Swiss Cottage WA2 2023.Ans

1 SWISS COTTAGE SECONDARY SCHOOL SECONDARY FOUR WEIGHTED ASSESSMENT 2 O Name: ( ) Class: MATHEMATICS 4052 Wednesday 10 May 2023 45 Minutes READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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 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 . 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. This document consists of 9 printed pages. Setter: Mr Ngoh Kia Joon, Ms Leung Yan Ru, Mr Ang Hanping [Turn over Home of Thoughtful Leaders: Serve with Honour, Lead with Humility Qn Mark Concept Application Careless Student Analysis/Remarks 1 6    2 4    3 2    4 8    5 3    6 7    Total Mark 30 Parent’s Signature

2 Mathematical Formulae Compound interest Total amount = nrP   1001 Mensuration Curved surface area of a cone = lr Surface area of a sphere = 24r Volume of a cone = hr2 3 1 Volume of a sphere = 3 3 4r Area of triangle ABC = Cbasin2 1 Arc length = r, where  is in radians Sector area = 2 2 1r, where  is in radians Trigonometry C c B b A a sinsinsin  Acbcba cos2222  Statistics Mean = f fx Standard deviation = 22      f fx f fx

3 1 A group of students participated in a competition to estimate the mass of a jar of marbles. The cumulative frequency diagram below shows the estimation by the students. (a) Use the graph to estimate (i) median, Answer .................................... g [1] (ii) interquartile range for the mass of the jar of marbles. Answer .................................... g [2] Cumulative frequency 0 10 20 30 40 50 60 70 80 100 200 300 400 500 600 700 Mass (grams) & ↑- I I W j Iv ⊥x80=40students 420 FX80=20students- LC=280:/RR: 520-280= 240 -x80=60students- >UK=520 240

4 (b) Estimate the number of students who answered that the mass of the jar of marbles is at least 500 g. Answer ....................................... [2] (c) To increase the difficulty of the competition, the organiser announced that a jar with greater mass of marbles will be used next week. Describe how the cumulative frequency curve for the estimation by students next week will differ from the current competition. ................................................................................................................................................ ...........................................................................................................................................[1] 2 The table below shows the distance, in km, ran by each of the members of a club, in a week. Distance (km) Number of members 05x 2 51 0x 4 10 15x 11 15 20x d 20 25x 4 25 30x 3 (a) (i) Complete the following cumulative frequency table for the data given. [1] Answer Distance (km) Number of members 5x 2 10x 15x 20x 23 25x 30x (ii) Find the value of d. Answer d =................................ [1] 500ormore Noofstudents(< 5w%)=57 9 " (>50g)=So- 57=23 23 highermedian Thecurvewillbeshiftedtotheright. mid-values 2. 5 75 12. 5 17· 5 22. 527-5 it 2730 d=23-17=6 6

5 (b) Find an estimate of the (i) mean of the distance ran, Answer .................................km [1] (ii) standard deviation of the distance ran. Answer .................................km [1] 3 6 3.1 , 5 1 2  A 2 3 4 1.8  B and 2 3 5 4 6 y  C . (a) Evaluate A + B. Answer ....................................... [1] (b) It is given that B = C, find the value of y. Answer ....................................... [1] mean: 2x25+4x75+..... +3x275- 2+4+... +3 = K5P 30 = 15 15 [Fp=2x252+4x752+...+3x275 =8087-5 8= J8087· 5-115 668= 66771= 6. 68(38t) (435)+(2Ps = (54:3) (5) (s)= (i3)1. 8: Iby=10.S y=2: 16 2. 16

6 4 A dance school offers dance sessions for cultural and international dance students on weekdays and weekends. Each student has a 10-week block of lessons with one session per week. The matrix D shows the number of students attending the dance lessons each week in one 10-week block. Cultural International 3 10 5 8 D (a) Evaluate the matric L = 10D. Answer ....................................... [1] (b) The dance school charges $80 for each cultural dance session and $90 for each international dance session. Represent the session charges in a 21 column matrix C. Answer ....................................... [1] (c) Evaluate the matrix G = LC. Answer ....................................... [1] (d) State what the elements of G represents. Answer ......................................................................................................................... ………………………………………………………………………………………………….. ...................................................................................................................................... [1] Weekday Weekend = 10(3"8) = (2010(301 C= (0) (890) $ = WD(30 l(= (Io(10) Itrepresentsthetotalamountcollectedbythe danceMudioforweekdayandweekendare$11400 and$11200respectively.

7 (e) The dance school wants to attract more students, so in the next 10-week block, the dance school reduces the price for cultural and international dance session by 10%. For this block of sessions, on weekdays, there are 5 cultural dance students and 12 international dance students. On weekends, there are 8 cultural dance students and 15 international dance students. By using matrix multiplication, calculate the total amount of money the dance school earns for this 10-week block of sessions. Answer ....................................... [4] To t a lstudents= 10(5g15) charges= 0. 9for10week block = attent= (5)To t a lchanges= (301200)() = (i)totalamount= (11)!3200) =(31230) :totalamountis$31230 $31230

8 5 Given that P is the point (1, 1), 3 1PQ   and 2 1PR  , find (a) QR  , Answer ....................................... [1] (b) the coordinates of the point X such that PQXR is a parallelogram. Answer ....................................... [2] A 7~- > - PatOR pS->R-DOR R = (2) - (= ( - 2