[Presbyterian High] [2023] 4E EM 4052 Prelims P2_MS

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 MARKING SCHEME For Examiner’s Use Qn 1 2 3 4 5 6 7 8 9 10 Marks Deducted Marks Category Accuracy Symbols Others Question No. Setter: Mr Tan Lip Sing Vetter: Mdm Cynthia Chua TOTAL MARKS 90

2 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 1 (a) Rearrange the formula 2 2 5 3 dc d += − to make d the subject. Answer d =…….…………………. [3] 2 2 22 22 22 2 2 5 3 ( 3) 5 35 53 ( 1) 5 3 53 1 35 1 dc d cd d cd c d cd d c dc c cd c cd c += − −= + −=+ −= + −=+ += − +=± − M1 M1 A1 (b) Write as a single fraction in its simplest form 2 31 2( 2) xx − −− . Answer ……………………………. [2] ( ) ( ) 2 2 2 2 31 2( 2) 31 2( 2) 32 2 1 2 xx xx x x x x − −− = + −− +−= − += − M1 A1

4 (c) Solve these simultaneous equations. 5 3 14 3 5 18 xy xy += += You must show your working. Answer x=……………………. or y=…………………. [3] ( ) 5 3 14 ......(1) 3 5 18 ......(2) 14 5(1): ......( 3)3 Substitute (3) into 2 : 14 53 5 18 3 9 70 25 54 1 3 xy xy xy xx xx x y += += −= −+= +− = = = M1 A1 A1 (d) Solve the equation 21 1 56 23 x xx − =−− . Answer x=……………………. or x=…………………. [3] 2 2 21 1 56 23 (2 1)(2 3) 5 6 4 6 2 35 6 4 13 9 0 (4 9)( 1) 0 1214 x xx xx x x xx x xx xx x or x − =−− − −=− − − += − − += − −= = = M1 M1 (Factorise) A1

5 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 n