TKGS 2024 S4 Prelim Math P2 Question Paper (with answer key)

TANJONG KATONG GIRLS’ SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR EXPRESS CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4052/02 Paper 2 7 August 2024 2 hour 15 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your class, index number and name on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE ON ANY BARCODES. 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. Gives answers in degrees to one decimal place. For  , use either your calculator value or 3.142. This document consists of 23 printed pages and 1 blank page. For Examiner’s use

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 2 Mathematical Formulae Compound interest Total amount = nrP      + 1001 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  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cos a b c bc A= + − Statistics Mean = fx f   Standard deviation = 22 fx fx ff  −   

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 [Turn over] 3 TURN OVER FOR QUESTION 1

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 4 1 (a) Solve the equation ( )3 2 1 2173 x x− =− . Answer x= ……………………………………... [2] (b) Simplify (i) 22 2 25 9 15 10 6 9 ab a ab b b − − + − Answer …………………………………………… [3] (ii) 3 2 3 4 12 cc ab ab . Answer …………………………………………… [2]

Tanjong Katong Girls’ School 4052/PRELIM/02/2024 [Turn over] 5 (c) (i) Solve the equation 2 790 2xx− + − = by completing the square . Give your solutions correct to two decimal places. Answer x= ………………. or ………………… [3] (ii) Explain why 2 79 18 2xx− + − = has no real solution. ……………………………………………………………………………….. ……………………………………………………………………………….. ……………………………………………………………………………….. …