2020 Sec 3 IP SCGS AMath EOY Question paper

CANDIDATE NAME CLASS 3 INDEX NUMBER ADDITIONAL MATHEMATICS Wednesday 07 October 2020 2 hours 15 minutes Candidates answer on the Question Paper. No additional materials are required. READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the spaces at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid/tape. Answer all the questions. 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 an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. 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. This question paper consists of 17 printed pages and 1 blank page SINGAPORE CHINESE GIRLS’ SCHOOL END-OF-YEAR EXAMINATION 2020 YEAR THREE INTEGRATED PROGRAMME

2 Mathematical Formulae ALGEBRA Quadratic Equation For the equation 02 = + +c bx ax, a ac b bx 2 42 − ± −= Binomial expansion ( ) ,2 1 2 21 nr r nnnnn b b ar nb anb ana b a + +     + +     +     + = + −−−  where n is a positive integer and ! ) 1 ( ) 1 ( )! ( ! ! r r n n n r n r n r n + − −=−=       .

3 [Turn Over 1. (i) Factorise 222 .x xy y+− [1] (ii) Hence or otherwise, find the values of x and y which satisfy the equations [3] 22 2 8 , 4 . y xy x xy −− = − +=

4 2. T he curve 2 12 2y xx= +− crosses the x -axis at 1x and 2x , where 2x > 1x . Without using a calculator, find the exact value of 2 1 x x , leaving your answer in the form 2 pq− , where p and q are integers. [5]

5 [Turn Over 3. (a) The equation of a curve is 236y x xc= ++ , where c is a constant. Find the range of values of c for which 2y> . [3] (b) Jason bought some shares in the stock market. The value of the shares can be modelled by the function 24 67yx x= −+ , where $y is the value of the shares in thousands and x is the time in years after the shares were first bought. (i) Express 24 67yx x= −+ in the form 2()y ax b c=−+ , where a, b and c are constants. [1] (ii) Find the minimum value of the shares and the corresponding time, in months, after the shares were first bought when this occurs. [2]

6 4. Solve the following equations. (a) ( 2) 48ttee += [3] (b) ( ) 2 343 4 216xx x −= [3]

7 [Turn Over (c) 6 4 16 3 1log ( 4) log log 4xx x+= + [5]

8 5. (i) Factorise 3 32xx−+ completely. [3] (ii) Hence or otherwise, express 3 23 32 x xx − −+ in partial fractions. [4]

9 [Turn Over 6. In the expansion of 10 kx x  + , the term independent of x is 70 3 times the coefficient of 4x . (i) Given that k is a negative constant, find the value of k. [5] (ii) Using the value of k found in part (i), find the coefficient of 6x in the expansion of 10 2(4 9 ) kxx x −+  . [3]

10 7. The coordinates of P, Q and R are (2,5) , ( 3, 2)− and (0, 3)− respectively. (i) Show that triangle PQR is a right-angled triangle. [2] (ii) Given that the point S ( ,0)x lies on the perpendicular bisector of PR, find the value of x. [4] (iii) Find the area of the quadrilateral PQRS. [2]