HCI 2024 Term 2 Common Test Practice 4

1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Term 2 CT Practice 4 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 Using appropriate substitu tion, solve the equation  1 0.5 153 0 5 .25 xx   [ 4 ] 2 Find the range of values of x for which 2(2 ) 8 (2 ) 1 5 0xx    [ 4 ] 3 By expressing 232 1 1 8xx in the form 2()ax b c  , where a, b and c are constants, (i) write down the minimum value of 232 1 1 8xx  , [ 2 ] (ii) hence, sketch the graph of 232 1 1 8yx x , indicating clearly all workings, intercepts and turning point. [3] 4 Express 322 2 3 23 32 2 4    in the form 26 ,pq r where p, q and r are rational numbers. [4] 5 The line 1 xy meets the curve 0439 22  xyx at two distinct points. Find the coordinates of these two points. [5] 6 Find the range of values of m for which the straight line 12 2yx m  meets the curve 2(3 )ym x . [ 4 ]

2 7 Show that for all real values of p and q, 22 2(1 ) 2 (2 1)y p x pqx q    is always negative for all real values of x. [3] 8 AMB is a right-angled triangle with angle 90 .AMB  BM is produced to C such that  24 c m .BM MC Given that the area of triangle 214 cm ,ABC find, without using a calculator, the length of AM in the form 2,ab where a and b are integers, [4] 9 Find the range of values of x that satisfy the inequality 221 4 1 2xx   . [4] 10 Solve the equation 32 2 2 .xx  [3] - End of Paper - Manage your time well during the test!