b xy in terms of p and q. [6] (b) Solve the equation 2log 8 2 log 7x x+= . [4] Question 2: (i) Use the substitution 2 xy = to express the equation ( )3 12 7 2 4 4x x x+ + = − as a cubic equation in y. [1] (ii) Show that 1 2y = is the only real solution of this equation. [4] (iii) Hence solve the equation ( )3 12 7 2 4 4x x x+ + = − . [1] Question 3: The two variables x and y are related by the equation 2 5 1y xy−= . The diagram shows part of a straight line graph obtained by plotting 1 y against x. Find (i) the coordinates of P and Q, [3] (ii) the value of  in degrees. [2]

2 Question 4: The expression 32ax x bx++ has remainder 3 when it is divided by 1x+ . When the expression is divided by 2x− , the remainder is 6. Find the remainder when the expression is divided by 3x− . [4] Question 5: (i) Factorise the expression 3x3 – 8x2 – 5x + 6 completely. [3] (ii) Hence, sketch the graph of 323 – 8 – 5 6y x x x=+ , indicate clearly the coordinates of the x-intercepts and y- intercept. [3] Question 6: The figure shows part of a straight line graph obtained by plotting values of the variables indicated. Express y as a function of x. [3] Question 7: Using long division, find the quotient and remainder when 5 4 3 2 – 3 2 – 2 3 1x x x x x+ + + is divided by 223x + . [3]