2024 Y6 Timed Prac Rev Paper 3 (Qns)

RAFFLES INSTITUTION H2 Mathematics (9758) 2024 Year 6   2024 Year 6 Timed Practice Revision Practice Paper 3 (Source: 2021 Year 6 Term 3 Common Test) The solution will be released in Ivy on 10 June (Monday) Total Marks: 100 Duration: 3h   **** Note that Qn 4 (Complex Numbers) will NOT be examined in the coming Timed Practice. So, you should complete this paper within 2 hrs 47 mins. 1 An arithmetic series has first term a and common difference d, where a and d are non-zero. If the first, fifth and eleventh term s of the arithmetic seri es are equal to the first, second and third terms of a geometric series respectively, find the exact sum of the first ten terms of the geometric series, in the form ka , where k is a simplified rational number. [4] 2 (i) By writing   2 21 23rr in partial fractions, find an expression for  2 2 21 23 n r rr  in terms of n. [3] (ii) Hence find the exact value of 21 21 21 19 21 21 23 23 25  . [2] 3 For a curve with equation 23 38xx y y  , find (i) the x-coordinate of the point at which the tangent is parallel to the x-axis, [4] (ii) the equation(s) of the normal(s) at the point(s) where 2.y [3]   4 The polar form of a complex number z is given by iezr  , where 0r and 0 π , and the complex number 13 i.33wz  (i) Find w in exact polar form in terms of r and . [3] (ii) Given that 5 * z w is real and positive, find the possible value(s) of  in exact form, leaving your answer(s) in terms of . [4]

5 The function f is defined by 2f : 2 5 3, , .x xx x x a   (i) State the greatest value of a such that the function 1f exists. [1]   For the rest of the question, use the value of a found in part (i). (ii) Find 1f in a similar form. [3]   (iii) Find the exact solution of 1f. x x  [3] (iv) The function g is defined for specific integer values of x as follows. x 5 4 1 0 2 g(x) 6 4 23 0 3 Find the value of b, where 1fg ( ) 3 .b  [1]   6 The curve C has equation 221 0 1 7 ,, 3 .3 xxyx x x     (i) Without using a calculator, find the set of values of y that C can take. [4]   (ii) Sketch C, labelling the relevant features in exact form. [5]

7 To build a Virtual Reality (VR) experience, a virtual world is created to contain geometric models. With reference to the origin O, every point in the virtual world is repres