HCI 2026 Revision Paper 1 for A-Math Class Test 1

1 Hwa Chong Institution Integrated Programme Secondary Three Additional Mathematics Name: ________________________ ( ) Class: _________ Date: _____________ Term 2 Additional Mathematics Test 1 Revision Paper 1 ________________________________________________________________________________ Answer all the questions. 1 Given that 19264 16 x x + = , find the value of x and hence, 64x in the form 2n where n is an integer. [4] 2 Solve the equation 7 2 2 0xx+ + = , explaining why you would or would not reject the solutions obtained. [4] 3 Given the area of a rectangle ABCD is 2(46 14 7) cm− and the length of the rectangle AB is (10 7) cm+ . Find, without using a calculator, (i) the width of the rectangle BC and show that BC = (6 2 7) cm− , [3] (ii) the exact value of 2AC in the form ( 7) cd+ , where c and d are integers. [3] 4 Solve the simultaneous equations: 3 2 2 5 25 , 3 5. xy yx + = =− [4] 5 (i) Express 22 12 11y x x=− + − in the form 2()y a x h k= + + , where a, h and k are constants. [3] (ii) Sketch the graph of 22 12 11y x x=− + − , labelling the turning point, the line of symmetry and the y-intercept of the curve. [3]