Greendale Sec 4048 01 QP

Name:_________________________________ ( ) Class:________ This document consists of 25 printed pages, including this cover page. Greendale Secondary School 2022 GREENDALE SECONDARY SCHOOL Preliminary Examination 2022 MATHEMATICS 4048/01 Paper 1 26 August 2022 Secondary 4 EXP/ 5 NA 2 hours 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 80. Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Strand Marks Question Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Strand Marks 80

Greendale Secondary School 2 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 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 1 For Examiner’s Use Only Answer all questions. 1 Work out 223 5 ( 5) 5 55 − −− × −× . Answer ______________________ [1] _____________________________________________________________________ 2 In the diagram, O is the centre of the circle through the points P, Q and S. The tangent to the circle at Q meets PS produced at T. POQ is a straight line and 38QPS∠= ° . Find angle OSQ. State your reasons clearly. Answer ______________________ ° [2] _____________________________________________________________________ O P S Q T

Greendale Secondary School 4 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 3 y is directly proportional to x3. Which of these diagrams best represents the graph of y against x? Diagram 1 Diagram 2 Diagram 3 Diagram 4 Answer Diagram ______________________ [1] _____________________________________________________________________ 4 In a village, the number of villagers from 2020 to 2022 are given as follows: Key: represents 100 villagers (a) State one misleading feature of the graph. ________________________________________________________ ______________________________________________________[1] (b) Explain how this feature affects the reader’s interpretation of the graph. ________________________________________________________ ______________________________________________________[1] _____________________________________________________________________ 2020 2021 2022 y x y x y x y x

Greendale Secondary School 5 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 5 (a) Express 327 as a power of 3. Answer ______________________ [1] (b) Simplify 23 424 5 25 xy xz zy ÷ Answer ______________________ [2] _____________________________________________________________________ 6 It takes 18 workers a total of 60 hours to construct 3 footbridges. Find the additional number of workers needed to complete 7 footbridges in 40 hours, given that they all work at the same rate. Answer ______________________ [2] _____________________________________________________________________

Greendale Secondary School 6 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 7 A teacher asked a student to think of 5 integers which are less then 20 and gave the following information: The mean of these numbers is 10, the median is 9 and the mode is 6. The smallest number is a third of the largest number. What were the 5 integers the student wrote? Answer ________ , ________ , ________ , ________ , ________ [2] _____________________________________________________________________ 8 Solve the equation 41 125 xx+ −= − . Answer x = ___________________ [3] _____________________________________________________________________

Greendale Secondary School 7 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 9 A fair five-sided spinner is numbered using the prime numbers 2, 3, 5, 7 and 11. In a game, players spin it twice and add the two numbers obtained. (a) Complete the possibility diagram. Answer + 2 3 5 7 11 2 4 7 9 13 3 5 6 8 10 5 8 12 16 7 9 10 12 14 18 11 13 14 16 22 [1] (b) Find the probability that the total of the two numbers is a (i) prime number, Answer ______________________ [1] (ii) perfect square. Answer ______________________ [1] (c) Explain why the spinner has to be fair in order to find the probabilities in (b). Answer _____________________________________________________________________ ________________________________________________________________ [1] _____________________________________________________________________

Greendale Secondary School 8 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 10 (a) Express 2 75xx−+ in the form ( ) 2 xp q−− . Answer ______________________ [2] (b) Write down the coordinates of the minimum point of the graph of 2 75yx x=−+ . Answer (_____ _____ , ) [1] _____________________________________________________________________ 11 The first four terms of a number sequence are 5, 12, 19 and 26. (a) If the nth term of the number sequence can be expressed in the form of pn + q, find the values of p and q. Answer p =____________ [1] q = _____________ [1] (b) Hence, find the largest value of n such that the nth term is less than 100. Answer ______________________ [1] _____________________________________________________________________

Greendale Secondary School 9 Secondary 4E / 5NA Preliminary Examination 2022 Mathematics Paper 1 For Examiner’s Use Only 12 (a) A sum of money is divided in the ratio 4 : 3. The larger part is $7.20. Find the smaller part. Answer $_____________________ [1] (b) Express the ratio 700 g to 1.75kg in its lowest terms. Give your answer in the form m : n, where m and n are integers. Answer ___________ : ___________ [1] _____________________________________________________________________ 13 Given that 2 17 r q =+ , (a) Evaluate r when q = –3. Answer