PRSS 2021 Sec 4E5N Prelim A Maths P1 - Mark Scheme

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] [M1 cao] Correct expression for D For real and distinct roots, [M1] State D > 0 [A1] (b) State the value(s) of p for which the curve is tangent to the x-axis. [1] For the curve to be tangent to y-axis,

4 PRSS_2021_Prelim_4E5N_AMaths_P1 , [A1] 2 Solve the following equations (i) , [4] [M1 – Change of Base] Let Therefore, [ M1 – Substitution Method ] or [M1] Values of y [A1] (ii) . [4] [M1] Break up the indices Let [M1] Correct Quadratic Equation

5 PRSS_2021_Prelim_4E5N_AMaths_P1 [M1] Substitution and values of both p found or , [A1] 3 In the expansion of , where m is a positive constant, the independent term of x is 126720. (a) Show that . [4] General Term [M1] General Term [M1cao] – Correct value of r [M1] Equate general term with [AG1] (b) Hence, find the coefficient of in the expansion of [3]

6 PRSS_2021_Prelim_4E5N_AMaths_P1 [M1] Value of r found Term with [M1] Find term with Coefficient of is 887040 [A1] 4 (a) Express in partial fraction. [3]