XMS SEC 4 EMATH 2023 WA2

This document consists of 10 printed pages and 0 blank page. [Turn over XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Weighted Assessment 2 2023 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Secondary 4 Express Setter: Mr Johnson Chua Vetter: Ms Vanessa Chia Candidates answer on the Question Paper. No Additional Materials are required. 4052 02 May 2023 45 minutes READ THESE INSTRUCTIONS FIRST Write your name, register 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. 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  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . At the end of the examination, fasten all your work securely together. 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 30. Errors Qn No. Errors Qn No. Accuracy Simplification Brackets Units Geometry Marks Awarded Presentation Marks Penalised For Examiner’s Use 30 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 A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 [Turn over Answer all the questions. 1 Given that 1 2 0 3 032 2 1 5 13 4 y x      −=     − − − −      , find the value of x and of y. Answer x = …………………………….. y = ………………………… [2] 2 Mr Gan weighed 8 male students. The median mass of the students was 63.5 kg. The interquartile range of the masses of the students was 4.5 kg. Mr Gan realised that the scale of the weighing machine was inaccurate. The correct mass of each student was 1.5 kg less than what he had recorded. Write down the correct values for the median mass and interquartile range. Answer Median mass: ………………………….kg…. Interquartile range: …………………………kg [2]

4 3 27 female patients and 30 male patients living in Xin-town are found to be infected with the E-virus. The ages of the patients are shown in the stem-and-leaf diagram below. Female Patients Male Patients 7 3 2 4 5 5 3 2 0 3 1 6 1 4 2 2 3 5 7 6 6 4 4 2 5 x 7 8 8 5 3 2 0 0 0 6 0 2 2 3 3 4 8 8 5 5 4 2 1 7 4 5 6 7 3 1 1 0 0 8 2 4 4 5 Key (Female Patients) 2 | 7 means 72 Key (Male Patients) 2 | 4 means 24 (a) Write down the range of the ages of the female patients. Answer ……………………………… [1] (b) Find the median age of the male patients. Answer ……………………………… [1] (c) Find the interquartile range for the male patients. Answer ……………………………… [2]

5 [Turn over (d) Write down all possible values of x given that both the male and female groups have the same percentage of patients who are younger than 55 years old. Answer x = …………………………… [2]

6 4 At supermarket A, a bag of flour costs $2.90, a tray of eggs costs $4.40 and a sack of rice costs $24. The same items can be bought in supermarket B where the flour costs $3.20, eggs cost $x and rice costs $25. This information can be represented by the matrix C = 2.9 4.4 24 3.2 25x   (a) Ron buys 3 bags of flour, 4 trays of eggs and 2 sacks of rice. Zoe buys 5 bags of rice, 3 trays of eggs and 3 sacks of rice. Represent this information in a 32 matrix D. Answer D =       [1] (b) Find, in terms of x, the matrix T = CD. Answer T = [2] (c) Explain what the elements in the first row of matrix T represent. Answer ………………………………………………………………………………… ….………………………………………………………………………………………. ….……………………………………………………………………………………[1] F E R A B

7 [Turn over (d) Ron would save $1.30 by buying his purchases from supermarket A. Find the value of x. Answer x = …………………………… [2] (e) On a particular week, supermarket A was offering a store-wide 20% discount promotion while supermarket B was offering a store-wide 10% discount promotion. (i) Write down a matrix P, such that the product of P and T would give the discounted prices which Ron and Zoe each has to pay if they purchase the items from supermarkets A and B respectively. Answer P = [1] (ii) Hence, using the value of x found in (d), find the product of the matrices P and T. Answer [1]

8 5 The speeds of 160 cars passing through a checkpoint one morning were recorded. The cumulative frequency curve below shows the speed, x km/h, and the number of cars with speed less than or equals to x km/h. (a) Use the curve to estimate (i) the median speed, Answer ……………………………… km/h [1] (ii) the interquartile range of the speeds, Answer ……………………………… km/h [2] (iii) the 30th percentile. Answer ……………………………… km/h [1] 160 120 80 40 0 Cumulative frequency 30 35 40 45 50 55 60 Speed (x km/h)

9 [Turn over (b) Explain why it is not possible to state the number of cars with speed less than 45 km/h. Answer ………………………………………………………………………………… ….……………………………………………………………………………………[1] (c) The speed limit on the road is v km/h. Given that 1 40 of the vehicles exceeded the speed limit, find the value of v. Answer v = …………………………… [1] (d) The speeds of 160 cars passing through the same checkpoint in the evening were also recorded. The box-and-whisker plot below shows the distribution of the speeds. Make two comments comparing the speed of the cars in the morning and in the evening. Answer ………………………………………………………………………………… ………………………………………………………………………………………….. ….……………………………………………………………………………………[2] 30 35 40 45 50 55 60 Speed (km/h)

10 (e) (i) Complete the grouped frequency table for the speeds of the cars passing through the checkpoint in the morning. Speed (x km/h) Frequency 30 35x 28 35 40x 36 40 45x 45 50x 50 55x 55 60x 4 [1] Calculate an estimate of the (ii) mean speed, Answer ………………………………km/h [1] (iii) standard deviation. Answer ………………………………km/h [1] (f) Explain why the mean speed of the cars is only an estimate. Answer ………………………………………………………………………………… ….……………………………………………………………………………………[1] --- End of paper---