Bendemeer 2024 Prelim Exam 4E5N EMath P1 QP

CANDIDATE NAME CLASS INDEX NUMBER ------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------- READ THESE INSTRUCTIONS FIRST Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid/tape. DO NOT WRITE ON ANY BARCODES. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For  , use either your calculator value or 3.142. This document consists of 24 printed pages. MATHEMATICS Paper 1 4052/01 20 Aug 2024 2 hours 15 minutes Candidates answer on the Question Paper. No additional materials are required. BENDEMEER SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) FOR EXAMINER’S USE 90

2 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 MATHEMATICAL FORMULAE Compound Interest Total amount = P n r      + 1001 Mensuration Curved surface area of cone = rl Surface area of a sphere = 4  r2 Volume of a cone = hr 2 3 1 Volume of sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = radiansin is where, r Sector area = radiansin is where,2 1 2 r Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean =   f fx Standard Deviation =        −     22 f fx f fx

3 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 [TURN OVER Answer all the questions. 1 Factorise each of the following completely. (a) 4𝑎2 − 𝑏2 Answer ........................................... [1] (b) 5𝑥 − 1 + 10𝑥2𝑦 − 2𝑥𝑦 Answer ........................................... [2]

4 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 2 (a) Simplify (2𝑥3𝑦)3. Answer ........................................... [1] (b) Use the laws of indices to solve the following equation for x. Show your working clearly. 22 × 53 + 1 125𝑥 = 54. Answer x =..................................... [2]

5 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 [TURN OVER 3 (a) Express 1176 as a product of its prime factors. Answer ........................................... [1] (b) The number 1176k is a perfect cube. Find the smallest positive integer value of k. Answer k = ..................................... [1] (c) The highest common factor of two distinct integers, n and 1176, is 28. Given that 500 < n < 1000, find the smallest possible value of n. Answer n = ..................................... [1]

6 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 4 The volume of a right pyramid is 4.8 × 10−8 m3 and its length of the square base is 1.5 × 10−3m. Giving your answer in standard form, find its height. Answer ........................................ m [2] 5 Benjamin invested $8000 at a rate of 3.3% per annum compounded monthly. What is the value of his investment at the end of 6 months? Answer $ .......................................... [2]

7 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 [TURN OVER 6 (a) In the Venn diagram below, shade the region 'PQ . [1] (b) A universal set  and its subset A and B are given by = {x: x is an integer and 0 < x < 12}, A = {x: x is a factor of 24}, B = {x: 2𝑥 − 7 ≥ 5}. (i) Write all the elements of  in the Venn diagram below. [2] (ii) Another number is included in the universal set . This number is in the region AB . Write down a possible value of this number. Answer ….......................................... [1] P Q  A B 

8 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 7 (a) The expression 2𝑥2 + 8𝑥 + 9 is equivalent to 2(𝑥 + 𝑎)2 + 𝑏. Find the value of a and the value of b. Answer a = ...................................... [1] b = ...................................... [1] (b) Sketch the curve 𝑦 = 2𝑥2 + 8𝑥 + 9 on the given axes below, clearly showing the y-intercept and the turning point. [2] y x 0

9 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 [TURN OVER 8 (a) Given that the formula of y is inversely proportional to the square of (𝑥 + 2) and the value of y = 1 3 when x = 7. Express y in terms of x. Answer y = ...................................... [2] (b) Hence, or otherwise, make x the subject of the formula. Answer x = ...................................... [2]

10 4052/01 / Sec 4E5N / Preliminary Examination / BDMS 2024 9 Explain why (2𝑛 + 3)2 − (4𝑛 + 3)(𝑛 − 6) is a multiple of 3 for all integer values of n. Answer ........................................................................................................................................ ........................................................................................................................................ [2] 10 Simplify 2𝑥+3 𝑥2+3𝑥+2 − 5 𝑥+1 as a single fraction. Answer .............................................. . [3]