AMKSS PRELIM 2023 4NA EMath P2 Question

[Turn Over Candidate Name Form Class Index Number ANG MO KIO SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY FOUR NORMAL ACADEMIC MATHEMATICS SYLLABUS A 4045/02 Paper 2 03 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. 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 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 19 printed pages and 1 blank page.

2 AMKSS 4NA Prelim Exam 4045/02/2023 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 4045/02/2023 [Turn Over Section A (62 marks) Answer all the questions in this section. 1 At the beginning of 2022, Hannah found a job as a temporary clerk and was paid a basic wage of $342 for a 36-hour week. (a) Calculate the basic hourly rate of pay. Answer $ [1] (b) For working overtime (above the 36 hours), Hannah would be paid one and a half times the basic hourly rate per hour for the first 10 hours and double the basic hourly rate for the remaining hours. (i) Calculate Hannah’s total wage for a week in which she worked 48 hours. Answer $ [2] (ii) In a certain week, Hannah’s total wage was $636.50, calculate the number of hours she worked during the week. Answer hours [2]

4 AMKSS 4NA Prelim Exam 4045/02/2023 2 The petrol consumption of a car is shown in the table below. Type of road Petrol used per 100 km Main roads 9.2 litres Other roads 8.0 litres (a) How much petrol is used on a journey of 350 km on a main road? Answer litres [2] (b) On other roads, how far can the car travel on 44 litres of petrol? Answer km [2] (c) A journey consists of 200 km on a main road and 160 km on other roads. Find the average amount of petrol used per kilometre of this journey. Answer litres [2]

5 AMKSS 4NA Prelim Exam 4045/02/2023 [Turn Over 3 (a) The scale of a map is 1 : 200 000. (i) If a road has a length of 5 cm on the map, find its actual length in km. Answer km [1] (ii) If a plot of land has an area of 3 cm2 on the map, find its actual area in km2. Answer km2 [2] (iii) If the actual area of a lake is 18 000 000 m2, calculate its area, in cm2, on the map. Answer cm2 [2] (b) Mr Tan signed up for a 10 years savings plan of $50000 with a compound interest of 5% per annum. Calculate the amount of interest he would receive at the end of the savings plan. Give your answer correct to the nearest cent. Answer $ [3]

6 AMKSS 4NA Prelim Exam 4045/02/2023 4 (a) The spinner in the diagram has an equal chance of landing on each of the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Find the probability that the spinner lands on (i) 11, Answer [1] (ii) a prime number, Answer [1] (iii) a number more than 3. Answer [1] (b) A man took 5 hours 49 minutes to drive from Nara to Tokyo. (i) He arrived at Tokyo at 14 15. At what time did he start his journey? Answer [1] (ii) The distance from Nara to Tokyo is 484 km. Find the average speed of the journey in metres per second. Answer m/s [3]

7 AMKSS 4NA Prelim Exam 4045/02/2023 [Turn Over 5 (a) Factorise (i) 22 81xy− , Answer [1] (ii) 10 15 6 9px qx py qy− + − . Answer [2] (b) Solve 35 12 2 1xx −=−+ . You must show all your working. Answer x= or [5]

8 AMKSS 4NA Prelim Exam 4045/02/2023 6 A mushroom-shaped shelter, fixed onto the ground, is made by joining a solid hemisphere of radius 3 m to a circular pole of radius 0.25 m and height 2 m, as shown in the diagram below. (a) The solid hemisphere is filled with insulation materials. Calculate the volume of hemisphere. Answer cm3 [2]

9 AMKSS 4NA Prelim Exam 4045/02/2023 [Turn Over (b) A painter is hired to paint the exposed area of the mushroom-shaped shelter. The painter thinks that he only requires 8 litres of paint to paint the shelter. Do you agree with him? Show your workings clearly. Answer 1 agree / disagree with him because [5] A litre of paint generally covers 10m².

10 AMKSS 4NA Prelim Exam 4045/02/2023 7 In the diagram, XY is parallel to PQ. Calculate the value of x in the diagram. Answer x= [3] X Y P Q Z