Bendemeer 2024_4NA_Prelim_P1_Markscheme

CANDIDATE NAME MARKING SCHEME CLASS INDEX NUMBER . This document consists of 19 printed pages and 1 blank page. MATHEMATICS (SYLLABUS A) 4045/01 Paper 1 30 July 2024 2 Hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number on all the work you hand in. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Answer all the 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 70. 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. For𝜋, use either your calculator value or 3.142. BENDEMEER SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY FOUR NORMAL (ACADEMIC) FOR ASSESSMENT USE 70

2 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 . Mathematical Formulae Compound interest Total amount = 𝑃 (1 + 𝑟 100) 𝑛 Mensuration Curved Surface area of a cone = 𝜋𝑟𝑙 Surface area of a sphere = 4𝜋𝑟2 Volume of a cone = 1 3 𝜋𝑟2ℎ Volume of a sphere = 4 3 𝜋𝑟3 Area of triangle ABC = 1 2 𝑎𝑏sin C Arc length = rθ, where θ is in radians Sector area = 1 2 𝑟2𝜃, where θ is in radians Trigonometry 𝑎 𝑠𝑖𝑛 𝐴 = 𝑏 𝑠𝑖𝑛 𝐵 = 𝑐 𝑠𝑖𝑛 𝐶 𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 𝑐𝑜𝑠 𝐴 Statistics 𝑀𝑒𝑎𝑛 = ∑𝑓𝑥 ∑𝑓 Standard deviation = √∑𝑓𝑥2 ∑𝑓 − ( ∑𝑓𝑥 ∑𝑓 ) 2

3 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 1 (a) Simplify 6𝑥2𝑦 8𝑥𝑦3. 3𝑥 4𝑦2 [B1] Answer ………………………… [1] (b) Simplify ( 𝑥3 27) − 1 3 . ( 27 𝑥3) 1 3 = 27 1 3 (𝑥3) 1 3 [M1] = 3 𝑥 [A1] Alternate method ( 𝑥3 33) −1 3 = 𝑥−1 3−1 [M1] = 3 𝑥 [A1] Answer ………………………… [2] 2 The diagram below shows a solution set for x on a number line. (a) Write down the range of values of x. −3 ≤ 𝑥 < 2 [B1] Answer ………………………… [1] (b) If x is an integer, state the largest value of x. 1 [B1] Answer ………………………… [1] -1 0 1 2 3 -2 -3

4 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 3 In a sale, the price of a handphone is reduced from $388 to $302. Calculate the percentage decrease in price. $388 - $302 = $86 [M1] 86 388 × 100% = 22.2% (to 3 s.f) [A1] Answer …………………………% [2] 4 The angles in a triangle