2023 CGS Prelim P1

Name: Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION MATHEMATICS 4052/01 Paper 1 21 August 2023 2 hours 15 mins Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name and index number on all 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 questions. 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 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 π , use either your calculator value or 3.142, unless the question requires the answer in terms of π . At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. This question paper consists of 25 printed pages. Question 1 2 3 4 5 6 7 8 9 10 11 12 Marks Question 13 14 15 16 17 18 19 20 21 22 23 24 Marks Table of Penalties Qn. No. Presentation –1 Accuracy/ Units –1 Parent’s/ Guardian’s Signature For Examiner’s Use 90

2 2023 Prelim S4 Mathematics P1 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rlπ 2Surface area of a sphere = 4 rπ 21Volume of a cone = 3 rhπ 34Volume of a sphere = 3 rπ 1Area of triangle = sin 2ABC ab C Arc length = , where is in radiansrθθ 21Sector area = , where is in radians2 r θθ Trigonometry sin sin sin abc ABC= = 222 2 cosa b c bc A=+− Statistics Mean = fx f ∑ ∑ 22 Standard Deviation = fx fx ff  − ∑∑ ∑∑

3 2023 Prelim S4 Mathematics P1 [Turn over Answer all the questions. 1 (a) It is given that m = 2π 2 22 h h k+ . Find m when k = 1.2 and h = 0.3. Answer m=……………………… [1] (b) Two numbers p and q, written as the products of their prime factors, are 2562 3 5p=×× and 23 2 3q= × . (i) Find the HCF of p and q. Answer ……………………… [1] (ii) Find the smallest positive integer k such that (p × q × k) is a perfect cube. Answer k =……………………… [1] (c) Estimate the percentage of the rectangle that is shaded. Answer ………………………% [1]

4 2023 Prelim S4 Mathematics P1 2 (a) Is 673 a prime number? Answer ………………………... [1] (b) Explain your reasoning. Answer ……………………………………