2017 SNGS Sec 4 EM Prelim P2

3 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/02 [Turn Over Answer all the questions. 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] 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] Q 10 km/h P X O 15 km/h Y

4 CHIJ SNGS Preliminary Examinations 2017 - Mathematics 4048/02 3 The diagram shows a circle ABCDE, with centre O. AEF is a straight line. Angle BAE = 100 and angle CEF = 120. AE = ED. EC is a diameter. (a) Show that triangle ACE and triangle DCE are congruent. [2] (b) Find, giving reasons for each answer, (i) angle ECD, [2] (ii) angle ABD, [1] (iii) angle ECB. [1] (c) Given that AC = 8 cm, find the diameter of the circle. [2] 4 The first four terms in a sequence of numbers, ..,.........,,, 4321 uuuu are given below. 1030 1 u 5231 2 u 13432 3 u