2022 Sec 3 Express A Math EOY Greenridge Secondary with Answer

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BP- 125 Name Register Number Class GREENRIDGE SECONDARY SCHOOL END.OF-YEAR EXAMINATION 2022 Secondary 3 Express sEcororiYscnooa 6iEE rEocE sEcono iv sdroo. csEExEDcE C'IEE BDCE SECOTDTRY iECorl]D ry oicErrdocEsEcoxa.iYoREEriDGEsEa)xo^iY ADDITIONAL MATHEMATICS Paper 1 28 September 2022 Wednesday 4049t01 For Examiner's Use Additional Materials: No Additional Materials are Required READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work you hand in Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer ALL questions. Write your answers and working on the question paper. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of a scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. PartnerlnLeaming 123 M 2h15min 1145 - 1400 90

1 BP-127 t3l PartnerlnLeaming 125 A cuwe has the equation y = to-'? + (2k - 4)x + 3k - 2 , where /r > 0, Find the set of values of* for which the curve lies completely above the x-axis.

BP-128 t4l2 A rectangular block has a square base. The length ofeach side of the base is ( J5 - Jr) m and the volume of the block is (tJi - zJi) m3. Find, without using a calculator, the height ofthe block in the form (ali+tJl) m, where a and 6 are integers ParlnerlnLeaming 126

J Solve the simultaneous equations 9',(27)v =1 z" +1Ji1, =rcJi BP- 129 t41 PartnerlnLeaming '127

4 (a) Find the values ofthe constant c for which the line 2y = x+ c is a tangent to the ^6CUrVe v=Z-r+-'x (b) Ifthe quadratic equation n(x'+o)+Zx1x+1)+(6n-2)x=-16 has 2real and distinct roots, given that z is a constant, determine the range ofvalues of rn. BP-130 t4l t4l PartnerlnLeaming 128

BP- r 31 5 (a) Find the value of each of the integers p and q for *h*h f-)l(r6i =2P x5c t2) (b) By using the substitution u = 3' , find the values ofr such that 32'+t -2 - 8x3x-t t5l PartnerlnLeaming 129 l

BP- 1 32 5 (a) Obtain the first four terms in the expansion of _tr in ascending powers of .r, 12)2 4 O) Hence, find the coefficient of x3 in the expansion of (1+x)'z x2 4 PartnerlnLearning 130 t3l

BP-133 7 (a) Solve the equation lg(x+12)=l+lg(2-x). t3l (b) Given that log, p = a, logrq =g a11d. L--2" ,express c in terms of a and D t4)q PartnerlnLeaming 13'l

E Desmond buys and sells shares in the stock market. The value of the shares he bought is given by the function y =3x7 -5x+7, wherey is the value of the shmes in thousands of dollars and r is the time in years after it was first bought. (a) What is the minimum value of the shares and when does it occur? (b) Sketch the graph of y=-rz -2x+6, showing clearly the coordinates ofthe minimum point and the intersections with the axes. PartnerlnLeaming 132 BP- 134 t4l t3l