2024 CGS EM Prelim Paper 2 with Ans Key

Name: Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION 2024 MATHEMATICS 4052/02 Paper 2 20 Aug 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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. Answer all the 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. 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. Question 1 2 3 4 5 6 7 8 9 10 Marks Table of Penalties Question No. Presentation –1 Accuracy/ Units –1 Parent’s / Guardian’s Signature This document consists of 22 printed pages For Examiner’s Use 90

2 Crescent Girls’ School 2024 Prelim S4 Math P2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP  + Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where 𝜃 is in radians Sector area = 21 2 r  , where 𝜃 is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 Crescent Girls’ School 2024 Prelim S4 Math P2 [Turn Over 1 20 students of class 4A took a test. The marks are shown in the stem and leaf diagram. 5 0 2 3 3 5 7 8 6 0 1 2 6 7 7 9 7 0 k 5 4 7 8 9 8 Key: 5|2 means 52 marks The marks are also represented in the box-and-whisker plot. (a) Find the value of k. Answer k = …………………… [1] (b) Would you prefer to use the mean or the median mark to describe the performance of class 4A? Give a reason for your answer. Answer …………………………………………………………………………… ……………………………………………………………………………… [2] (c) Class 4B took the same test as class 4A. A student from 4B was subsequently transferred to 4A and a new box-and-whisker plot for 4A was then drawn. It is given that the plot remained unchanged. How many marks did the transfer student obtain in the test? Answer ……………………marks [1] 50 56 64 71 98

4 Crescent Girls’ School 2024 Prelim S4 Math P2 2 (a) Given that 2 32 qpr= − + , express r in terms of p and q. Answer ………………………………… [2] (b) Simplify ( ) 423 0 2 2 35 xy xy xy −  . Answer …………………… [4]

5 Crescent Girls’ School 2024 Prelim S4 Math P2 [Turn Over (c) (i) Factorise 294x − . Answer ………………………… [1] (ii) Hence, express 2 32 9 4 3 2 x xx −−− as a single fraction in its simplest form. Answer …………………… [3]

6 Crescent Girls’ School 2024 Prelim S4 Math P2 Answer ……………………° [1] (ii) angle BAC , Answer ……………………° [2] 3 A, B, C and D are points on the circumference of a circle with centre O. BA produced and CD produced meet at X. Angle 24BCO = , angle 30ACD = and angle 74XAD = . (a) Stating the reasons clearly, find (i) angle ABD , A B C D E O X

7 Crescent Girls’ School 2024 Prelim S4 Math P2 [Turn Over (iii) angle ECO . Answer ……………………° [2] [2] (b) W is a point on the same side of the major segment formed by the chord AD. Given that angle 45AWD = , state with reason whether the point W lies on the circumference of the circle, outside the circle or inside the circle.

8 Crescent Girls’ School 2024 Prelim S4 Math P2 4 In the diagram, OP ⎯⎯ → = p , OQ ⎯⎯ → = q , 2 3OP OM ⎯⎯ → ⎯⎯ → = , 1 3OQ OS ⎯⎯ → ⎯⎯ → = , OQ SN ⎯⎯ → ⎯⎯ → = and 3.SM SR= (a) Express, as simply as possible, in terms of p and q , (i) ,MS ⎯⎯ → Answer MS ⎯⎯ → = …………………… [1] (ii) ,PN ⎯⎯ → Answer PN ⎯⎯ → = …………………… [2] O Q P M R S N

9 Crescent Girls’ School 2024 Prelim S4 Math P2 [Turn Over (iii) PR ⎯⎯ → . Answer PR ⎯⎯ → = …………………… [3] (b) Write down two facts about P, R and N. Answer …………………………………………………………………………… ……………………………………………………………………………………… ……………………………………………………………………………… [2]

10 Crescent Girls’ School 2024 Prelim S4 Math P2 (c) Find the numerical value of Area of Area of MPR MON . Answer Area of Area of MPR MON = ………………… [2] (d) The coordinates of A and B are ( )6,5 and ( )8,1 respectively. (i) Express AB ⎯⎯ → as a column vector. Answer AB ⎯⎯ → = …………………… [1] (ii) Find |AB⃗⃗⃗⃗⃗ |. Answer |AB⃗⃗⃗⃗⃗ | = …………………… [2]