CGS 2025 EMATH PRELIM P2 MS

Name: Solution Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION 2025 MATHEMATICS 4052/02 Paper 2 26 August 2025 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. 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 90. 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 𝜋𝜋, use either your calculator value or 3.142. Question 1 2 3 4 5 6 7 8 9 10 Marks 10 8 7 9 9 8 9 10 10 10 Table of Penalties Question No. Presentation –1 Accuracy/ Units –1 Parent’s / Guardian’s Signature This document consists of 24 printed pages For Examiner’s Use 90

2 Crescent Girls’ School 2025 Prelim S4 Math P2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP + Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 24 rπ Volume of a cone = 21 3 rhπ Volume of a sphere = 34 3 rπ Area of triangle ABC = 1 sin2 ab C Arc length = rθ , where 𝜃𝜃 is in radians Sector area = 21 2 r θ , where 𝜃𝜃 is in radians Trigonometry sin sin sin abc ABC= = 2 22 2 cosa b c bc A=+− Statistics Mean = fx f ∑ ∑ Standard deviation = 22fx fx ff ∑∑ − ∑∑ 

3 Crescent Girls’ School 2025 Prelim S4 Math P2 [Turn Over 1 (a) Solve the inequality 34 532 2 x xx + <− −< . Solution: 7 2 and 5 3 4 234 34 1 06 0 34 3 4 22 10 xx xx xx x x xx −< < − −< ++ + +< − >> 10 7x > Answer …………………… [3] (b) It is given that 2 )(7 2 3 ma xF a −= , where 0m ≠ and 0a ≠ . (i) Find, in terms of a, the value of F when xa= − and 3m = . Solution: 2 )3(7 2( ) 3 72 aaF a a −−= = − Answer F = ………………… [1] (ii) Express x in terms of F, a and m. Solution: 2 2 2 ) 7 2 7 2 7 (7 2 3 372 2 3 3 3 2 2 a a am aF m ma xF a aFax m aFx m aFx m −= −= = = ± −± − = − Answer x = ………………… [2]

4 Crescent Girls’ School 2025 Prelim S4 Math P2 (c) Solve the equation 23 752 xx xx + +=+− . Solution: 22 2 22 2 2 23 752 ( 2)( 2) 3 ( 5) 7( 5)( 2) 15 7( 3 10) 4 15 4 7 21 70 3 6 66 0 2 22 0 43 xx xx x x xx x x x xxx xx xx xx xx x +