2023 Beatty Sec 4NA Math P2 QP

[Turn over BEATTY SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY FOUR NORMAL (ACADEMIC) CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS (SYLLABUS A) 4045/02 Paper 2 4 August 2023 Setter: Mr Lawrence Koh 2 hours Candidates answer on the Question Paper Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your name, class and register 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. Section A Answer all questions. Section B 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 60. 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 This document consists of 15 printed pages and 0 blank pages.

2 Mathematical Formulae Compound interest Total amount = nrP )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 = Cabsin2 1 Arc length = r , 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 Mean = f fx   Standard Deviation = 22          f fx f fx

[Turn over 1 When written as a product of its prime numbers, 3 2504 2 3 7   . (a) Write 540 as a product of its prime numbers. Answer ……………………… [1] (b) Hence, find the greatest integer that will divide both 504 and 540 exactly. Answer ……………………… [1] 2 A bank pays investors 3.2% per annum compound interest, compounded half-yearly. Ahmad invested $10 000 for a period of 3 years. Calculate the interest earned after 3 years. Leave your answer correct to the nearest dollar. Answer $…………...… ……. . [3]

4 3 In the diagram, PQR is similar to STR . Find (a) angle RST , Answer ……………………… [1] (b) the length of ST. Answer ST = ………… ..... cm [2] 4 Four tennis balls are packed tightly in a cylindrical tube. The radius of a tennis ball is r cm. Show that the empty space in the tube is one third of the total volume of the tube. Answer [3] 60º 48º 7.3 10 8 P Q T S R

5 [Turn over 5 (a) Solve 22 4 7 0x x   using the quadratic formula. Answer x… … … ..... or …… ..…. [3] (b) Solve these simultaneous equations. 4 6 2 3 0 x y x y      Answer x = …………...… …. ….. y = …………...… … …... [3]

6 6 The points A, B, C and D lie on the circumference of a circle centre O. AOD is the diameter of the circle. 30BAC   and 68CDA   . (a) Explain why angle ACD is 90°. Answer ………………………………………………………………………….……… ……………………………………………………………………………......………… [1] (b) Find (i) angle ABC, Answer ……………………… [1] (ii) angle OBA. Answer ……………………… [2] 68º 30º B DO A C

7 [Turn over 7 In the right-angled triangle ABD, 8 cm and 12 cm.AB AD  C lies on BD, such that 1 rad.ACB  Find (a) ADB in radians, Answer ……………………… [2] (b) the length of BC, Answer ………...… … …... cm [2] (c) the area of triangle ACD. Answer ……… … ...……... cm2 [3] 1 rad 812 D B A C

8 8 (a) Expand and simplify     2 3 2a b b a b   . Answer ………………… ….. …… [3] (b) Factorise the following expressions. (i) 412 3 x Answer ……………… ….. ……… [2] (ii) 4 10 6 15y yz z   Answer ………………… ….. …… [2]

9 [Turn over 9 (a) Complete the table of values for 2 12 69 xy x   . Give your answers correct to one decimal place. x 1 1.5 2 2.5 3 5 7 9 y 6.1 2.3 0.4 -0.5 -1 -0.8 4.3 [1] (b) Draw the graph of 2 12 69 xy x   for 1 ≤ݔ≤ 9. [3] (c) Write down the coordinates of the minimum point of the curve. Answer (… …... … … , … … ...…… ) [1] (d) By drawing a suitable tangent, find the gradient of the curve when 7x . Answer … …….. ……...…… …… ... [2] (e) Use your graph to solve the equation 2 12 79 x x  . Answer x………..... or ……..…. [2]

10 10 The table below shows the walking speed of people across different age groups. https://www.medicalnewstoday.com/articles/average-walking-speed#average-speed-by-age (a) Find the walking speed of secondary school going students. Answer ……………….… m/s [2] As part of BT70 celebrations, staff and students formed a mass display of the school celebratory logo in the school field. Mr Lee assigned specific groups to form part the logo. The scale drawing of the logo is 1 cm : 20 m. (b) Estimate the actual distance, in metres, of the logo formed by the Secondary 4 and 5 students. Answer …………...……... m [2]