2023 SNGS MA IP EOY P2 QP

This document consists of 21 printed pages and 1 blank page. . [Turn over Name: _________________________ ( ) Class :_____________ YEAR FOUR INTEGRATED PROGRAMME END OF YEAR EXAMINATION MATHEMATICS Paper 2 Wednesday 27 September 2023 2 hours 15 minutes Candidates answer on the Question Paper. ______________________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name, class, and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a pencil for any diagrams or graphs. Do not use paper clips, highlighters, glue, or correction fluid. Answer all questions. 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. At the end of the examination, staple all your work securely together with this cover sheet. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. Paper 1 / 90 Q1 Q4 Q7 Paper 2 / 90 Q2 Q5 Q8 Q3 Q6 Q9 Total /180

2 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 Mathematical Formulae Compound interest Total amount n rP      + =1001 Mensuration Curved surface area of a cone = π rl Surface area of a sphere = 24π r Volume of a cone 21 π3 rh= Volume of a sphere 34 π3 r= Area of a triangle ABC 1 sin2 ab C= Arc length θr= , whereθ is in radians Sector area 21 2 r θ= , whereθ is in radians Trigonometry sin sin sin abc ABC= = 222 2 cosa b c bc A=+− Statistics Mean fx f= ∑ ∑ Standard deviation 2 2 fx fx ff  = −  ∑∑ ∑∑

3 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 [Turn over [Turn over for Question 1]

4 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 1 (a) Simplify 269 5 pq p q÷ . Answer ………….……….….…………. [1] (b) Solve 63 022 1yy −=−+ . Answer y = …….………….…………. [2] (c) (i) Express 2 3 12xx−+ in the form 2()xa b++ , where a and b are constants. Answer ………….……….….…………. [2] (ii) Hence, solve 2 3 12 11xx−+= . Answer x =…….…..… or .….….……. [2]

5 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 [Turn over (d) Simplify 2294 6 43 2 mn am an bm bn − +−− . Answer ………….……….….…………. [4]

6 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 2 (a) Valerie deposited $4000 in a savings account that pays compound interest of 3.8% per annum, compounded monthly. Calculate the amount of interest Valerie receives at the end of 2 years. Answer $……………….….…………. [3] (b) Ashley invested S$4000 in a savings account in Hong Kong when the exchange rate between Hong Kong dollars and Singapore dollars was HK$ 1 = S$0.15. The savings account pays 4.2% per annum simple interest. The investment matured after 3 years when the exchange rate between Hong Kong dollars and Singapore dollars was HK$ 1 = S$0.19 Find the total amount she received after 3 years. Give your answer in Singapore dollars correct to the nearest cent. Answer S$……………….…...………. [4]

7 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 [Turn over (c) Kenneth purchased a refrigerator on hire purchase. The cash price of the refrigerator was $6000. He paid $2000 down payment and subsequently made 24 monthly instalments. The hire purchase scheme charges a simple interest of 2.5% per annum. Find the amount of each monthly instalment. Answer $……………….….…………. [3] (d) Sarah had lunch at a Japanese restaurant which offered a 10% discount. The marked price of the meal was $75. Given that there was a service charge of 10% and the GST was 8%, find the amount she had to pay. Answer $……………….….…………. [3]

8 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 3 A group of 40 students took a Mathematics test. The cumulative frequency curve below shows the distribution of their marks. (a) Use the graph to estimate (i) the median mark, Answer ………….……….….…………. [1] (ii) the interquartile range, Answer ………….……….….…………. [2] 5 10 15 20 25 30 35 60 80 100 50 70 90 Cumulative Frequency Marks 0 40 40

9 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 [Turn over (iii) the passing mark, if 90% of students pass the test. Answer ………….……….….…………. [2] (b) Two students were selected at random. Find the probability that one of the students obtained less than 55 marks and the other obtained more than 85 marks. Answer ………….……….….…………. [2] (c) The same group of students took a Science test. The box-and-whisker plot shows the distribution of their marks. Make two comparisons between the performance of the students in the two tests. ……………………………………………………………………………………………... ……………………………………………………………………………………………... ……………………………………………………………………………………………... ……………………………………………………………………………………………... …………………………………………………………………………...……………… [2] 60 80 100 50 70 90 40

10 CHIJ SNGS Year 4 Integrated Programme End of Year Examination 2023 – Mathematics Paper 2 A B C D 6 Diagram 1 A B C D Diagram 2 4 In Diagram 1, ABCD is part of a circle of radius 6 cm, with the shaded parts removed from the circle. DC = AB and AC intersects BD at right angles at the centre of the circle. (a) Calculate the area of ABCD. Leave your answer in terms of π. Answer ………….…..…….….……cm 2 [3]