Greendale Sec 4048 02 QP

Name:_________________________________ ( ) Class:________ This document consists of 25 printed pages, including this cover page and 1 blank page. Greendale Secondary School 2022 GREENDALE SECONDARY SCHOOL Preliminary Examination 2022 MATHEMATICS 4048/02 Paper 2 23 August 2022 Secondary 4 EXP/ 5 NA 2 hours 30 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number and name 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 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 . 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 100. No of additional booklets/ writing paper used No of additional graph paper used Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Strand Marks 100

Greendale Secondary School 2 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curve surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 – 2bc cos A Statistics Mean = ∑ ∑ f fx Standard deviation = 22       − ∑ ∑ ∑ ∑ f fx f fx

Greendale Secondary School 3 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 Blank Page [Turn over for Question 1]

Greendale Secondary School 4 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 Answer all questions. 1 (a) Solve the inequality 3 12 1 34 xx−+< . Answer _____________________ [2] (b) Express as a single fraction in its simplest form ( ) 2 72 4343 x xx − −− . Answer _____________________ [2] (c) Simplify 1 10 2 649 m n −   . Answer _____________________ [2]

Greendale Secondary School 5 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 (d) Simplify 2 2 50 32 5 11 12 x xx − −− . Answer _____________________ [3] (e) Solve the simultaneous equations. 4 5 16 6 3 10 xy xy −= += Answer x = _____________________ y = _____________________ [3]

Greendale Secondary School 6 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 2 Two bus companies use 3 different types of buses – Small, Medium and Big. The table below shows the number of bus trips on 3 consecutive days. The information for the number of trips on Days 1, 2 and 3 can be represented by the matrices 8 15 20 30 65 P  = , 10 15 20 35 12 6 Q  = and 68 13 14 95 R  = respectively. (a) Evaluate 1 ()3A PQR= ++ Answer A =            [2] Bus companies Company A Company B Number of bus trips Day 1 Small 8 15 Medium 20 30 Big 6 5 Day 2 Small 10 15 Medium 20 35 Big 12 6 Day 3 Small 6 8 Medium 13 14 Big 9 5

Greendale Secondary School 7 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 (b) Describe what is represented by the elements of A. Answer _________________________________________________________ _________________________________________________________ ______________________________________________________[1] (c) Let ( )111B= . (i) State which matrix, 3AB or 3BA, exists. Answer ___________________________________________________ ________________________________________________[1] (ii) Describe what the elements of the matrix that exists in (c)(i) represent. Answer ___________________________________________________ ________________________________________________[1] (d) The number of passengers per trip on a small, medium and big bus is 12, 25 and 50 respectively. (i) Write down the product of P and two other matrices such that the elements in this product represent the total number of passengers the two bus companies carry on Day 1. You need not evaluate this product. Answer [2] (ii) Company A charges $22 per passenger. Find the total amount that Company A collects on Day 1. Answer [2]

Greendale Secondary School 8 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 3 (a) Complete the table of values of 83 10yx x= +− . Give your answer correct to 1 decimal place. x 0.5 1 1.5 2 3 4 5 6 y 7.5 1 0.2− 0 1.7 4 6.6 [1] (b) On the grid, draw the graph of 83 10yx x= +− for 0.5 6 x≤≤ . [3] y x 8 1 2 – 2 4 6 2 3 10 4 0 5 6

Greendale Secondary School 9 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 (c) Use your graph to find the solutions of the equation 83 15x x+= in the range 0.5 6 x≤≤ . Answer x = __________ or [2] (d) (i) On the grid in part (b), draw the line 21yx= + for 06 x≤≤ . [2] (ii) Write down the x-coordinates of the points where this line intersects the curve. Answer x = __________ and [2] (iii) These values of x are the solutions of the equation 250x Bx C+ += . Find the value of B and of C. Answer B = _____________________ C = _____________________ [3]

Greendale Secondary School 10 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 2 4 The diagram shows the position of four points A, B, C and D on level ground. B is due east of A, the bearing of D from B is 242o, angle CBD = 130o and angle BAD = 36o. BD = 480 m and BC = 630 m. (a) Find (i) the bearing of A from D, Answer _____________________ ° [1] (ii) the distance of AD. Answer ____________________m [3] B A 130o 36o D N C 480 630