Kranji 4048 02 QP

Name: ___________________________ ( ) Class: ______ KRANJI SECONDARY SCHOOL Preliminary Examination Secondary 4 Express / 5 Normal Academic MATHEMATICS 4048/02 Paper 2 Friday 26 August 2022 2 hours 30 mins KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI SECONDARY KRANJI READ THESE INSTRUCTIONS FIRST: Do not open this question paper until you are told to do so. 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 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 your 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 number of marks for this paper is 100. Setter: Ms Madeleine Chew This question paper consists of 30 printed pages, including the cover page. [Turn over Question Marks 1 2 3 4 5 6 7 8 9 10 11 Total 4E5N Session 1

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = r , where  is in radians Sector area = , where  is in radians Trigonometry Statistics Mean = Standard deviation = n rP      + 1001 hr 2 3 1 3 3 4 r Cabsin2 1 2 2 1 r C c B b A a sinsinsin == Abccba cos2222 −+=   f fx 22       −     f fx f fx

3 Answer all the questions. 1 (a) Brandon plans to invest $5000 in a bank. The bank pays 4% per annum interest compounded monthly. Calculate the total amount at the end of 3 years, correcting your answer to the nearest dollar. Answer $ ……..………………………… [1] (b) In 2021, Alice was paid a basic salary of $82 500, which is an increase of 7% from her basic salary in 2020. Calculate her basic salary in 2020, correcting your answer to the nearest cent. Answer $ ……..………………………… [2] (c) Rearrange the formula 7mb = 3b + 2m to make b the subject. Answer b =……..………………………… [2]

4 (d) Using factorisation, solve the equation 221 2 11xx=− . Answer x = ……..……… or ……………… [2] 2 Nurul bought some jars of cookies for $500. She paid $n for each jar of cookies. (a) Write down an expression, in terms of n, for the number of jars of cookies she bought. Answer ………..………………………… [1] Nurul found that 2 jars of cookies were spoilt and could not be sold. Nurul sold each remaining jar of cookies for $3 more than she paid for it. (b) Write down an expression, in terms of n, for the total sum of money she received from the sale of the jars of cookies. Answer ………..………………………… [1] (c) Given that she made a profit of $92 from the sale of the jars of cookies, form an equation in n and show that it reduces to 2 49 750 0nn+−= . Answer [3]

5 (d) Solve 2 49 750 0,nn+−= giving your solutions correct to 3 decimal places. Answer n = …………….……… or …………….……… [3] (e) Explain why one of the solutions in part (d) need to be rejected. Answer ………..………………………………………………………..……… …………………………………………………………………………………. [2] (f) Hence, find the selling price of each jar of cookies sold by Nurul, giving your solution correct to the nearest dollar. Answer $……..………………………… [2]

6 3 The tickets for a musical is divided into 4 categories. Table 1 shows the price of a ticket for each category. Table 1 Category 1 Category 2 Category 3 Category 4 $218 $138 $66 $40 Table 2 shows the number of tickets sold for the afternoon and evening show on a particular Saturday. Table 2 Category 1 Category 2 Category 3 Category 4 Afternoon Show 35 120 75 16 Evening Show 60 93 112 27 (a) Represent the information in Table 1 by a column matrix P. Answer P = ( ) [1] (b) There was an early bird discount in the first week of ticket sale: • 25% for Category 1 and Category 2 • 15% for Categories 3 and Category 4 By multiplying matrix P with a suitable matrix, find the matrix whose elements represent the cost of each category of ticket during the first week of ticket sale. Answer ( ) [2]

7 (c) Represent the information in Table 2 by a 2 ´ 4 matrix T. Answer T = ( ) [1] (d) Evaluate the matrix S = TP. Answer S = ( ) [2] (e) Explain what each element in matrix S represent. Answer ………..………………………………………………………..……… …………………………………………………………………………………. …………………………………………………………………………………. [1]

8 4 In the diagram, the points A, B, C and D lie on a circle, centre O. It is given that angle BAD = 62° and OC bisects angle BCD. (a) Find, giving reasons for each answer, (i) angle BCD, Answer ………..………………………… [1] (ii) angle BOC, Answer ………..………………………… [2] A 62° D C O B

9 (b) Given that the radius of the circle is 6 cm, find the shaded area. Answer ………..…………………… cm2 [3]

10 5 A shopping basket can be modelled by a frustum of an inverted pyramid as shown below. The solid frustum is obtained by removing the top portion of an inverted right rectangular pyramid. The flat rectangular base of the frustum has length 40 cm and width 25 cm. The remaining vertical height is 27 cm. The flat rectangular top of the frustum is 48 cm by 30 cm. (a) Calculate the exact total surface area of the solid frustum. Answer ………..………………….. cm2 [3] 27 48 30 40 25