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 are in the ratio 3:4:5. Calculate the size of each angle in degrees. Total number of units = 3+4+5 = 12 12 units → 180° [M1] 1 unit → 180° 12 = 15° 3 units → 15° x 3 = 45° 4 units → 15° x 4 = 60° 5 units → 15° x 5 = 75° Ans: 45°, 60° and 75° [A1] Answer ………°, ………° and ..…….° [2]

5 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 5 The diagram shows a regular hexagon ABCDEF. AB and DC are produced to meet at G. Find angle BGC. Exterior angle of hextagon = 360 6 = 60° [M1] angle BGC = 180° − 60° − 60° = 60° [A1] Answer …………………………° [2] 6 Use a scale factor of 2 3 to draw a reduction of the given figure. [2] B A C D E F G

6 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 7 (a) Solve 𝑥 𝑥+3 = 24. 𝑥 = 24(𝑥 + 3) 𝑥 = 24𝑥 + 72 23𝑥 = −72 𝑥 = −3 3 23 𝑜𝑟 − 72 23 . [B1 – No marks if 3 s.f] Answer x =………………………… [1] (b) Given that 57×5−2 54 = 5𝑎, find the value of a. 57−2−4 = 5𝑎 [M1] 51 = 5𝑎 By comparing power a = 1 [A1] Answer a =………………………… [2]

7 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 8 Triangles ABC and DEC are similar. All the lengths are in centimetres. A C B (a) Calculate x. Since Triangles ABC and DEC are similar, 6 9 = 𝑥 12 [M1] 𝑥 = 12×6 9 = 8 [A1] Answer x =…………………cm [2] (b) Find y in terms of z. 𝑧 𝑦 = 6 9 [M1] 𝑦 = 9 6 𝑧 𝑦 = 3 2 𝑧 [A1] – no marks if did not simplify. Answer ………………………… [2] D E 9 6 12 x y z

8 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 9 The first four terms of a sequence are 5, 9, 13 and 17. (i) Find an expression, in terms of n, for the nth term of the sequence. Ans: 𝑇𝑛 = 4𝑛 + 1 [B1] [No marks if not simplified i.e. 5+4(n-1)] Answer ………………………… [1] (ii) Find the 25th term of the sequence. 𝑇25 = 4(25) + 1 = 101 [B1] Answer ………………………… [1] (iii) Jane says that 212 is a term in this sequence. Is she correct? Explain your answer. 4𝑛 + 1 = 212 4𝑛 = 211 𝑛 = 211 4 = 52.75 Since n is not an integer, 212 is not a term in this sequence. Jane is not correct. [B1] Answer …………………………………………………………………………….………………… ………………………………………………………………..…………………….………………… [1]

9 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 10 A map is drawn to scale of 1: 25 000. (a) The distance on the map between the school and Mary’s house is 4 cm. Find the actual distance, giving your answer in kilometres. 1cm: 25 000 cm 1km = 1000m = 100, 000cm 1cm : 25000 / 100,000 = 0.25 km [M1] 4cm: 0.25 x 4 = 1 km [A1] Answer …………………………km [2] (b) The area of the playground is 75000 m2. Calculate the area of the playground on the map. Give your answer in cm2. 1cm : 250 m 1cm2: 62 500 m2 [M1] 1m2 : 1 62500 cm2 75 000 m2 : 75000 62500 = 1.20 cm2 [A1] Answer ………………………… cm2 [2]

10 4045 Paper 1/ Sec Four NA / Prelim Exam / BDMS 2024 11 (a) Write 90 as the product of its prime factors. Ans: 2 x 32 x 5 [B1] 2 90 3 45 3 15 5 5 1 Answer ………………………… [1] (b) Find the highest common factor (HCF) of 90 and 216. 23 × 33 = 216 Ans: 2 × 32 = 18 [B1] Answer ………………………… [1] (c) Find the smallest positive integer value of k such that 90k is a perfect square. Ans: 2 x 5 = 10 [B1] Answer k = …………………… [1]