HCI 2024 Term 2 Common Test Practice 3

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Term 2 CT Practice 3 Name: _________________________________ ( ) Class: _________ Date: _____________ Duration: 1 hour Marks: 40 _________________________________________________________________________________ • Answer all questions. • Omission of essential working will result in loss of marks. • The number of marks for each question or part question is shown in [ ]. • The use of calculators is allowed. ___________________________________________________________________________________ 1 The line 3 1yx+= intersects the curve 22 2 2 25x xy y+ + = at the points A and B. Find the coordinates of A and B. [4] 2 (i) Express 2 6y x x= − − + in the form ( )2 y k x h= − − , where h and k are constants. [2] (ii) Sketch the graph of 2 6y x x= − − + , showing clearly the turning point, x- and y-intercepts. [3] 3 Using a suitable substitution, solve the equation ( ) 213 28 3 9 0xx+ − + = . [4] 4 (a) Solve the equation 3 2 5.x+ = + [3] (b) Without using a calculator, find the values of the integers a and b for which the solution 20 27 80 12xx + = − is 15 .4 ab+ [5] 5 (a) Solve the inequality ( )2 12 1 6 0 4x − −  . Represent its solution on a number line. [4] (b) Find the range of values of c for which 2 7 9 8 x x x c+ −  + for all values of x. [3]

2 6 The equation of a curve is ( ) 2 3 2 ky k x kx= − − + , where k is a constant. (i) Find the range of values of k for which the curve cuts the x-axis at two distinct points and has a minimum point. [4] (ii) In the case where 4k = , find the values of c for which the line y x c=+ will meet the curve. [3] 7 A set of flash cards consists of a square card of sides x cm and a rectangular card with dimensions x cm by y cm, where x  y. Given that the sum of the areas of the square and the rectangle is 84 cm 2 and the sum of their perimeters is 52 cm, form two simultaneous equations in terms of x and y. Hence, find the dimensions of the rectangular card. [5] End of Test