2017 SNGS Sec 4 EM Prelim P2 Solutions

3 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/02 1 (a) Solve the simultaneous equations .1943 ,82   yx xy [3] (b) Simplify 22 22 65 4 yxyx yx   . [3] (c) (i) Express 372  xx in the form .)( 2 bax  [2] (ii) Hence solve the equation ,0372  xx giving your answers correct to two decimal places. [2] 1(a) 82  yx 194)82(3  yy 52 y 5.2y 3x 1(b) 22 22 65 4 yxyx yx        yxyx yxyx 23 22      yx yx 3 2   1(ci) 3)2 7()2 7(737 2222  xxxx = 4 1152 7 2      x 1(cii) 04 1152 7 2      x 4 1152 7 2      x 905.32 7      x 41.041.7  xx

4 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/02 2 The diagram shows a road junction at O with PO perpendicular to OQ and OP = 60 km. A cyclist, X, starts from P and travels towards O at a constant speed of 10 km/h. At the same time, another cyclist, Y, starts from O and travels towards Q at a constant speed of 15 km/h. (a) Cyclist X leaves from P and cyclist Y leaves from O at noon. Given that t is the time in hours, write down, in terms of t, (i) the distance of X from O after t hours, [1] (ii) the distance of Y from O after t hours. [1] (b) After t hours, the cyclists are 80 km apart. Write down an equation in t to represent this information and show that it reduces to .01124813 2  tt [2] (c) Solve the equation .01124813 2  tt [3] (d) Find the distance of cyclist X from O when the cyclists are 80 km apart[1] 2(ai) t1060 cm 2(aii) 15t cm