2023 BPGHS Prelim P2

BUKIT PANJANG GOVERNMENT HIGH SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4/5 GCE 'O' LEVEL SYLLABUS MATHEMATICS Paper 2 4052 / 02 Date: 22 August, 2023 Duration: 2h 15 min Time: 0750 – 1005 h READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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 paper clips, glue or correction fluid. Answer in this question paper. You should follow the instructions below. If you need additional answer paper or graph paper ask the invigilator for answer paper or graph paper. 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 𝜋𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋𝜋. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. [Turn over] Additional Materials: Graph paper

2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 24 rπ Volume of a cone = hr2 3 1π Volume of a sphere = 3 3 4 rπ Area of triangle ABC = Cabsin2 1 Arc length = θr , where θis in radians Sector area = θ2 2 1 r , where θis in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx ∑ ∑ Standard deviation = 22fx fx ff ∑∑ −∑∑ 

3 1 (a) Solve 2 10 153 xx −−= . Answer x = [2] (b) Simplify 3 5 82 3 16 xy x y ÷ , leaving your answer in positive indices. Answer [2]

4 (c) (i) Express 2 65yx x=−+ in the form 2()y xa b= ++ , where a and b are constants. Answer [1] (ii) Hence solve 2 6 5 10xx− += and give your solution correct to three decimal places. Answer x = or [2]

5 (d) Simplify 23 4 1 .1 qq q q ++ + − Answer [4]

6 2 There are two travel agencies located in University X that provide loan packages for undergraduates to travel before they start working. Travel Agency A Travel Agency B Charges r % per annum simple interest. Charges r % per annum compounded monthly