XMSS E Math Prelim P2 2024 (QP)

XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Preliminary Examination 2024 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Paper 2 Setter: Mr Johnson Chua Vetter: Ms Vanessa Chia Moderator: Mr Johnson Chua 4052/02 22 August 2024 2 hours 15 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your name, index number and class in the spaces at the top of this page. 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 the 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 in the space below the question. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. 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  , use either your calculator value or 3.142. Errors Qn No. Errors Qn No. Accuracy Simplification Brackets Units Geometry Marks Awarded Presentation Marks Penalised This document consists of 23 printed pages and 1 blank page. [Turn over For Examiner’s Use 90 Parent’s/Guardian’s Signature:

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c ABC== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff −  

3 1 (a) Solve 2 7 7 025 xx+− −= . Answer x = …………………………… [2] (b) Solve the equation (2 3)( 4) 2xx− − = . Answer x = …………………………... [4]

4 (c) Simplify 2215 3 28 x x y y  , leaving your answer in positive index form. Answer ……………………………….. [1] (d) Simplify 22 3 2 6 6 ax bx a b a ab b + − − +− . Answer ….…………………………… [3]

5 [Turn over 2 (a) Account A pays 3% per year compound interest, compounded monthly. Account B pays 3% per year compound interest, compounded yearly. Cody has some money to invest for 5 years. Explain which account Cody should invest his money in. …………………………………………………………………………………. …………………………………………………………………………………. …………………………………………………………………………………. [1] (b) Ezra invests $20 000 in an account that pays x% per year compound interest. He leaves the money in the account for 3 years. At the end of 3 years, there is $22 823.32 in the account. Find the value of x, leaving your answer in one decimal place. Answer x =…………………………… [3]

6 (c) The cash price of a new car is $156 000. (i) Cillian buys the car on hire purchase. He pays a deposit of 40% in cash. He then makes 36 monthly payments of $2800. What is the total amount that Cillian pays for the car? Answer $……………………………... [2] (ii) The original value of the car is its cash price of $156 000. Each year, the value of the car decreases by 8% of its value at the start of the year. At the end of 3 years, Cillian decides to sell the car. Calculate the percentage loss Cillian will make, compared to the total amount he pays for the car. Answer………………………………% [3]

7 [Turn over (d) The exchange rate between US dollars (US$) and Singapore dollars (S$) is US$1 = S$1.35. The exchange rate between Singapore dollars (S$) and Canadian dollars (CA$) is S$1 = CA$1.02 Jude is planning a trip to America and Canada. He finds the following hotel prices on a website. The Grand New York, US$368 per night The Ontario Inn, CA$250 per night. Jude books 2 nights at The Grand New York and 3 nights at The Ontario Inn using his credit card. The credit card company converts the prices to Singapore dollars and Jude is charged a fee of 1.5% for the currency conversion. Calculate the total amount Jude pays for both hotels, including the credit card fee. Answer S$……………………………. [3]

8 3 A group of 80 students took a Physics test. The cumulative frequency curve below shows the distribution of their marks. (a) Use the curve to estimate (i) the median mark, Answer ….…………………………… [1] (ii) the interquartile range, Answer ….…………………………… [2] (iii) the 60th percentile. Answer ….…………………………… [1] Cumulative Frequency Mark

9 [Turn over (b) The passing mark for the test was x marks. 85% of the students passed the test. Find the value of x. Answer x = …………………………… [2] (c) The same group of students took a Chemistry test. The box-and-whisker plot shows the distribution of their marks. (i) Make two comparisons between the performances of the students in the two tests. 1. ……………………………………………………………………… ………………………………………………………………………… ………………………………………………………………………… 2. ……………………………………………………………………… ………………………………………………………………………… ………………………………………………………………………… [2] (ii) There was an error in a question from the Chemistry test. Every student is awarded an additional mark as a result of the errata. Describe the effect this change would have on the box-and-whisker plot. ………………………………………………………………………… ………………………………………………………………………… [1] | | | | | | 0 10 20 30 40 50 Chemistry test marks

10 4 (a)  ={integers x: 2 16x } A = {multiples of 4} B = {factors of 48} (i) List the elements in B’. Answer ….…………………………… [1] (ii) List the elements in A’ ∩ B. Answer ….…………………………… [1] (iii) A number, p, is chosen at random from the set A ∪ B. Find the probability that pB . Answer ….…………………………… [1]