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 ……………………………………………………………………………………… ……………………………………………………………………………………… [1] 3 In a library, the ratio of the number of books to magazines is 3 : 2. In a donation drive to help an overseas primary school, many books and magazines were given away. If the number of books is reduced by 40% and the number of magazines is reduced by 20%, find the new ratio of the number of books to the number of magazines. Answer ………………………... [2] 4 (a) Simplify 3 2 7 21 .28 xx yy÷ Answer ……………………… [2] :

5 2023 Prelim S4 Mathematics P1 [Turn over (b) Factorise 32 7 4 28ppp+ −− completely. Answer ……………………… [2] 5 The stem and leaf diagram below shows the scores of 16 students in a Science class test. Stem Leaf 2 5 5 7 3 0 0 1 2 x 8 4 2 3 5 7 7 y 9 Key: 2|5 represents 25 marks Given that the median score is 36 marks, and the mean score is 37 marks, find the value of x and of y. Answer x = ………………………, y = ……………………… [3] 6 Solve the inequality 31 33 52 x xx− ≤+< + . Illustrate your solution on the number line. [3] Answer

6 2023 Prelim S4 Mathematics P1 7 Study the number pattern, then find the values of the unknowns in lines (a), (b) and (c). 2 121 1 2 3123=−+×× 2 121 234 2 3 4=−+×× 2 121 345 34 5=−+×× (a) 2 121 10 11 12 suv=−+×× (b) 2121 15 16 17w =−+ (c) 2 121 10626 xyz=−+ Answer (a) s = ………………, u =………………, v = ……………… [1] Answer (b) w = ………………………... [1] Answer (c) x = ………………, y = ………………, z = ……………… [1]

7 2023 Prelim S4 Mathematics P1 [Turn over 8 Given that y is inversely proportional to 2 1x + and the difference in the values of y when 1x= and when 3x= is 4. (a) Express y in terms of x. Answer y =………………………... [2] (b) Find the value of y when 2x=− . Answer y =………………………... [1] 9 A piece of metal is heated to 375oC and then left to cool for 15 minutes. The temperature of the metal decreases at a rate of 18 oC/min for the first 5 minutes and then decreases at a rate of 7 oC /min for the next 10 minutes. Find the time taken for the metal to cool to a temperature of 250 oC. Answer ………………………...min [3]

8 2023 Prelim S4 Mathematics P1 10 Keith walks a distance of 1.2 km at an average speed of 6 km/h and takes a break for 15 minutes. He then continues to run a further distance of 800 m in 4 minutes. Calculate, in km/h, his average speed for the whole journey. Answer ………………………...km/h [2] 11 216 cubes, each having edges of 2.6 cm, measured to the nearest 0.1 cm, fit exactly into a larger cubic box. Find the (a) greatest possible length of the cubic box. Answer ………………………...cm [1] (b) least possible volume of the cubic box. Answer ………………………...cm3 [2]

9 2023 Prelim S4 Mathematics P1 [Turn over 12 ABCDEF is a regular hexagon. (not drawn to scale) (a) State the name of the triangle EOD . Answer ……………………………………………………………………………………………. [1] (b) Find (i) reflex angle EOC. Answer Reflex angle EOC =………………………...° [2] (ii) .angle ANB Answer angle ANB= ………………………...° [2] N

10 2023 Prelim S4 Mathematics P1 13 In a park XYZ, XY = 100 km and YZ = 45 km. X is due west of Y and the bearing of Z from Y is 300°. The point Y is marked in the space below. Construct the park XYZ using the scale 1 cm : 10 km. [2] Construct on the diagram drawn below, (i) the perpendicular bisector of XY, [1] (ii) the bisector of angle ZXY. [1] (iii) A bench B is in the park, equidistant from X and Y and nearer to XZ than XY. Mark a possible position of B on the diagram drawn. [1] Answer Y N