2024 Outram Prelim P1 QP

1 Subject : Mathematics Level (Stream) : Secondary Four Express & Five Normal Academic Paper : 4052/01 Date : 21 August 2024 Duration : 2 hours 15 mins Marks : 90 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 staples, paper clips, highlighters, glue or correction fluid. Answer all questions on the Question Paper. 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 or 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. 90 This document consists of 23 printed pages, including this cover page. OUTRAM SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 Class Index No Name: __________________________________________________

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

3 1 A running route is 42.2 km long and a runner took 4 hours 45 minutes to finish the route. Calculate the speed of the runner in metres per second. Answer ………………..……………….. m/s [2] 2 (a) Simplify 1 12 4 6256 g f −   . Answer ……………………..……………….. [2] (b) 15 9 15 81k− =  Find the value of k. Answer k = ………………..……………….. [3]

4 3 Given that sin 0.8211 = , find the two possible values of  , where 0o ≤  ≤ 180o. Answer  = ………………..……………….. [2] 4 The number A = 27 × 511 × 78. (a) Prove that A is divisible by 245. Answer ……………………..………………..……………………..…………………… ……………………..………………..……………………..…………………… [2] (b) The number A × k is a perfect square. Find the smallest possible integer value of k. Answer k = ………………..……………….. [1] (c) The number B = 25 × 36 × 73. Find the highest common factor (HCF) and lowest common multiple (LCM) of A and B as a product of its prime factors. Answer HCF = ……………..……………….. [1] LCM = ……………..………………. [1]

5 5 Zen invests $42000 at a rate of 1.6% per annum compounded monthly. Calculate the value of the investment at the end of 3 years. Answer $ …………………..……………….. [2] 6 (a) Express x2 + 6x + 10 in the form of (x + h)2 + k. Answer ……………………..……………….. [2] (b) Using your answer in (a), (i) write down the equation of the line of symmetry of the curve y = x2 + 6x + 10. Answer ……………………..……………….. [1] (ii) Explain why the equation x2 + 6x + 10 = 0 does not have any solutions. Answer ……………………..………………..……………………..……………… ……………………..………………..……………………..……………… [1]

6 7 (a) Paul is 25% heavier than Mike. Mike is 25% lighter than Oscar. Find the ratio of the weight of Paul to that of Oscar. Answer ……………………..……………….. [2] (b) Rachel bought 8 watches for $900 each. She sold 4 watches at a profit of 80%, and 3 watches at a loss of 50%. She kept one watch for herself. Calculate Rachel’s net profit. Answer $ …………………..……………….. [3]

7 8 A company produces light bulbs. The lifespan, in hours, of 240 light bulbs is tested. The cumulative frequency curve shows the distribution of lifespan of the light bulbs. Cumulative frequency 20 40 60 140 80 100 120 160 240 180 200 220 100 200 300 400 500 600 700 0 Lifespan (hours)

8 (a) Use the diagram to estimate (i) the median lifespan of the light bulbs Answer ………...………..……………….. h [1] (ii) the interquartile range of the lifespan of the light bulbs. Answer ………...………..……………….. h [2] (b) Light bulbs with a lifespan of over x hours can be sold. Only 80 of the light bulbs tested meet this requirement. Find the value of x. Answer x = ………………..……………….. [1]

9 9 The diagram, which is not drawn to scale, shows the three lines. (a) Show that k = 1. Answer: [1] (b) Find the coordinates of point D. Answer D ( ...…….. , ....…… ) [1] y + 4 = 0 2y + 3x = 2 y – x = k

10 10 Write as a single fraction in its simplest form 79 33 yy yy +−+− . Answer ……………………..……………….. [2] 11 (a) Factorise completely. (i) 33x2y + 11xy. Answer ……………………..……………….. [1] (ii) x3 + x2 – 9x – 9. Answer ……………………..……………….. [3]