2024 ACSI Prelim P2

90 Anglo-Chinese School (Independent) PRELIMINARY EXAMINATION 2024 YEAR FOUR EXPRESS MATHEMATICS PAPER 2 4052/02 Wednesday 7 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces on top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all 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 90. 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. This document consists of 19 printed pages and 1 blank page. [Turn over INDEX NUMBER CANDIDATE NAME CLASS

2 ACS(Independent)MathDept/EM2/y4/2024/Prelim Mathematical Formulae Compound Interest Total amount = ( )1 100 nrP + Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 2r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of a triangle = 2 1 absin C Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sin sin sin == a 2 = b 2 + c 2 – 2bc cos A Statistics Mean = fx f   Standard deviation = 22         −     f fx f fx

3 ACS(Independent)MathDept/EM2/y4/2024/Prelim [Turn Over Answer all the questions. 1 (a) Solve the equation 2( 5) 3 1.xx− = − Answer x = ……….………...………. [2] (b) Solve the inequality 7 4 3( 2).yy−  + Answer …….…….…………..……… [2] (c) Given that 1 1 1 23p q r−= , (i) find p when 1q=− and 2,r Answer p = ……….………...……… [2] (ii) rearrange the formula to make q the subject. Answer q = ……….………...……… [3]

4 ACS(Independent)MathDept/EM2/y4/2024/Prelim (d) Solve the equation 53 32 2 1 x xx −=+− . Give your solutions correct to 2 decimal places. Answer x = ……...…. or ……...……. [5] 2 (a) A manufacturing company produces electronic components for various devices. They are analyzing the production data for the past 3 months, which includes quantities of components produced and the corresponding costs. The data is presented in the table below: Month Quantity Produced (in units) Cost per unit (in dollars) May 55.8 10 0.0211 June 64.3 10 0.0183 July 57.6 10 0.0203 (i) Express the total quantity produced from May to July in standard form correct to 3 significant figures. Answer …….…….…………..……… [1]

5 ACS(Independent)MathDept/EM2/y4/2024/Prelim [Turn Over (ii) Calculate the average cost per unit for these 3 months. Express your answer in cents. Answer …….…….…………… cents [2] (iii) Given that the percentage increase in the quantity produced from July to August is 11.8%, calculate the quantity produced in August. Leave your answer in standard form correct to 3 significant figures. Answer ……..….………..…..… units [2] (b) The company wants to build a prototype of a particular electr onic component they are manufacturing. The radius of the actual electronic component is 53.8 10 − m. In a scale drawing, the radius of the prototype of the electronic component is 1.9 cm. (i) Find the scale used for the drawing. Give your answer in the form n : 1. Answer …….…….…………….. : 1 [2] (ii) Given that the prototype has a total surface area of 81.81 10 − m2, find, in cm2, the actual total surface area of the electronic component. Give your answer in standard form. Answer .…………..……..………. cm2 [2]

6 ACS(Independent)MathDept/EM2/y4/2024/Prelim 3 In Diagram I below, ABCDE is a regular pentagon, centre O. OA = OB = 4 cm. (a) State the value of angle AOB. Answer Angle AOB = ..……….…… ° [1] (b) Calculate the area of the pentagon ABCDE. Answer .…………..……..………. cm2 [2] (c) Diagram II shows a design for a new badge. The vertices of the regular pentagon ABCDE are joined by circular arcs whose centres are the opposite vertices. For example, the arc AB has centre D and radius AD. (i) Find angle ABD. Give reasons for each step of your working. Answer Angle ABD = ..……….…… ° [2] A B C D E O A B C D E O Diagram I Diagram II O •

7 ACS(Independent)MathDept/EM2/y4/2024/Prelim [Turn Over (ii) Show that the length of BD is approximately 7.61 cm. Answer [2] (iii) Calculate the area of the shaded segment in Diagram II. Answer .…………..……..………. cm2 [3] (iv) Calculate the area of the face ABCDE of the badge. Answer .…………..……..………. cm2 [2]

8 ACS(Independent)MathDept/EM2/y4/2024/Prelim 4 Here are the first four terms of a sequence. 5 10 172 3 5 7 (a) Find the fifth term of the sequence. Answer ..….…….….………..……….. [1] (b) nT is the nth term of the sequence. Find an expression, in terms of n, for nT . Answer nT = ....…….………….……… [2] (c) Find the value of 25 24 .TT− Answer 25 24TT−= ....…….……….…… [1] 5 The diagram shows a solid ornament in the shape of a cylinder with an upright cone cut out at one end and a hemisphere attached to the other end. The vertical heights of the cone and cylinder are x cm and 2x cm respectively. (a) Find the ratio of the volume of the cone to that of the cylinder, expressing your answer as a fraction in the simplest form. Answer ..….…….…………..……… [1] x cm 2x cm

9 ACS(Independent)MathDept/EM2/y4/2024/Prelim [Turn Over (b) If the volume of the cylinder is 345 cm3 and its height is 8 cm, calculate (i) the radius of the cylinder, Answer …………….…....……… cm [2] (ii) the curved surface area of the cone, Answer .…………..……..………. cm2 [3] (iii) the quantity of paint needed to paint the exterior of the ornament with a 0.2 mm thick coat of paint. Answer .…………..……..………. cm3 [3]

10 ACS(Independent)MathDept/EM2/y4/2024/Prelim 6 In the diagram, OABC is a parallelogram and D is the midpoint of BC. BE and OC produced intersect at point F. It is given that BE : BF = 1 : 3, OC : OF = 1 : 2, OA = a and .OC= c (a) Express and simplify the following vectors in terms of a and c, (i) ,BF Answer BF =….…….……………… [1] (ii) ,AE Answer AE =….…….……………… [2] E B A F C O D c a