2022 FMSS Prelim P2

NAME: ____________________________ ( ) CLASS: _______ MATHEMATICS 4048/02 Paper 2 Date: 24 August 2022 Duration: 2 hours 30 minutes Candidates answer on the Question Paper. ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name, index number and class 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 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 i s 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 of the marks for this paper is 100. For Examiner’s Use Table of Penalties Question Number 100 Presentation  1  2 Parent’s / Guardian’s Signature Rounding off  1 Setter: Mr Joel Li This question paper consists of 27 printed pages.   FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2022 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 2 Mathematics Paper 2 Mathematical Formulae Compound interest Total amount = P Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of a triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = n r      + 1001 rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == Abccba cos2222 −+=   f fx 22       −     f fx f fx

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 3 Mathematics Paper 2 Answer all the questions. 1 (a) Solve the inequality 3232 xx −+ . Answer ……………………………………… [2] (b) It is given that WE Wx= + . (i) Find the value of E when W = 30 and x = 18. Answer E = ………………………………… [1] (ii) Express W in terms of E and x. Answer W = ………………………………… [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 4 Mathematics Paper 2 1 (c) Solve the equation 31 512xx =−+− . Give your solutions correct to 2 decimal places. Answer x = ………………… or .…………….…… [5]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 5 Mathematics Paper 2 2 (a) Evane plans to travel to the United States of America (USA) for a holiday. (i) He goes to the travel fair and is given an early bird discount of 15% for a 7-day tour package that costs $2888. Calculate the amount of money he has to pay the travel agent after the addition of 7% Goods and Service Tax (GST) on the discounted price. Answer $ …………………………… [3] (ii) He then goes to the money changer to change S$3800 into US dollars. Calculate the amount of US dollars he receives if the exchange rate was US$1 = S$1.43. Leave your answer to the nearest dollar. Answer US$ ……………………… [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 6 Mathematics Paper 2 2 (a) (iii) In the following month, he cancelled his holiday plans as he contracted COVID. He changed all his US dollars back at the rate US$1 = S$1.38. Calculate the loss as a percentage of the original amount he changed as a result of the new exchange rate. Answer ……………….…….…% [2] (b) The marked price of a laptop is $ 2300. By selling the laptop at a 10% discount, a merchant makes a loss of 5% on its cost price. Find the cost price of the laptop. Answer $ ……………….…….… [3]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 7 Mathematics Paper 2 3 When x copies of a book are produced, the cost, $y, of each copy is given by the formula x y 360010+= . x 100 200 300 400 600 900 1200 y 46 28 22 p 16 14 13 (a) Find the value of p. Answer p = ……………………………… [1] (b) On the grid on page 9, draw the graph of x y 360010+= for 100 1200x . [3] (c) Use your graph to estimate the number of books to be printed if the cost of producing each book is $30. Answer ………..…………………… books [1] (d) (i) By drawing a tangent, find the gradient of the curve when x = 400. Answer ………..……………….……… [2] (ii) Use your answer to (d)(i) to state briefly what the gradient represents. Answer …………………………………………………………………………… …………………………………………………………………………………[1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 8 Mathematics Paper 2 (e) In order to sell x books, the selling price of each book must be $ 32 50 x − . (i) On the same axes on page 9, draw the graph of 32 50 xy=− to represent the selling price of the books. [2] (ii) Using your graphs, find the range of the number of books that should be printed if no loss is to be made, assuming all the books will be sold. Answer ………..……………….……… [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 9 Mathematics Paper 2 Answer (b) 0 400 600 800 1200 200 5 10 15 20 25 30 y ($) 35 40 45 x (no. of books) 1000 50

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2022 10 Mathematics Paper 2 4 The diagram shows a solid consisting of a right circular cone attached to a hemisphere with a common base which is a circle of radius 6 cm. The volume of the cone is equal to twice the volume of the hemisphere. (a) Show that the height of the cone is 24 cm. Answer [2] (b) Find the total surface area of the solid. Answer ………..……………….… cm2 [3]