2024 4NA Prelim Peirce Secondary school P2

ClassRegister No. Candidate Name PEIRCE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY 4 NORMAL ACADEMIC MATHEMATICS 4045/02 Paper 2 2 August 2024 2 hours Additional Materials: Plain Paper (for rough work) INSTRUCTIONS TO CANDIDATES Candidates answer on the Question Paper. Write your name, class and register number on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions from Section A and only one question from Section B. 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 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. Forπ, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. For Examiner’s Use PARENT’S SIGNATURE Total This paper consists of 23 printed pages and 1 blank page. Setter: Mr Goh [TURN OVER Mathematical Formulae Compound interest

Total amount = (1)100nrP+ Mensuration Curved Surface area of a cone = prl Surface area of a sphere = 24rπV olume of a cone = 213rhπV olume of a sphere = 343rπArea of triangle ABC = 1sin2abCArc length = rθ, where θ is in radians Sector area = 212rθ, where θ is in radians Trigonometry sinsinsinabcABC== 2222cosabcbcA=+− Statistics Mean = fxf∑∑Standard deviation = 22fxfxff⎛⎞∑∑−⎜⎟∑∑⎝⎠ Section A (62 marks) Answer all the questions in this section. 1 Factorise the following completely. (a) 2253rr+− Answer …………………………………… [2] (b) 5102axaybxby+−−

Answer ……………………………………………………… [2] (c) 23649y− Answer ……………………………………………………… [ 1] 2 Mdm Lee wants to invest $150 000 with an investment company over a duration of 15 years. There are 2 options, A and B. Option A Mdm Lee will immediately receive a one-time payout of $40000. Subsequently, for the next 15 years, Mdm Lee will receive a yearly payout of $12000. Option B The investment company will invest $150 000 based on 3.8% per annum compounded yearly. Mdm Lee will receive the total investment after 15 years. Which option should Mdm Lee choose ? Show all workings clearly. Answer [ 3] 3 (a) Johnny took the 1400 hrs train from Alpha city to Oasis. Johnny arrived in Oasis at 1840 hrs and the average speed of the train is 200 km/h. Calculate the distance of the train ride.

Answer ……………………………………………………… km [2] (b) Janelle cycled for 40 km for 6 hours. She rested for 30 minutes before continuing her journey at an average speed of 50 km/h for 9 km. Calculate the average speed of Janelle. Answer ……………………………………………………… km/h [3] 4 A solid object is made up of a right-pyramid and a cuboid. The sides of the base of the cuboid are 10 cm each and the height of the cuboid is 25 cm. The vertical height of the right-pyramid is 12 cm. For design purpose, a cylindrical hole of radius 3 cm and height 10 cm is being removed the object below. Calculate the volume of the remaining object.

Answer ……………………………………………………… cm 3 [3] 5 (a) Simplify 252(3)216yxyx× . Answer ………………………………………………[ 2] (b) Simplify 463()g−. Answer ………………………………………………[ 2] 6 The table below is for the graph 6yxx=+.

x12345681012 y7q55.56.278.810.612.5 (a) Find the value of q. Answer q = …………………… [ 1] (b) On the grid next page, plot the graph of 6yxx=+. [2] (c) By drawing a suitable tangent, find the gradient of the graph at x = 1.5. Answer ………………………………………………[2] (d) By drawing the line 636yx=+ on the same graph paper, find the y-coordinate of the point of intersections of the graphs 6yxx=+ and 636yx=+. Answer y = …………………… or y = ……………………. [3] 7 (a) Write 3123xx−+− as a single fraction, simplifying the numerator. 130oAO D B C E 25

Answer ………………………………………………[ 2] (b) Solve the equation 232140xx−−= Answer ……………………………………………… ……………… [3]

8 (a) Anson intends to buy a laptop which costs 13500 Chinese Yuan (CNY) from an online seller. The details of the deal is as follows. • Discount by online seller is 20% • Goods and Service Tax (GST) is 9% • Shipping fee is $ 30 SGD (GST not applicable) • Currency conversion is $1 SGD : 5.36 Chinese Yuan (CNY) Calculate the total amount paid by Anson for the purchase of the laptop. Answer …………………………………………… SGD [2] b) Jamie wants to buy a plasma TV from an electronics shop in Singapore on hire purchase plan. The terms of the hire purchase plan are as follows. • Cash price of plasma TV : $3000 • Deposit $500 • Number of years: 3 years • Interest rate : 2.75% simple interest per annum Calculate the monthly instalment paid by Jamie. Yellow Red Yellow Yellow Red Red 1st draw 2nd draw ⎟⎠⎞⎜⎝⎛106⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛

Answer $…………………………………………… SGD [3] 9 2520 expressed as the product of its prime factors is 753223×××. (a) 2520k is a perfect cube. Find the smallest positive value of k. Answer ……………………………… [1] (b) Write 756 as a product of its prime factors. Answer …………………………………….…… [1]

(c) Find the highest common factor (HCF) of 756 and 2520. Leave your answer in prime factorisation form.

Answer …………………………………….…………… [1] (d) Find the smallest positive integer value of m such that the lowest common multiple (LCM) of 2520, 756 and m is 52920. Answer …………………………………….…………… [2] 10 The populations of the world’s poorest countries in the world are shown in the table below. Country Population (millions) *GDP-PPP per capita (USD $) * Gross domestic product (GDP) per captia is often used as the standard metric for measuring level of poverty. To better compensate for differences in living costs and rates of inflation, economists also factored power parity (PPP) to assess an individual’s buying power in any given country. South Sudan ! 15 455 Burundi 13.563 916 Central African Republic 5.579 1123 Democratic Republic of the Congo 99.01 1552 Mozambique 32.97 1649 (https://gfmag.com/data/economic-data/poorest-country-in-the-world/) (a) Calculate the total population of the 5 countries. Give your answer in standard form. Answer …………………………………….…………… [2]

(b) Luxembourg is the richest country in the world with a population of 670 000 and GDP-PPP per capita (USD $) of 143743. Express the GDP-PPP per capita of Luxembourg as a percentage of the GDP-PPP per capita of South Sudan ! . Answer …………………………………….…………… % [1]

(c) Interpret the meaning of the value found in (b). Answer ………………………………………………………………………….. …………………………… … …. ………………………………………………………………………………………………………… …………… ………………………………………………………………………………………………………… ………[1]

11 In the diagram below, ABC is a straight line and ABD is an equilateral triangle. AD is parallel to CE. (a) Find DBC∠. State the reason(s) clearly. Answer DBC∠ =