Swiss Cottage Mock WA2 2023.QP

SWISS COTTAGE SECONDARY SCHOOL SECONDARY FOUR MOCK WA2 O Name: ( ) Class: MATHEMATICS Candidates answer on the Question Paper. 38 mins 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 25. This document consists of 9 printed pages. [Turn over Home of Thoughtful Leaders: Serve with Honour, Lead with Humility Qn Mark Concept Application Careless Student Analysis/Remarks 1 4    2 8    3 9    4 4    Total Mark 25 Parent’s Signature

2 Mathematical Formulae Statistics Mean = fx f  Standard deviation = 22fx fx ff  

3 1 The cumulative frequency graph shows the distribution of the scores of 60 students in a test. (a) Use the curve to find ( i ) the percentage of students who scored at least 16 marks, Answer …………………………… % [1] ( i i ) the median score, Answer ……………………………… [1] 0 Cumulative Frequency Score

4 (iii) the interquartile range. Answer ……………………………… [1] (b) Three students were found cheating during the test. Their scores were 13, 17 and 19. The mean score for the test was 25. Given that their scores were removed from the list, describe how this would affect the mean. Answer …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… [1]

5 2 Mevin set up a stall at a bazaar selling face masks, hand sanitisers and hand wash. The selling prices of the items were $2.50, $3 and $4.50 respectively. The table below shows the quantity of each item sold at different periods of the day over two weeks. Week 1 Week 2 F a c e mask Hand sanitiser Hand wash Face mask Hand sanitiser Hand wash Morning 105 98 71 84 75 12 Afternoon 54 43 20 42 39 35 Evening 161 102 68 93 51 24 The quantity of the items sold for the two weeks can be represented by the matrices A 105 98 71 54 43 20 161 102 68  and B 84 75 12 42 39 35 93 51 24  (a) Represent the price of each item in a 31 column matrix P. Answer P = ………………………… [1] (b) Evaluate the matrix T= (A + B)P. Answer T = ……………………..…... [2]

6 (c) State what each element in matrix T represents. Answer …………………………………………………………………………… …………………………………………………………………………… …………………………………………………………………………… [1] After observing that his sales dropped in the second week, Mevin decided to lower the price of the face mask, hand sanitiser and hand wash by 10%, 5% and 20% respectively. (d) Write down a 33 matrix Q such that QP represents the new prices of each item. Answer Q = …..……………… [1] (e) Given that R111, evaluate SRAQP and state what each element in matrix S represents. Answer S = ………………. ……………………………………………………………………………………. ……………………………………………………………………………………. ……………………………………………………………………………………. [3]

7 3 (a) Point A has coordinates (2 , 1 ) and 6 9AB  . (i) Find the equation of the line AB. Answer …………………….. [2] (ii) Find OB . Answer …………………….. [2] The points A, B and C are collinear and 12 uAC   . (iii) Find u. Answer u = .………….......... [2]

8 ( b ) PQRS is a trapezium with QR // PS and 3QR = 2PS q T is a point on QS such that :1 : 3QT QS. PQ p and QR q. Express each of the following, as simply as possible, in terms of p and/or q. ( i ) SQ  Answer SQ ………………. [1] ( i i ) PT  Answer PT ……………… [1] ( i i i ) SR Answer SR……………… [1] p P Q R S T

9 4 (a) The weights of 200 girls in dance academy A were recorded and shown in the table below. Weight (x kg) Number of girls 40 45x 25 45 50x p 50 55x 70 55 60x 50 60 65x 10 (i) Find p. Answer p ………………. [1] (ii) Calculate an estimate of the standard deviation of the weights. Answer …………………. kg [1] (iii) The weights of the girls in dance academy B were recorded. The median weight was found to be 57 kg. Make a comparison between the weights of the girls in dance academy A and B. Answer …………………………………………………………………………….. …………………………………………………………………………….. …………………………………………………………………………….. …………………………………………………………………………….. …………………………………………………………………………….. [2] End of paper