[Presbyterian High] [2023] 4E EM 4052 Prelims P2 QP

Name: Register Number: Class: PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4052/02 PAPER 2 16 August 2023 Wednesday 2 hours 15 minutes PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL PRESBYTERIAN HIGH SCHOOL 2023 SECONDARY FOUR EXPRESS PRELIMINARY EXAMINATION DO NOT OPEN THIS QUESTION PAPER UNTIL YOU ARE TOLD TO DO SO. INSTRUCTIONS TO CANDIDATES: Write your name, index number and class on the spaces provided abov e. 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. 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 answers in degrees to one decimal place. For π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. Note that all the diagrams in this paper are not drawn to scale. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. For Examiner’s Use Qn 1 2 3 4 5 6 7 8 9 Marks Deducted Marks Setter: Mr Tan Lip Sing Vetter: Mrs Joyce Yeo This pap er consists of 25 printed pages (including this cover page) and 1 blank page. Category Accuracy Notations Others Question TOTAL MARKS 90

2 Presbyterian High School 4052/02/4E Prelim/2023 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = C absin2 1 Arc length = θr , where θ is in radians Sector area = θ2 2 1 r , where θ is in radians Trigonometry C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Statistics Mean = ∑ ∑ f fx Standard deviation = 22      − ∑ ∑ ∑ ∑ f fx f fx

3 Presbyterian High School 4052/02/4E Prelim/2023 TURN OVER FOR QUESTION 1

4 Presbyterian High School 4052/02/4E Prelim/2023 1 (a) Rearrange the formula 2 2 5 3 dc d += − to make d the subject. Answer d =…….…………………. [3] (b) Write as a single fraction in its simplest form 2 31 2( 2) xx − −− . Answer ……………………………. [2]

5 Presbyterian High School 4052/02/4E Prelim/2023 (c) Solve these simultaneous equations. 5 3 14 3 5 18 xy xy += += You must show your working. Answer x=……………………. y=……………………. [3] (d) Solve the equation 21 1 56 23 x xx − =−− . Answer x=……………………. or ..…………………. [3]

6 Presbyterian High School 4052/02/4E Prelim/2023 2 (a) Before departing London for Singapore, Peter bought 3000 Singapore dollars from the bank. The exchange rate between British pounds (£) and Singapore dollars ($) was £1= $1.71. He also had to pay the bank an additional commission fee of 1.5% for the exchange of currency. Calculate the total amount of pounds, inclusive of commission, he paid the bank. Give your answer correct to the nearest pound. Answer £ …….…………………. [2] (b) Peter bought a laptop while he was in Singapore. He paid $6 64.20 inclusive of the 8% GST (Goods & Services Tax) for the laptop after getting a discount of A% on the original price. The laptop’s original price is $750 before GST. (i) Find the GST amount paid for the laptop. Answer $ ……………………………. [2] (ii) Calculate the value of A. Answer A = ……………………… [2]

7 Presbyterian High School 4052/02/4E Prelim/2023 (c) Mary invests $20 000 in a n endowment plan that offers 4% per year compound interest. H ow much interest will she receive after 10 years? Give your answer correct to the nearest cent. Answer $ …………………………. [2] (d) A map of a province has a scale of 1 : 500 000. (i) The length of an expressway on the map is 25 cm. Calculate the actual length, in kilometres, of the expressway. Answer ……………………… km [1] (ii) The area of a reservoir is 180 km2. Calculate the area, in square centimetres, of the reservoir on the map. Answer ……………………… cm 2 [2]

8 Presbyterian High School 4052/02/4E Prelim/2023 y x 0 9 5 1 2 3 4 5 6 7 8 1 2 3 4 Question 3

9 Presbyterian High School 4052/02/4E Prelim/2023 3 The variables x and y are connected by the equation 2 4 5 xy x= + . The table below shows some corresponding values of x and y, correct to 2 decimal places. x 0.5 1 1.5 2 2.5 3 4 5 y 8.05 4.20 3.12 2.80 2.85 3.13 4.20 5.80 (a) On the grid provided, draw the graph of 2 4 5 xy x= + for 0.5 5 x≤≤ . Plot the points given in the table and join them with a smooth curve. [3] (b) By drawing a tangent, find the gradient of the curve at 3x= . Answer ……………………………. [2] (c) (i) On the same grid, draw the line 17 2yx= − for 05 x≤≤ . [1] (ii) Write down the x-coordinates of the points where this line intersects the curve. Answer x=……………………. or ……………………. [2]

10 Presbyterian High School 4052/02/4E Prelim/2023 (iii) Find the equation, in the form 3220x ax bx c+ + += , which is satisfied by the values of x found in (c)(ii). Answer …………………………………. [2] (d) Use your graph to find the values of x in the range 05 x≤≤ for which 2 40.2 2 3x x+−= . Answer x=……………………. or ……………………. [2]