OPSS Prelims 2024 4E Math P1 QP

1 ORCHID PARK SECONDARY SCHOOL Preliminary Examination 2024 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 1 Secondary 4 Express / 5 Normal (Academic) Setter: Mr Wong Yiu Hang 4052/01 15 August 2024 2 hours 15 minutes 90 Marks Additional Materials: NIL 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. Use a pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question it must be shown in the space below the question. 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. The total number of marks for this paper is 90. This document consists of 21 printed pages. For Examiner’s Use Total Calculator Model :

2 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 = 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 Mathematical Formulae

3 [Turn Over Answer all the questions 1 (a) The approximate mass of the earth is 5.976 × 1024 kg. How many times is the earth heavier than an average male adult who weighs 75 kg? Give your answer in standard form correct to 3 significant figures. Answer: …….………………………… [1] (b) The sum of 3 consecutive even numbers is estimated to be 300 when rounded off to 1 significant figure. Find the largest possible set of the 3 numbers, Answer: …….…… , …………… , ..……… [1] 2 (a) Solve the inequality 2𝑦 − 1 < 11𝑦 4 < 1 4 Answer: …….………………………… [2] (b) Given −25 ≤ 𝑥 ≤ 50 and −15 ≤ 𝑦 ≤ −5, what is the smallest possible value for 𝑥 + 𝑦2? Answer: …….………………………… [1]

4 3 (a) Write 756 as a product of its prime factors. Answer: …….………………………… [1] (b) Given that 495 = 32 × 5 × 11, find the smallest positive integer p such that 756p is a multiple of 495. Answer: …….………………………… [1] (c) The number 756 × 𝑎 𝑏 is a perfect cube where a and b are both prime numbers. Find the smallest possible value of a and smallest possible value of b. Answer: a = …….………… , b = ……………… [2]

5 [Turn Over 4 Simplify 𝑎2−3𝑎+2 9𝑎2−1 ÷ 2𝑎−2 6𝑎−2. Answer: …….………………………… [2] 5 (a) Simplify (2𝑥3𝑦2)−4 (10𝑥−2𝑦3)2 ÷ √27𝑥−3𝑦63 . Answer: …….………………………… [3]

6 (b) Solve 3𝑥+2 × 3(35) = 1. Answer: …….………………………… [2] 6 (a) Factorise 𝑎3 − 2𝑎2𝑏 − 4𝑎 + 8𝑏. Answer: …….………………………… [2] (b) Solve 3𝑥+2 9𝑥 = 1 7𝑥−3. Answer: …….………………………… [3]

7 [Turn Over 7 Peter has $20 000 to invest in either Bank A, Bank B or Bank C for 5 years. The table below shows the investment plans. Bank Interest rate per annum A 3.0 % compound interest, compounded annually B 3.2 % simple interest annually C Fixed interest of $3000 after 5 years Which plan should he invest in? Explain your answer. ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………….. [3]

8 8 A carton contains 17 good apples and 3 rotten apples. A fruit seller picks three apples in random from the carton and puts them into a smaller box for sale. (a) Find the probability that there is at least 1 rotten apple in the box for sale. Answer: …….………………………… [2] (b) When Student A is asked to find the probability that the box contains two good apples and one rotten apple, he claims that the answer is 17 20 × 16 19 × 3 18. Do you agree with the Student A’s claim? Explain your answer. ……………………………………………………………………………………………… ……………………………………………………………………………………………… ……………………………………………………………………………………………… ………………………………………………………………………………………….. [2]

9 [Turn Over 9 A set of Pollutant Standards Index (PSI) taken from different parts of Singapore is as follows. 28 30 48 19 70 50 32 72 Represent the data using a box-and-whisker plot. [3]

10 10 Sketch the graph in the spaces below. (a) 𝑦 = 4 𝑥 [1] (b) 𝑦 = −2𝑥3 [1] (c) Hence, state the number of solutions for the equation 4 𝑥 + 2𝑥3 = 0 Answer: …….………………………… [1] x 0 x 0