2023 SNGS emath Prelim P2 Solutions

Name: _________________________ ( ) Class:_____________ PRELIMINARY EXAMINATION GENERAL CERTIFICATE OF EDUCATION ORDINARY LEVEL MATHEMATICS Student Copy 4052/02 Paper 2 Friday 18 August 2023 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue, correction fluid or correction tape. Answer all 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  , use either your calculator value or 3.142. Paper 1 / 90 Q1 Q4 Q7 Paper 2 /90 Q2 Q5 Q8 Q3 Q6 Q9 Total /100 ________________________________________________________________________________ This document consists of 22 printed pages. [Turn Over

2 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 Mathematical Formulae Compound interest Total amount n rP      += 1001 Mensuration Curved surface area of a cone lr= Surface area of a sphere 24 r= V olume of a cone hr 2 3 1= V olume of a sphere 3 3 4 r= Area of a triangle ABC Cba sin2 1= Arc length r= , where  is in radians Sector area 2 2 1 r= , where  is in radians Trigonometry C c B b A a sinsinsin == Acbcba cos2222 −+= Statistics Mean  = f xf Standard deviation 22       −=     f xf f xf 1

3 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 [Turn Over 1 (a) Solve the inequality 2 1 5 34 xx−+ . Answer …………………..………….. [2] (b) It is given that ( ) 235d b c=+ . (i) Find d when b = −2 and c = − 6.2 . Answer d = ………………..………….. [1] (ii) Express b in terms of c and d. Answer b = ………………..………….. [2]

4 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 (c) Solve the equation 3 221 x xx −=− . Give your solutions correct to 2 decimal places. Answer x = ……………… or …..……….….. [5]

5 CHIJ SNGS Preliminary Examinations 2023 - Mathematics 4052/02 [Turn Over Distance 8 93 10 10 1001000 −=   23 10 −= km (s