BWSS 2023 Sec 4N Math Prelim Paper 1

I believe, therefore I am MATHEMATICS SYLLABUS A Secondary 4 Normal Academic/ 4 Normal Technical (OOS) 1 August 2023 2 hours Candidates answer on the Question Paper. Additional Materials: Writing papers upon request 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 a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is required for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 70. 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 your answer to three significant figures. Give answer in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . DO NOT OPEN THIS PAPER UNTIL YOU ARE TOLD TO DO SO This document consists of 18 printed pages, including this cover page. Class Full Name Index Number Preliminary Examination 2023 For Examiner’s Use 70 N Calculator Model No.: 4045/01

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3 Answer all the questions. 1 The table shows the maximum and minimum temperatures of three cities in a day during the month of January. City Beijing Geneva Helsinki Maximum temperature 2°C 5°C – 1°C Minimum temperature – 8°C – 1°C – 7°C (a) Find the average of the minimum temperatures of Beijing and Geneva. Answer ……..................................°C [1] (b) State the city with the biggest difference between its maximum and minimum temperatures. Show the calculations you make. Answer ……....................................... [1] 2 A bag contains only red, blue and yellow marbles. 1 6 of the marbles are yellow. The ratio of red and blue marbles is 2 : 3. (a) Write the ratio of yellow marbles : blue marbles in its simplest form. Answer .................... : ................. [1] (b) If the bag contains 16 yellow marbles, how many blue marbles are there? Answer ........................................ [1]

4 3 Express 71 km/h in m/s, giving your answer correct to 2 significant figures. Answer ..................................... m/s [2] 4 (a) Subtract the sum of –3x2 + 15 – 10x and 9x2 + 3x – 14 from –7x + 15x2 + 1. Answer ……....................................... [2] (b) The cube root of r is equal to 24x divided by the square root of 9x2. Find the value of r. Answer r = …....................................... [2]

5 5 The body mass index, BMI, for a person with mass m kg and height h metres, is given by the formula BMI = 𝑚 ℎ2 (a) The body mass index for a person in the healthy range is 18.5 ≤ BMI < 23. If Belinda’s height is 172cm, find the maximum mass of Belinda to stay within the healthy range. Give your answer as an integer. Answer ……..................................... kg [2] (b) Rearrange the formula to make h the subject. Answer h = …....................................... [1] 6 A monitor cost 1 5 as much as a laptop. The total cost of the monitor and laptop after a 30% discount is $2730. Find the cost of the laptop before discount. Answer $ ......................................... [2]

6 7 Find the smallest prime number satisfying the inequality – 2x ≤ 5x – 18. Answer …......................................... [2] 8 In a sequence, a constant number is subtracted from the previous number to obtain the next term. The first four terms of the sequence are 35, p, q and 11. (a) Find the values of p and q. Answer p = …......................................... q = …......................................... [1] (b) Find an expression for the nth term of the sequence. Answer …......................................... [1]

7 9 (a) Benny says the diagram above is part of a regular polygon. Is he correct? Explain your answer. Answer ………………………............................................................................................... ……………...………..………………..……………………..………………………………… ………….…………………………………………………………………..…….………. [2] (b) ABCG is a rhombus and angle GAB is 98°. CGD, EGD and FGE are congruent triangles whereby GC = GD = GE = GF and angle GCD is 70°. Find angle AGF. Answer …......................................... [2] 80° 98° 70° C B A F E D G

8 10 In the diagram, ABC is a straight line, CD = 12cm, BD = 13cm and angle BCD = 90°. (a) Find as a fraction in its simplest form, the value of (i) sin x°, Answer …......................................... [2] (ii) cos y°. Answer …......................................... [1] (b) Find the shortest distance from C to BD. Answer …..................................... cm [2] A B C x° D y°

9 11 When written as the product of their prime numbers, 588 = 22 × 3 × 72 140 = 22 × 5 × 7 (a) Find the smallest integer k such that 140k is a square number. Answer k =......................................... [1] (b) Identical cubes are placed in a rectangular box measuring 504mm by 588mm by 140mm. Find the least number of cubes to fit the box exactly. Answer …................................ cubes [3] 12 A number is selected randomly from 2-digit numbers that are less than 25. Find the probability of selecting a prime number. Answer …......................................... [2]

10 13 Triangle Q is an enlargement of Triangle P on the 1-centimetre grid. (a) Find the scale factor of the enlargement. Answer …......................................... [1] (b) Triangle P is enlarged by a scale factor of 0.8 to Triangle R. Find the area of Triangle R. Answer …......................................... cm2 [2] P Q