RI Post+Prelim+Revision+P1 Qns

RAFFLES INSTITUTION H2 Mathematics 9758 2025 Year 6 Term 4 Post-Prelim Revision Paper 1 (Source: Other JCs’ Prelim Qns) Total number of marks: 100 3 hour Please attempt this paper in one sitting under exam conditions within 3 hours before the lesson on 17 Oct 2025 (Friday). 1 (i) A quadratic curve passes through the point  1, 4 and has its turning point at 2,5 . Find the equation of the curve. [4] (ii) Given instead that a cubic curve passes through the same point  1, 4 and has the same turning point as stated in part (i). Explain whether it is possible to obtain a unique equation of the curve based on given information. [1] 2 The diagram shows part of the graph cos2 ,xyx for 05 x , which represents the path of a roller coaster. The horizontal distance travelled by the roller coaster is denoted by x units and its vertical distance travelled is denoted by y units. (a) Show that cos 2dc o s 2 2sin2 lnd xyx xx xxx   . [2] (b) At the point on the graph where x  , find the rate at which the roller coaster is moving vertically when it is moving horizontally at a rate of 8 units per hour. [2] (c) Find the acute angle that the tangent to the graph where x  makes with the horizontal. [1] 3 Do not use a calculator to solve this question. (i) Solve the inequality 2 6 145 x xx   . [3] (ii) Hence solve the inequality 2 2 6 145 xx xx   . [2]

Raffles Institution H2 Mathematics 2025 Year 6 _______________________________________________________________________________________________ ______________________________________ Y6 H2 Math Term 4 Post Prelim Revision: Paper 1 Page 2 of 6 4 A sequence is defined by the recurrence relation 1 1 1 n n n uu u    , for 1n . (a) State what happens to the sequence when 1 0u  . [1] It is now given that 1 2u  . (b) Find 2 345 6, , , and uu u u u . [2] (c) By observing the pattern in part (b), find 4 1 n r r u   in terms of n. [2] 5 Elly started planking as an exercise and she c ontinues the exercise every day to build her core muscles. If she meets her target duration, she increases the target duration of the exercise by an additional 4 seconds on the next day. On any day, she will stop her exercise once she meets her target duration for the day. However, Elly does not always meet her target. Each day when Elly misses her target, she decreases her target duration by 5% on the following day. On Day 1, Elly carries out 20 seconds of planking, and she hopes to reach her target of 2 minutes by the end of 30 days. (a) Assume that Elly met her targets for the fi rst 11 days but missed her target duration from Day 12 to Day 15. Determine whether Elly will be able to reach her target of 2 minutes by the end of 30 days, if she met all her targets from Day 16 onwards. [3] Due to the difficulty level, Elly decides to rest art the programme by incr