AMKSS PRELIM 2023 4NA EMath P1 Question

[Turn Over Candidate Name Form Class Index Number ANG MO KIO SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY FOUR NORMAL ACADEMIC MATHEMATICS SYLLABUS A 4045/01 Paper 1 02 August 2023 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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 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 of the 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 π, use either your calculator value or 3.142. For Examiner’s Use 70 This document consists of 16 printed pages.

2 AMKSS 4NA Prelim Exam 4045/01/2023 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curve 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 C c B b A a sinsinsin == a2 = b2 + c2 – 2bc cos A Statistics Mean =   f fx Standard deviation = 22       −     f fx f fx

3 AMKSS 4NA Prelim Exam 4045/01/2023 [Turn Over 1 Write these numbers in order of size, starting with the largest. 73% 3 7 3 2 3  0.63 Answer , , , , [2] largest 2 Calculate 3309.6 18.57 6.43− . (a) Write your answer correct to 4 significant figures. Answer [1] (b) Write your answer to part (a) in standard form. Answer [1] 3 The result obtained from an experiment was 9.5036 m/s. How many significant figures did a student correct the result to if he reported it as 9.50 m/s? Answer [1]

4 AMKSS 4NA Prelim Exam 4045/01/2023 4 22 7 33 25 5 25 p q x x x x −+=− + − Find p and q . Answer p= q= [3] 5 ( ) 22 10 5x x x a b+ − = + + (a) Find a and b . Answer a= b= [2] (b) Hence solve 2 10 5 0xx+ − = , give your answer correct to 2 decimal places. Answer x= or [2]

5 AMKSS 4NA Prelim Exam 4045/01/2023 [Turn Over –4 –3 –2 –1 0 1 2 3 4 6 (a) Represent 34 x−   on the number line. [1] (b) Find the smallest integer value of y satisfying 3 1 15y− +  . Answer [2] 7 The quantities x and y are in the ratio 9 : 4 . The quantities y and z are in the ratio 12 : 7 Write down the ratio ::x y z in its simplest form. Answer : : [2] 8 (a) Find the lowest common multiple (LCM) of 168 and 540. Answer [2] (b) Find the smallest positive integer value of a such that 540a is a perfect cube. Answer a= [1]

6 AMKSS 4NA Prelim Exam 4045/01/2023 9 y is inversely proportional to the cube of x. Given that y = 3 when x = 2, find y when x = 4. Answer y= [2] 10 The first five terms of a sequence are 1, – 4 , – 9, – 14, – 19. (a) Write down the next two terms of the sequence. Answer , [1] (b) Find an expression, in terms of n , for the nth term of the sequence. Answer [1] (c) Is – 110 a term of this sequence? Explain you answer. Answer [1]

7 AMKSS 4NA Prelim Exam 4045/01/2023 [Turn Over 11 The stem-and-leaf diagram shows the score of students for the examination. 4 0 0 1 5 1 2 2 2 3 6 2 2 4 6 7 1 4 8 0 3 3 8 9 9 Key 2 1 represents 21 marks (a) What is the highest score? Answer [1] (b) Find the median score. Answer [1] (c) Find the modal score. Answer [1] (d) Student A told his friends that 35% of the students failed the examination. Given that the passing mark was 53, is Student A’s statement correct? Give a reason for your answer. Answer [1]

8 AMKSS 4NA Prelim Exam 4045/01/2023 12 In the grid below, draw an enlargement of the given figure using a scale factor of 2 . [2] 13 2 2u v t=− (a) Find the value of u when 4v= and 10t =− . Answer u = [1] (b) Rearrange the formula to make t the subject. Answer t= [2]

9 AMKSS 4NA Prelim Exam 4045/01/2023 [Turn Over 14 The diagram shows the distance-time graph of a vehicle. (a) How far did the vehicle travel for the first half an hour? Answer km [1] (b) At what interval did the vehicle move at a slower average speed? Explain your answer. Answer [1] (c) Calculate the average speed of its whole journey. Answer km/h [2]

10 AMKSS 4NA Prelim Exam 4045/01/2023 15 Regina did a survey and recorded the following information. Type of food ordered via delivery platform % of participants in survey Hawker Food 48% Restaurant 8% Fast Food 35% Others 9% (a) Explain why is it not possible to calculate the number of participants who ordered food from restaurant. Answer [1] (b) Find the angle of the sector representing the participants who ordered fast food if she wants to present her results in a pie chart. Answer [2]