[Tampines] [2023] 4E EM 4052 Prelims P2 QP

This document consists of 24 printed pages TAMPINES SECONDARY SCHOOL Secondary Four Express / Five Normal Academic PRELIMINARY EXAMINATION 2023 NAME CLASS REGISTER NUMBER MATHEMATICS 4052/02 Paper 2 25 August 2023 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number in the spaces at the top of this page. 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. 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  , use either your calculator value of 3.142, unless the question requires the answer in terms of  . 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 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Total

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle ABC = Cabsin2 1 Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 [Turn over for Question 1]

4 1 (a) It is given that 64 qrp q −= where q is non-zero. (i) Find p when q = 4 and r = −9. Answer p = [1] (ii) Express q in terms of p and r. Answer q = [3] (b) Solve 54 266 xx+=−− . Answer x = [3]

5 (c) Solve the inequality 503 7 6 3xx−  + . Answer [2] (i) Represent your answer in part (c) on the number line below. Answer x [1] (ii) Hence state the least integer value of x. Answer x = [1]

6 2 (a)  = {integers x: 0 < x ≤ 10} A = {prime numbers} B = {(x – 5)(4 – x) = 0} (i) Complete the Venn Diagram to illustrate this information. Answer [1] (ii) List the elements in (A  B). Answer [1] (iii) C is a proper subset of A. Anthony claims that n(C) ≤ 4. Explain with reasons if Anthony’s claim is valid. Answer [2]   A B 

7 (b) A L-shaped block is made of 3 squares of 1-cm2 each and has a perimeter of 8 cm. The following pattern shows L-shaped blocks joined together. 1 L-shaped block 2 L-shaped blocks 3 L-shaped blocks The values for the perimeter of the 1 L-shaped block and 2 L-shaped blocks are given below. Number of L-shaped blocks 1 2 3 4 Perimeter (cm) 8 14 a b (i) Find a and b. Answer a = b = [2] (ii) Write down the perimeter of a n L-shaped block in terms of n. Answer [1] (iii) If the perimeter of a n L-shaped block is 2258 cm, find the number of squares in this n L-shaped block. Answer [2]

8 3 (a) The population of Singapore was estimated at 5 985 000 in June 2023. (i) Write 5 985 000 in standard form. Answer [1] The land area of Singapore is 734.3 km2. (ii) Find the population of Singapore per km2. Write your answer in standard form, correct to 2 significant figures. Answer [2] (b) The value of a painting in 2022 was 20% more than its value in 2021 but 16% less than its value in 2023. If the painting is valued at $20 000 in 2023, find its value in 2021. Answer $ [3]

9 (c) Mr and Mrs Raj are travelling from Singapore to Malaysia. In Singapore, the exchange rate is 100 Singapore Dollars ($) = 335 Malaysian Ringgit (RM) . In Malaysia, the exchange rate is 100 Malaysian Ringgit (RM) = 33.5 Singapore Dollars ($). Mr Raj wants to change $1000 into Malaysian Ringgit in Singapore. Mrs Raj claims that there is no difference whether Mr Raj changes the money in Singapore or Malaysia. Do you agree with Mrs Raj? Justify your answer, showing all workings clearly. Answer [3]

10 4 (a) 11 2PQ = and 3 4QR −= . (i) Find PR . Answer units [2] (ii) Q is the point (2, 3). Find the position vector of P. Answer [2] (b) ABCD is a trapezium where AB is parallel to DC. The diagonals AC and BD intersect at X. AB = 6a, DC = 4a and BC = 4b. (i) Find the ratio AX : XC. Answer : [1] D A B C X 4a 6a 4b