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. (a) Alice took the package from Travel Agency B and her tour package value is $8000. At the end of 5 months, the total amount is $8134.23. Show that r is approximately 4.00. [4] Answer

7 (b) Bernice took a loan from Travel Agency A and intends to pay within 6 months by monthly instalment. Her tour package to Australia was $5000. Calculate the monthly instalment, using the same value for r from question (a). Answer $ [3] (c) Bernice wants to add on a snorkeling session for her tour. The price of a snorkeling session in Australia is AUD 240. The diagram shows the conversion chart of 1 Singapore Dollar to Australian Dollar. Find the highest possible price of snorkeling in Singapore Dollar if she made the conversion between 21 April to 21 May. Answer SGD [2] 21 Apr 21 May

8 3 Waiting time in minutes The cumulative frequency curve shows the waiting time of 80 passengers at a bus station on 1 May 2023. (a) (i) State the median waiting time. Answer mins [1] (ii) Find the interquartile range of the waiting time. Answer mins [2] No of passengers at a bus station On 1 May 2023 10 20 30 40 50 60 70 80 50 60 70 80 40 0

9 (b) The waiting time of the buses on 1 June 2023 were recorded by 78 passengers. The table present some key statistical data. Median k Lower quartile 54 Upper quartile 67 (i) Determine the range of k in the form of akb<< if the waiting time on 1 June 2023 is shorter than that on 1 May 2023. Answer [2] (ii) Make another comment comparing the waiting time on 1 May 2023 and on 1 June 2023. Answer [1] (c) On the same cumulative frequency graph, draw the cumulative frequency curve for 1 June 2023 if the minimum and maximum waiting time are the same as that on 1 May 2023. [2] (d) 80 passengers recorded their waiting time on 1 July 2023, and each waiting time recorded was 2 minutes more than those recorded on 1 May 2023. (i) State the median waiting time for 1 July 2023. Answer mins [1] (ii) State the interquartile range for 1 July 2023. Answer mins [1]

10 4 In the diagram, ABC, ADE, AFG, DFB and EGC are straight lines. F is a point on DB such that FB = 2DF. AB is produced to the point C such that 4 3.AB AC= AD is produced to the point E such that : 3:1.AD DE = (a) By proving similarity, explain why BD is parallel to CE. [4] Answer (b) It is given that AF = p, AB = q. Express, as simple as possible, in terms of p and/or q. (i) FB    Answer [1] A B G C E D F p q