TPS 4NA Prelim P1 2023

This document consists of 21 printed pages TAMPINES SECONDARY SCHOOL Secondary Four Normal Academic PRELIMINARY EXAMINATION 2023 NAME CLASS REGISTER NUMBER MATHEMATICS SYLLABUS A 4045/01 Paper 1 04 August 2023 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST For Examiner’s Use Write your name, class and register 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, 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 or 3.142, unless the question requires the answer in terms of  . At the end of the examination, fasten all your work securely together. 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 70. [Turn over NA

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 = 2 2 1 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 Answer all questions. 1 (a) Calculate the exact value of 11.2×3 8.2−4.7 . Answer (a) [1] (b) Calculate √5.1 + 3.752. Give your answer correct to 1 decimal place. Answer (b) [1] 2 0.312̇ 5 7 𝜋 2 21 √64 For the above values, state which (a) is/ are recurring decimal/s? Answer (a) [1] (b) has/ have a factor of 3? Answer (b) [1] (c) is/ are rational number/s? Answer (c) [1]

4 3 Find the largest integer satisfying −4𝑥 ≥ 73. Answer [2] 4 Given that 𝑥2 + 10𝑥 + 21 = (𝑥 + 𝑎)2 + 𝑏, (a) find 𝑎 and 𝑏. Answer 𝑎 = 𝑏 = [3] (b) Hence, solve 𝑥2 + 10𝑥 + 21 = 0 Answer 𝑥 = or [3]

5 5 The following histogram summarises the average daily amount of pocket money from a group of 50 students. (a) How many students have an average daily pocket money of $3 to $4? Answer (a) [1] (b) Find the probability of a student having at least $5 of average daily pocket money, leaving your answer in simplest form. Answer (b) [1]

6 6 A baker is left with 250 eggs and plenty of other ingredients. (a) Using the above recipe, calculate the maximum amount that can be received from selling the cupcakes made with these remaining eggs, given that each cupcake is sold at $1.80. Answer (a) $ [3] (b) Calculate the percentage of these 250 eggs which were not used. Answer (b) % [2]

7 (c) Find the ratio of butter: flour and milk. Answer (b) : [2]

8 7 The distance-time graph shows the movement of an electric toy car. (a) ‘The toy car is travelling at a greater speed at CD than at AB.’ Justify whether the above statement is correct. Answer [2] (b) What is the duration when the toy car is at rest? Answer (b) [1]

9 (c) Describe the motion of the electric toy car at DE. Answer [1] (d) Find the average speed of the toy car for the whole journey. Answer (d) 𝑚/𝑠 [2]

10 8 (a) Written as a product of prime factors, 1050 = 2𝑥 × 3 × 5𝑦 × 7. Find the values of 𝑥 and 𝑦. Answer (a) 𝑥 = 𝑦 = [2] (b) Find the smallest positive integer 𝑘, such that 1050𝑘 is a perfect square. Answer (b) 𝑘 = [1] (c) Given that 700 = 22 × 52 × 7, find the highest common factor of 700 and 1050. Answer (c) [2]