2024 4NA Ahmad Ibrahim Paper 2

1 _________________________________________________________________________ This document consists of 20 printed pages. AISS PRELIM/4045/02/2024 [Turn over AHMAD IBRAHIM SECONDARY SCHOOL GCE N-LEVEL PRELIMINARY EXAMINATION 2024 SECONDARY 4 NORMAL (ACADEMIC) Name: Class: Register No.: MATHEMATICS SYLLABUS A Paper 2 Candidates answer on the Question Paper. 4045/02 31 July 2024 2 hours 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, glue or correction fluid. Section A Answer all questions. Section B Answer one question. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total number of marks for this paper is 70. 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. For Examiner’s Use / 70

2 AISS PRELIM/4045/02/2024 [Turn over Mathematical Formulae Compound Interest Total amount = n rP    + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry sin sin sin a b c A B C== a2 = b2 + c2 − 2bc cos A Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 AISS PRELIM/4045/02/2024 [Turn over Section A (62 marks) Answer all the questions in this section. 1 (a) By rounding the numbers to 1 significant figure, estimate the value of 82.98 8.93 4.45  . You must show your working. Answer ……………………… [2] (b) The number of coronavirus cases as of June 2022 in Singapore is 1 397 074. The total number of coronavirus cases in the world is 548 million. Calculate the percentage of coronavirus cases in Singapore compared to the cases in the world. Give your answer in standard form. Answer ……………………… [2]

4 AISS PRELIM/4045/02/2024 [Turn over 2 The table shows the number of goals scored in 20 soccer matches. 2 1 1 3 4 1 4 0 1 5 4 3 1 0 2 5 2 1 3 3 (a) Represent the information by completing the dot diagram below. [2] (b) State the median number of goals. Answer ……………………… [1] (c) What is the probability of the soccer match ending with a single goal? Answer ……………………… [1]

5 AISS PRELIM/4045/02/2024 [Turn over 3 ABCDEF… represents part of a regular 15-sided polygon. (a) Calculate angle ABC. Answer …………………… [2] (b) Given that triangle ACD is congruent to triangle FDC and angle CFD = 20, calculate angle ADC. Answer …………………… [3]

6 AISS PRELIM/4045/02/2024 [Turn over 4 (a) Find 240 as a product of its prime factors. Answer ……………………… [1] (b) Find the smallest positive integer value of a such that 240a is a perfect square. Answer ……………………… [1] (c) Green pens are sold in packets of 240. Black pens are sold in packets of 210. Amy wants to buy the same number of green and black pens. What is the smallest number of packets of each type of pens she could buy? Answer Green : …………… Black : …………… [3]

7 AISS PRELIM/4045/02/2024 [Turn over 5 A car costs $22 500. Andy bought a car at a 10% discount. (a) He intends to sell it for a cash price of $28 888. Calculate his percentage profit. Answer …………………… [2] (b) Andy has two interested buyers, Mary and Jane. Mary offers to pay a deposit of 20% of the cash price and 58 monthly instalments of $510 each. Jane offers to pay a deposit of 15% and 60 monthly instalments of $520. Which buyer should Andy sell it to? Explain your answer. [3] Answer

8 AISS PRELIM/4045/02/2024 [Turn over 6 The coordinates of points A and B are (2, 5) and (5, 9) respectively. (a) Calculate the length of the line segment AB. Answer ……………………… [2] (b) Find the equation of the line AB. Answer ……………………… [2] (c) The point C lies on AB produced. Given that AB = BC, find the coordinates of point C. Answer (……… , ………) [2]

9 AISS PRELIM/4045/02/2024 [Turn over 7 (a) Factorise (i) 3 2 12 8uv v u+ − − , Answer ……………………… [2] (ii) 22 11 5xx−+ . Answer ……………………… [2] (b) Simplify 3293 48 xx . Answer ……………………… [2]

10 AISS PRELIM/4045/02/2024 [Turn over 8 The diagram shows the speed-time graph of a car. The car travelled with an acceleration of 2.5m/s² to reach a speed of 20 m/s in the first t seconds. Find (a) the value of t, Answer ……………………… [1] (b) the speed of the car at 36 seconds, Answer ……………..…… m/s [2] (c) the total distance travelled. Answer …………………… m [2]