PRSS 2021 Sec 4E5N Prelim A Maths P1 - Question Paper

3 PRSS_2021_Prelim_4E5N_AMaths_P1 Answer all the questions. 1 (a) Find the range of values of p for which the equation has real and distinct roots. [3] (b) State the value(s) of p for which the curve is tangent to the x-axis. [1]

4 PRSS_2021_Prelim_4E5N_AMaths_P1 2 Solve the following equations (i) , [4] (ii) . [4]

5 PRSS_2021_Prelim_4E5N_AMaths_P1 3 In the expansion of , where m is a positive constant, the independent term of x is 126720. (a) Show that . [4] (b) Hence, find the coefficient of in the expansion of [3]

6 PRSS_2021_Prelim_4E5N_AMaths_P1 4 (a) Express in partial fraction. [3] (b) Hence, evaluate . [3]

7 PRSS_2021_Prelim_4E5N_AMaths_P1 5 The curve , for has a stationary point at point A. Find (i) , [2] (ii) the x-coordinate of A, [2]

8 PRSS_2021_Prelim_4E5N_AMaths_P1 (iii) the nature of A. [3]

9 PRSS_2021_Prelim_4E5N_AMaths_P1 6 (a) Given that , find (i) , [1] (ii) . [2]

10 PRSS_2021_Prelim_4E5N_AMaths_P1 (b) The diagram below shows a right angled triangle ACD. It is given that , , and . Express in terms of y. [4] A D C y cm 3 cm 3 cm B

11 PRSS_2021_Prelim_4E5N_AMaths_P1 7 A curve has the equation . (a) Explain why the curve has no turning point. [2] (b) Given that y is increasing at a rate of 0.4 units per second at the instant when , find the rate of change of x at that instant. [3]

12 PRSS_2021_Prelim_4E5N_AMaths_P1 (c) A curve is such that and has a turning point . Find the equation of the curve. [4]