TPS 4NA Prelim P2 2023

This document consists of 21 printed pages and 1 blank page TAMPINES SECONDARY SCHOOL Secondary Four Normal Academic PRELIMINARY EXAMINATION 2023 NAME CLASS REGISTER NUMBER MATHEMATICS SYLLABUS A 4045/02 Paper 2 7 August 2023 2 hours Candidates answer on Question Paper. READ THESE INSTRUCTIONS FIRST 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. 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. [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 = 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 Section A (62 marks) Answer all the questions in this section. 1 (a) By writing each value correct to 1 significant figure, estimate the value of 245.5 0.5391 5.49  . Show your working. Answer ………………….……….. [2] (b) Write 0.000015 in standard form. Answer ………………….……….. [1] (c) The population of Singapore is 5.45 million in 2021. The area of Singapore is 87.3 10 m2. (i) Write 5.45 million in standard form. Answer …………………………... [1] (ii) Find the average area, in square metres per person, in Singapore in 2021. Answer ………………. m2/person [1]

4 2 The stem-and-leaf diagram shows the heights of 12 students. Stem Leaf 11 7 8 12 0 5 5 5 p 9 13 2 2 4 14 2 Key: 11 | 7 means 117 cm (a) If the median height is 126 cm, find the value of p. Answer p = ….………….……….. [2] (b) Find the range of the heights. Answer …….………….…….. cm [1] (c) 25% of the students have a height of less than x cm. Find the largest integer value of x. Answer x = ...………….…………. [2]

5 3 A hotel and an airport are 8 km apart. The distance between the hotel and the airport is 3.2 cm on a map drawn to the scale of 1 : n. (a) Find the value of n. Answer n = ……………………… [2] (b) The actual area of the airport is 30 km2. Find the area, in square centimetre, of the airport on the map. Answer …….…..…………… cm2 [2]

6 4 (a) ABCDE is a regular pentagon. Calculate (i) angle BAE, Answer ………………….……….. [2] (ii) angle DCE, Answer ………………….……….. [1] (iii) angle BEC. Answer ………………….……….. [1]

7 (b) Angle ABC = ( )4 21x− , angle BAC = ( )3 12x+ and angle ACD = ( )167 x− . BCD is a straight line. Find the value of x. Answer x = …………….……….. [2]

8 5 A man is standing at point S, on top of a vertical cliff SR. The cliff is 200 m above sea level. A boat Q is 210 m away from the base of the cliff. (a) Find the length QS. Answer ……..……….………… m [2] (b) Find the angle of depression of Q from S. Answer ………………….……….. [2]

9 6 (a) P, Q and R are three points on the circumference of the circle. O is the centre of the circle. Angle POR = 2.15 radians and OR = 5 cm. Find the area of the shaded segment PQR. Answer …………….……….. cm2 [3] (b) Find the percentage of the circle that is shaded. Answer …………….……...….. % [3] Answer …………….……….. cm2 [4]

10 7 (a) 2p – 1 is an odd number, where p is an integer. (i) Find, in terms of p, the next odd number after 2p – 1. Answer ………………….……….. [1] (ii) Find, in terms of p, the sum of these two odd numbers. Answer ………………….……….. [1] (iii) Hence, explain why the sum of two odd numbers is always even. Answer [1]