TPS 4NA Prelim P2 2023 MS

This document consists of 7 printed pages TAMPINES SECONDARY SCHOOL Secondary Four Normal Academic PRELIMINARY EXAMINATION 2023 NAME MARKING SCHEME CLASS REGISTER NUMBER MATHEMATICS SYLLABUS A 4045/02 Paper 2 7 August 2023 2 hours Candidates answer on Question Paper. 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 number of 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. [Turn over NA

2 Section A (62 marks) Answer all the questions in this section. 1a 245.5 0.5391 5.49 200 0.5 5 100 5 20  = = = M1 A1 – no mark if no/wrong working b 0.000015 = 51.5 10 − B1 ci 65.45 10 B1 cii 8 6 7.3 10 5.45 10   = 133.945 = 134 m2/person B1 – no ecf. Accept 21.34 10 2a 125 1262 125 252 127 x x x + = += = p = 7 M1 A1. Don’t accept 127 b 142 – 117 = 25 cm B1 c 25 12 3100= 3 students has height less than x cm x = 125 M1 A1 3a 3.2 cm : 8 km 1 cm : 2.5 km 1 : 250 000 M1 A1 b 1 cm2 : 6.25 km2 OR 10.24 cm2 : 64 km2 Area on the map = 30 6.25 OR 30 10.2464 = 4.8 cm2 M1 for squaring both sides A1

3 4ai Angle BAE = ( )5 2 180 5 −   = 108o M1 for ( )5 2 180−   A1 ii Angle DCE = 180 108 2 −  = 36o B1 iii Angle BEC = 108 – 36 – 36 = 36o OR Angle BEC = angle ECD = 36o (alt angles) B1 b 3 12 4 21 167 8 176 22 x x x x x + + − = − = = OR Angle ACB = 180 (3 12) (4 21) 180 (167 ) 180 3 12 4 21 13 189 7 13 176 8 22 x x x x x x x x x x x − + − − = − − − − − + = + − = + = = M1 A1

4 5a 2 2 2 2 200 210 84100 290 m QS QS QS =+ = = M1 A1 b 200tan 210 43.6 SQR SQR =  =  M1 A1 6a Area of segment = ( ) ( ) ( )( ) ( ) 2115 2.15 5 5 sin 2.1522 − = 26.875 – 10.461235 = 16.4 cm2 M2 – accepts A1 b Area of circle = ( ) 2 5 = 78.54 cm2 ()% 100%78.54 20.9% a= = M1 M1 ecf – allows using rounded of 16.4 A1 no ecf 7ai 2p + 1 B1 ii 2 1 2 1 4 pp p − + + = B1 ecf iii 4p is a multiple of two OR 4p can be divided by 2. Hence, even. B1 b 2 2 2 6 5 0 6 6 4(2)( 5) 2(2) 6 76 4 3.68 or 0.68 xx x + − = −  − −= −= =− M2 (M1 for 26 4(2)( 5)−− ) A1 c 4 3 4 (1) 2 5 11 (2) 4 10 22 (3) (1) (3) 13 26 2 1 2 xy xy xy y y x + = −−− − =− −− − =− − − = = =− M1 – showing any suitable substitution or elimination method A2

5 8 a x –1 0 1 2 3 4 5 6 y 2 B1 9 4 –7 –18 –23 –16 B1 9 10 5 0 –5 –10 –15 –20 –25 –1 1 2 3 4 5 6

6 b 5 to 6 points plotted correctly 7 or more points plotted correctly Correct shape and turning points Smooth curve, no multiple line, no crooked lines and curve cuts through all marked points B1 ecf B1 ecf B1 c –5.25 1.5 B1 – tangent B1 – Gradient. Accept students’ answers if curve, tangent, formula are accurate. d (4, –23) B1 – no range, exact answer e Accepts any k = 2 to 10, including decimals B1 9a 62.5% - $881 100% - 100 88162.5 = $1409.60 M1 A1 b 2-year plan 881 130.12 24 $4003.88 SIM only 1-year plan 2253 45.42 24 $3343.08 + = + = Disagree. Sim-only plan is cheaper and have more voice call time and SMS workings (must be for 24 months) M1 M1 A1 – Disagree as Sim only cheaper c Excess charge 22 $10.80 $237.60 Total monthly subscription 130.21 237.60 $367.81 = =+ = M1 A1 d Percentage decrease M1

7 130.21 115 100%130.21 11.7% −= = A1 10a E = kT 2 ( ) 2 2 320 4 320 16 20 20 k k ET = = = = M1 or find k = 20 A1 b ( ) 2 2 20 20 10 2000 ET E = = = B1 – ecf c 2 2 2 2 20 180 20 180 20 9 3 ET T T T T = = = = = M1 – ecf A1 – ecf

8 Section B (8 marks) 11a Angle AOC = 124o  at centre = 2  s at circumf Angle ADC = 118o  s in opp seg OR angles at a point +  at centre = 2  s at circumf Angle BAO = 28o Tan perp rad + alt angle B1 B1 B1 for either tan perp rad or alt angle bi Angle CAB = 74 – 46 = 28o 2 2 2 60 90 2(60)(90)cos 28BC = + −  2 2164.166 46.5 km BC BC = = M1 M1 – ecf A1 ii Angle ACB = 180 – 46 = 134o Bearing of A from C = 360 – 134 = 226o M1 A1

9 12ai 5 3 6,,14 14 14 B1 ii 5 6 6 5 15 14 15 14 2 7     +        = M1 A1 bi 28.5 mins B1 – do not accept whole numbers ii 34.5 – 21 = 13.5 mins B1 – do not accept whole numbers iii 120 – 28 = 92 customers waited less than p min p = 35 mins B1 ci 40.4 mins B1 ii 5.92 B1 --- End of Paper ---