S4 E-Math JURONGVILLE P1 2024 EXAM555

This document consists of 20 printed pages. [Turn Over JURONGVILLE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 Secondary 4 Express/ 5 Normal Academic STUDENT NAME CLASS INDEX NUMBER MATHEMATICS 4052/01 Paper 1 1 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number in the spaces on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE ON ANY BARCODES. Answer ALL the questions. 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 marks for this paper is 90. 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. DO NOT OPEN THE BOOKLET UNTIL YOU ARE TOLD TO DO SO For Examiner’s Use 90 O O O O

2 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 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 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 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 [Turn Over Answer ALL the questions. 1 Solve 3 2 4 3 =+ − x x . Answer …………………………... [1] 2 Ronald drew the following graph to show the number of calories he consumed for lunch in a working week. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. ……………..………………………...…………………………...…………………………...… ……………..………………………...…………………………...…………………………...… ………….…..…………………………...…………………………...……………………… [2] 600 700 800 900 1000 1100 Monday Tuesday Wednesday Thursday Friday DRASTIC DECREASE IN CALORIES CONSUMED Calories consumed 500

4 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 3 (a) Express 546 as a product of its prime factors. Answer …………………………... [1] (b) The lowest common multiple of 14, 26 and p is 546. Find two possible values of p which are odd. Answer …………………………... [2] 4 Jayden bought a box of pencils for 90 cents. When he sold it, he made a profit of 200% of his cost. Calculate his selling price. Answer $………………………... [2] 5 Factorise fully pxpwwxw 4836 2 −−+ . Answer …………………………... [2]

5 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 [Turn Over 6 It is given that      number prime a is : 3 of multiple a is : 511 andinteger an is : xxB xxA xxx = = = (a) Illustrate the information in the following Venn diagram. [2] (b) List the elements of 'AB . ……..………………………...…………………………...…………………………...… ….…..…………………………...…………………………...……………………… [1] 7 (a) Simplify 3 0 (2 ) 16 maa a  , giving your answer in the form of k na , where k is a constant. Answer …………………………... [1] (b) Given that 735 ÷ 2401−1 = 49p, find the value of p. Answer …………………………... [2] A B

6 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 8 The sum of the interior angles of a regular polygon is eight times that of an octagon. (a) Find the number of sides of the regular polygon, Answer …………………………... [2] (b) Find an exterior angle of the regular polygon. Answer …………………………... [1] 9 A six-faced die was thrown 28 times. The table shows the number of times that each possible score occurred. Score 1 2 3 4 5 6 Frequency 8 6 6 2 4 2 The die was thrown 2 more times. Amanda calculated the mean score of all the 30 times mentally and gave the answer as 3.1. Is Amanda’s calculation correct? State your reasons clearly. Answer: Therefore, Amanda’s calculation is * correct / incorrect since …………………………………………………………………………………………………… …………………………………………………………………………...…………………... [3] *Delete whichever is inappropriate. Pulau Ubin

7 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 [Turn Over 10 When n is a positive integer, (2n +3) is an odd number. (a) Write down an expression, in term of n, for the next consecutive odd number. Answer …………………………... [1] (b) Find and simplify an expression, in terms of n, for the difference between the squares of these two odd numbers. Answer …………………………... [2] (c) Hence explain why the difference between the squares of two consecutive odd numbers is always a multiple of 8. …………………………………………………………………………………………… …………………………………………………………………………………………… ………………………………………………………………………………………… [1]

8 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 11 The diagram below shows a segment of a circle. AB = 12.5 cm. (a) Find the centre of the circle by construction and mark it with a letter O. [3] Answer (b) Find the radius of the circle. Answer …………………………... cm [1] A B

9 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 [Turn Over 12 In the diagram below, the coordinates of A, B and C are )0,4(− , (2, 0) and (0, 8) respectively. (a) Find the equation of the curve. Answer …………………………... [2] (b) Find the coordinates of D, the maximum point of the curve. Answer D = (…………,……….) [2] y x A B C D O

10 Jurongville Secondary School 4E5N PRELIM / 4052_01 / 2024 13 Study the pattern of numbers below. Find the values of a, b and c if n = 6. Answer a =…… b = ………c = ……... [3] 14 Given the coordinates of two points A and B are )5,13( − and )2,9( respectively and point C is such that 𝐴𝐶→ 21 m= , find (a) |𝐴𝐵→ |, Answer …………………………... [2] (b) the value of m if A, B and C are collinear. Answer …………………………... [2] 1 1 8 0 −3 1 4 5 27 27 9 9 64 a b c Figure 1 Figure 2 Figure 3 Figure 4 ……… Figure n