HCI 2024 Term 2 Common Test Practice 2

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Term 2 CT Practice 2 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 equation of a curve is y = mx2 + (c – m)x – (c + 3). Given that m > 0, show that the curve cuts the x-axis at two distinct points. [3] 2 (a) Find the exact value of x if 218 32x+− = . [3] (b) Simplify 11 5 3 5 3 + +− . [2] (c) Find the area of a right angled triangle ABC, given that angle ABC is a right angle, ( )5 3 2 cmAB=+ and 54 cm 2 BC =− . Leave your answer in the form 2ab+ . [3] 3 (a) Find the range of values of x for which (2 1) 2522 xx x+  + . [3] (b) Given that the curve whose equation is 2()y p x q= − − crosses the x-axis at the points (1,0) and (3,0), (i) find the value of p and of q, [4] (ii) the maximum value of y. [1] 4 Find the values of q for which the line 8y qx=− is a tangent to the curve 2 4xy= . Leave your answer in exact values. [4]

2 5 Solve the simultaneous equations: 27 x ÷ 3 y = 9, 2 2x × 4 1–y = 64. [4] 6 Sketch the graph of 23 8 9,y x x= − + showing clearly the coordinates of the turning point and the y-intercept [5] 7 Using a suitable substitution, solve the equation 12 2 3xx+−+= . [4] 8 Solve the equation : 3 4 0xx− − = . [4] Please finish in 1 hour!!