HCI 2024 Term 2 Common Test Practice 1

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Term 2 CT Practice 1 Name: _________________________________ ( ) Class: _________ Date: _____________ Duration: 1 hour Marks: 40 __________________________________________________________________________________ • 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 x + y = 3 meets the curve x2 – 2x + 2y2 = 3 at two distinct points. Find the coordinates of these two points. [4] 2 Find the possible values of k for which the line 1−= kxy does not intersect the curve 32+= xy . [3] 3 Using a suitable substitution, solve the equation 14 16 66xx− += . [4] 4 Sketch the graph of 24 24 20y x x= − + , indicating clearly the coordinates of the turning point, x and y intercepts. [4] 5 The area of a rectangle ABCD is given by m2, and the length of side AB is m. Find, without using a calculator, the length of side BC in the form of m, where a and b are real numbers. [3] 6 Given that 3 1 4 48 2 3 3 3 − +− + can be expressed in the form of 3ab+ , find the value of a and of b . [4] 7 Show that 24 12 10xx−+ is always positive for all real values of x . [3] 8 Show that the roots of 2 ( 2) 2x p x p+ − = are real. [3] ( )1 3 2+ ( )28+ ( 2)ab+

2 9 Solve the equation 25 50 2 12xx− − − = . [3] 10 Find the solution set of each of the following inequalities: (i) 1832 + xx [2] (ii) 9)2( 2 +x [2] Hence, state the set of values of x which satisfy both of these inequalities. [1] 11 The given diagram shows a quadratic curve with a y-intercept of 48 which crosses the x-axis at 4x=− and 6x= . (i) State the equation of the line of symmetry for the curve. [1] (ii) Find the equation of the parabola in the form 2 where 0y ax bx c a= + +  . [3] Time yourself to finish in 1 hour!! x y