RVHS 2023 JC1 Promos 9649

1 9649 / 01 / 2023 [Turn over RIVER VALLEY HIGH SCHOOL 2023 JC 1 Promotional Examination Higher 2 Name CLASS 2 3 J INDEX NUMBER FURTHER MATHEMATICS Paper 1 Additional Materials: List of Formulae (MF26) Answer Papers Cover Page 9649/01 27 September 2023 3 hours READ THESE INSTRUCTIONS FIRST Do not open this booklet until you are told to do so. Write your name, class and index number in the space at the top of this page. Write your name and class on the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 signi ficant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. Unsupported answers from a graphing calculator ar e allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calcul ator are not allowed in a question, you are required to present the mathematical steps us ing mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for poor presentation in your answers. At the end of the examination, place the cover page on top of your answer paper and fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. This document consists of 6 printed pages and 2 blank pages.

2 9649 / 01 / 2023 1. (a) Prove by mathematical induction that 52nn is divisible by 3 for all positive integers n. [4] (b) Hence, find the greatest common divisor of the numbers in the set      115 25 2 ,nn n   . (The greatest common divisor of a set of numbers is the largest integer that can divide all the numbers in the set.) [3] 2. (i) Use Simpson’s rule with five ordi nates to find an approximation to 5 24 2 d 87 Ix xx   , giving your answer to 4 decimal places. [2] (ii) Find the exact value of I and deduce from part (i) an approximate value of 1 1sin , 3    giving your answer to 4 decimal places. [3] 3. Solve the differential equation 2 2 2 d 48 e c o s 24 s i n 2d xz zx xx    , given that 0z and d 1d z x  when 0x . [7] 4. A deck of 25 playing cards consists of 3 diffe rent colours – blue, yellow and red. Each card has a picture of a fruit on it. The number of cards of each type are given in the following table: Apple Kiwi Watermelon Grapes Blue 1 3 2 4 Yellow 1 2 1 2 Red 2 2 1 4 A c