BDKSS 4N Prelim P2 2023

[Turn Over Name Class Index Number BROADRICK SECONDARY SCHOOL SECONDARY 4 NORMAL (ACADEMIC) PRELIMINARY EXAMINATION 2023 MATHEMATICS Paper 2 Candidates answer on the Question Paper. 4045/02 August 2023 2 hours READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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. Write the question number attempted in the left column in the box provided. Section A Section B Answer all the questions. Answer one question. 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 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 the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142. For Examiner’s Use Error in Question Number Marks Deducted Rounding-off Reasoning Presentation This document consists of 19 printed pages. Setter(s) : Ms Yeo Li Shan For Candidate’s Use For Examiner’s Use Question Number Marks Obtained 1 2 3 4 5 6 7 8 9 10 11 or 12 Total Marks / 70

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved Surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = ab2 1 sin C Arc length = rθ, where θ is in radians Sector area = 2 2 1 r , where θ is in radians Trigonometry C c B b A a sinsinsin == Abccba cos2222 −+= Statistics f fxMean  = Standard deviation = 22        −  f fx f fx

3 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 [Turn Over Section A (62 marks) Answer all the questions in this section. 1 (a) Work out 25.2 ( 2) 3− −  . Answer …..….........…..…………… [1] (b) Write 87.1 million in standard form. Answer …..….........…..…………… [1] (c) Write 0.054321 correct to 3 significant figures. Answer …..….........…..…………… [1] (d) Express 4 1 3 36 xx−+− as a single fraction. Answer …..….........…..…………… [2]

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 4 2 (a) 549 7 7n= Find the value of n. Answer n = ….........……………… [2] (b) Simplify 1 3 3 8 x −   . Answer ……….........……………… [2] 3 In the diagram below, angle PQR = 90°. QRT is a straight line. (a) Expressing your answers as a fraction in the simplest form, find (i) cos QPR , Answer ….........…………………… [1] (ii) sin PRT . Answer ….........…………………… [1] (b) Find the area of triangle PRT. Answer ….........………...…….. cm2 [1] P Q R T 8 cm 6 cm 10 cm 3 cm

5 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 [Turn Over 4 An advertisement on the sale of a particular type of Headphones is shown below. (a) Calculate the percentage discount of the Headphones during the sale. Answer .........……………..…….. % [2] (b) Mr Kay intends to buy the Headphones on hire-purchase during the sale. He pays a deposit of 10% of the discounted price and then 12 monthly instalments at 5% simple interest per annum. Calculate the extra amount he pays as a percentage of the discounted price. Answer ..….......……………..….. % [3] Sale $504.00 NOW $399.00

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 6 5 (a) Factorise (i) 225 1x − , Answer ….........……………..…….. [1] (ii) 4 10 6 15ax x ay y− + − . Answer ….........……………..…….. [2] (b) Solve 11 113xx +=+− . Answer x = ….........………...……… [4]

7 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 [Turn Over 6 (a) Determine if triangle XYZ is a right-angled triangle. Answer [2] (b) Calculate angle XZY. Answer ….........………..…...……..° [3] X Y Z 4.5 2 5.2

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 8 7 (a) Complete the table of values for 82yx x=+ . x 0.5 1 2 3 4 5 6 7 y 17 10 8 8.7 11.6 13.3 [2] (b) Draw the graph of 82yx x=+ for 0.5 7 x . [3] 0 1 2 3 4 5 6 7 18 16 14 12 10 8 6 4 2 0 x y

9 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 [Turn Over (c) Using your graph, solve the equation 82 11x x+= . Answer x = ……….. or x = ………… [2] (d) By drawing a suitable tangent, find the gradient of the graph when 1x= . Answer .....………………………… [2]

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 2 10 8 A paper weight is made by removing a hemisphere with diameter 10 cm from the bottom of a solid wooden cylinder with base diameter 10 cm and vertical height 8 cm. (a) For the paper weight, calculate its (i) volume, Answer ….........………………. cm3 [2] (ii) total surface area. Answer ….........………...…….. cm2 [3] 10 cm 8 cm