Manjusri 4045 02 PRELIM 2024 QP

This document consists of 19 printed pages and 1 blank page [Turn over MANJUSRI SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION Name Class Index Number MATHEMATICS Secondary Four Normal (Academic) / NT SBB Paper 2 Candidates answer on the Question Paper. 4045/02 2 August 2024 2 hours READ THESE INSTRUCTIONS FIRST Write your Name, index number and class 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. In Section A and answer one question in 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. For π, 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. Parent’s / Guardian’s Signature: …………………….. For Examiner’s Use Total / 70

2 4045/02/PRELIM/2024 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr 2 Volume of a cone = 3 1πr2h Volume of a sphere = 3 4πr3 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 sin sin sin= = a2 = b2 + c2 – 2bc cos A Statistics Mean = ∑ ∑ f fx Standard deviation = 22       − ∑ ∑ ∑ ∑ f fx f fx

3 4045/02/PRELIM/2024 [Turn Over Section A (62 marks) Answer all the questions in this section. 1 Work out (a) 21 6 0.5(2) 2 −− − , Answer ……………………........ [1] (b) 25.3 4.83 2.4× . Answer ………………………..... [1] 2 The table shows the land size of 4 countries. Countries Area in km2 India 3.29 × 109 Myanmar 6.77 × 105 Indonesia 1.49 × 106 Vietnam 331 114 Calculate the total land sizes of the four countries, giving your answer in standard form. Answer ………………………..... [1] 3 (a) Written as a product of its prime factors, 8640 = 235xy×× .Find the values of x and y. Answer x = ….…. , y = ….…….. [2] (b) Written as a product of its prime factors, 3378 2 3 7=×× . Find the smallest positive integer p, such that 378p is a square number. Answer ………………………..... [1]

4 4045/02/PRELIM/2024 4 Solve these simultaneous equations. 5 3 23 2 18 xy xy −= += Show your working. Answer x = ….…. , y = ….……. [3] 5 Jane bought a bottle of perfume at £62.00 in UK for her mother, inclusive of tax. The exchange rate between Singapore dollars (S$) and Pound sterling (£) was S$1= £0.58. When she returned to Singapore, she found that the same perfume was priced at S$102 , before the 9% GST is charged. The price of the perfume is cheaper in which country, Singapore or UK? Answer …………………….…. [3] Dleon

5 4045/02/PRELIM/2024 [Turn Over 6 The stem-and-leaf diagram shows the height, in cm, of plants in a plant nursery. 4 3 5 1 7 6 0 1 7 3 6 6 8 4 Key 4|3 = 43 (a) State (i) the modal height, Answer …………………..…. cm [1] (ii) the median height, Answer …………………..…. cm [1] (b) Calculate (i) the mean height, Answer ..…………………..... cm [2] (ii) the standard deviation. Answer …………………..…. cm [1]

6 4045/02/PRELIM/2024 7 Rose received a bonus of $5000. She wanted to save it in a bank for 5 years. The bank offered two plans. Explain which plan should Rose choose? Show your working clearly. Answer She should choose Plan ……… because …………………………………………………… …………………………………………………………………………………………… [4] Plan A 3% simple interest per annum Plan B 2.8 % compound interest compounded yearly

7 4045/02/PRELIM/2024 [Turn Over 8 The points P, Q and R lie on the circumference of a circle. PQ = 34 cm, QR = 16 cm and PR = 28 cm. Determine if PQ is a diameter. Answer ……………………………………………………………………………………… ………………………………………………………………………………………………. …………………………………………………………………………………………… [3]

8 4045/02/PRELIM/2024 9 The table shows the information of students from 4B and 4C. Boys Girls 4B 23 14 4C 19 16 Two student supporters are selected at random from the two classes without replacement. Find the probability that (a) the first student chosen is a 4B boy and the second student is a 4C girl, Answer ………………………… [1] (b) both students chosen are girls, Answer ………………………… [1] (c) at least one of the students chosen is from 4B. Answer ………………………… [2]

9 4045/02/PRELIM/2024 [Turn Over 15 km 10 A, B and C are three ships on the sea. Calculate (a) ∠ABC, Answer …………………… ° [3] (b) the area of ∆ ABC, Answer ………………… km2 [2] (c) the shortest distance from A to BC. Answer …………………… km [2] B 22 km 8 km A C

10 4045/02/PRELIM/2024 11 A hat in the shape of a cone is shown below in figure 1. The measurements are in cm. Figure 1 Figure 2 The cone is made from a sector (Figure 2) by joining AB and AC together. The circumference of the circle of the base of the cone is the arc length of the sector. Find (a) the radius, r, of the base circle of the cone, Answer …………………… cm [2] (b) the circumference of the base circle of the cone, Answer …………………… cm [1] (c) ∠BAC, in radians. Answer ……………… radians [2] 13 12 r A C B A