BDKSS 4N Prelim P1 2023

[Turn Over Name Class Index Number BROADRICK SECONDARY SCHOOL SECONDARY 4 NORMAL (ACADEMIC) PRELIMINARY EXAMINATION 2023 MATHEMATICS SYLLABUS A Paper 1 Candidates answer on the Question Paper 4045/01 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. 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 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 For Examiner’s Use This document consists of 17 printed pages. Setter(s) : Ms Yeo Li Shan 70

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 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 1 [Turn Over Answer all the questions. 1 330.25 0.2 0.0211 • Write these numbers in order of size, starting with the largest. Answer ………….. , ………….. , ………….. , ………….. [2] largest smallest 2 (a) A box contains red and black discs only. 2 7 of the discs are red. Write the ratio red discs : black discs. Answer ….........…… : ……..…….. [1] (b) Express 1.2 litres as a percentage of 150 ml. Answer ….........……………..….. % [2] 3 Find the smallest prime number satisfying 28x− − . Answer ….........……………..…….. [2]

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 4 4 P is inversely proportional to x2. When x = 2.5, P = 20. Find the value of P when x is 5. Answer P = .........…….……..…….. [2] 5 (a) sin 0.7x= Given that x is an obtuse angle, find x. Answer x = ......……………..….….. [1] (b) cos123 cos y=−  Given that y is an acute angle, find y. Answer y = ......……………..….….. [1]

5 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 [Turn Over 6 245ma=− (a) Find m where 5a=− . Answer m = ......…………..….….. [1] (b) Rearrange the formula to make a the subject. Answer a = ......……………..….….. [2] 7 (a) Explain why x = 40°. Answer ......................................................................................................................... ......................................................................................................................... [1] (b) Find y, stating your reasons. Answer y = .…...……...…………... [2] 62° y° 140° x°

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 6 8 The graph shows the number of students who borrowed books from the school library. Kerry claims that the number of students who borrowed books has been decreasing from January to September. The State one feature of the chart that may be misleading and explain why. Answer ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... [2] Number of students 100 80 60 40 20 January February March September

7 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 [Turn Over 9 These triangles are similar. All the lengths are in centimetres. Find the length of PQ. Answer PQ = .…...……...…….. cm [2] 10 Solve x = 2(x + 3). Answer x = …..…………….......….. [2] 130° 2x P Q 130° 1.5x 7.5 cm

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 8 11 $1500 is placed in an account earning compound interest of r% per year. At the end of 5 years, the total amount in the account is $1592.19. Calculate r. Answer r = ......…..……...……….... [3] 12 (a) It is given that 1575 = 223 5 7 . (i) Express 405 as a product of its prime factors. Answer .......…...…………………... [1] (ii) Find the highest common factor of 1575 and 405. Answer .......…...…………………... [1] (b) Q3 is equal to the square of 3625 n , where n is a positive integer. Write Q, in terms of n, as the product of its prime factors. Answer Q = .…...……...…………... [2]

9 Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 [Turn Over 13 Tan spent a total of $3000 for his holiday. He spent: 9 20 on flight tickets and accommodations, and 40% of the remainder on entertainment and transport. The rest of the money was spent on food and shopping. Find the percentage of the money he spent on food and shopping. Answer ......…..……………...….. % [3]

Broadrick Secondary School, Preliminary Examination 2023, Sec Four Normal (Academic), Mathematics Paper 1 10 14 The following table shows the exchange rates of some currencies displayed in a bank against Singapore Dollars (SGD). Code Foreign Currency Unit Selling (SGD) Buying (SGD) CAD Canadian Dollar 1 1.0278 1.0028 JPY Japanese Yen 100 0.9447 0.9297 (a) Kate has 250 CAD. By using the “Buying” rate, calculate the amount in SGD Kate will receive if she exchanges 250 CAD to SGD? Answer ......…………...….….. SGD [2] (b) Lim has 500 SGD. By using the “Selling” rate, calculate the amount in JPY Lim will receive if he exchanges 500 SGD to JPY? Give your answer correct to the nearest Yen.