BWSS 2022 3NA Math EOY P2 QP

Class Full Name Index Number I believe, therefore I am MATHEMATICS Paper 2 Secondary 3 Normal Academic 10 October 2022 2 hours Candidates answer on the Question Paper 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. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total number of 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 the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142. DO NOT OPEN THIS PAPER UNTIL YOU ARE TOLD TO DO SO Setter: Mdm Joyce Toh This document consists of 19 printed pages including this cover page. N END OF YEAR EXAMINATION 2022 Calculator Model : 4045/02 For Examiner’s Use 70

2 Mathematical Formulae Compound Interest n rP      += 1001amount Total Mensuration rl= cone a of area Surface Curved 24 sphere a of area Surface r= hr 2 3 1 cone a of Volume = 3 3 4 sphere a of Volume r= cabABC sin2 1 triangleof Area = radiansin is where,length Arc r= radiansin is where,2 1 areaSector 2 r= Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics f fx  =Mean 22 deviation Standard        − = f fx f fx

3 Answer all the questions. 1(a) A passenger aircraft has 280 seats. In a particular flight, 226 seats are occupied. Calculate the percentage of empty seats in the aircraft for that flight. Answer ............................................. % [2] (b) The cost of a seat in 2010 is $988. Calculate the cost of a seat in 2009 if the cost in 2010 was an increase of 20.5% on the price in 2009. Answer $ ............................................. [2]

4 2 Scientists estimated that an ant can consume an average of 0.024 kg of food per day. An ant colony has 2.5 million of ants. (a) Write 2.5 million in standard form. Answer ................................................. [1] (b) Estimate the total amount of food consumed in a day by the colony of ants. Leave your answer in standard form. Answer ............................................... kg [2] (c) Assuming that the rate of consumption of food is constant throughout a day, calculate the time taken, in seconds, for the entire ant colony to consume 12 kg of food. Answer ............................................... sec [2]

5 3(a) Expand and simplify (3x + 5y)(2x – 3y). Answer ................................................. [2] (b) Write 3 52 4 +− xx as a fraction in its simplest form. Answer ................................................. [2] (c) Make p the subject of the formula 5 7 rpm += . Answer ................................................. [2]

6 4 The line passes through the points (1, 2) and (7, −2). (a) Find the equation of the line. Answer ................................................. [3] (b) The line cuts the x–axis at point A. Find the coordinates of A. Answer A = (…….....….. , ...................) [1] (c) Find the equation of a line parallel to the x–axis and passes through the point (7, −2). Answer ................................................. [1] A

7 5 It is given that n is a positive integer. p is found by adding 7 to 3 times of n. q is found by subtracting 1 from n and multiplying the result by 2. The result of multiplying p to q is 170. (a) Show that 3n2 + 4n – 92 = 0. Answer [2] (b) Solve 3n2 + 4n – 92 = 0. Give both answers correct to 2 decimal places. Answer n = ……..….… or n = ….…...…… [2] (c) Hence, find value of p. Answer p = ……........................................ [1]

8 6 The coordinates of point P are (3, 4) and point Q are (12, –5). ` y P (3, 4) O x Q (12, –5) (a) Find the equation of line OP. Answer ............................................. [1] (b) OPRQ is a parallelogram. Find the coordinates of point R. Answer (...................., .....................) [1]

9 (c) Find the perimeter of the triangle OPQ. Answer ......................................... units [3] 7 The number of oatmeal, chocolate chip and almond cookies in a bag is in the ratio of 4: 3: 1. (a) Express the number of oatmeal cookies as a percentage of the total cookies in the bag. Answer ............................................ % [1] (b) If there are 18 more chocolate cookies than almond cookies, find the total number of cookies in the bag. Answer .................................... cookies [2]

10 (c) If 6 oatmeal cookies are removed from the bag, find the new ratio of oatmeal cookies : chocolate chip cookies : almond cookies. Answer ............................................... [2] 8 FRESH washing powder is sold in two sizes, medium and large. Which of the two sizes gives a better value? Show all your working clearly. Answer .................................... size washing powder gives a better value because ................... ……………………………………………………………………………………….………….. ………………………………………………………………………………………………….. [3]