Bukit View 2023 Prelim 4N Math P1 Marking Scheme

4NA Mathematics Paper 1 Prelim 2023 (Marking Scheme)Answer all the questions.1.List the following numbers in descending order, starting with the largest.1.82 342 3.14342 1.82  3.14 ------ B1 for 2 correct positions------B2 for all correctAnswer ……..….…, …………... , ……...……, ……...….. [2] (largest) (smallest)-------------------------------------------------------------------------------------------------------------------------2.(a) Solve the inequality 438y.438y9.5y ------ B1Answer …….…..……….……… [1](b) Find the smallest integer satisfying 438y. – 9 ------ B1Answer …….…..……….……… [1]-------------------------------------------------------------------------------------------------------------------------3.Factorise 362xypyxqpq completely. 362xypyxqpq= (3)2(3)yxpqxp= (2)(3)yqxp ------ M1 (first line factorisation)------ A1 Answer ………………………… [2]

24.Draw a reduction of the figure using a scale factor of 23.Answer ----------- B2/1/0[2]-------------------------------------------------------------------------------------------------------------------------5.Solve 15)1(3x.15)1(3x 3315x3153x312x4x------ M1 (expand)------ A1 / B115)1(3x1513x15x4x ------ M1 (÷3)------ A1 / B1Answer x = ………..………………. [2] -------------------------------------------------------------------------------------------------------------------------

36.Quadrilaterals ABCD and PQRS are similar.All the lengths are in centimetres.(a)Calculate x. Since figures are similar:668x 8364.5xxcm ------ M1 (O.E)------ A1 / B2Answer x = …..……………………. [2](b)Find y in terms of z.68yz 34zy ------ B1Answer y = ………..………………. [1] -------------------------------------------------------------------------------------------------------------------------7.2, 9, 16, 23, 30, …(a)Write down the next 2 terms in the sequence. 37 , 44 ----- B1 Answer …………..… , …………..… [1](b)Find an algebraic expression for the nth term in the sequence.7n – 5 ----- B2Answer …………..………………..… [2](c)Find the 154th term of this sequence.7(154) – 5 = 1073 ----- B1 Answer …………..………………..… [1] PQRSx6y72°8ABCD68z72°

48.It is given that y is inversely proportional to the square of x. When x = 6, y = 4.Find the value(s) of x when y =100. 2kyx (where k is a constant)246k436k144k 2144yxwhen y =100, 2144100x2144100x21.44x1.44x 1.2x ----- M1 (finding k correctly to inverse proportion)----- M1 (Substituting 100 correctly ‘their’ equation)----- A1Answer x = ….………………………. [3]-------------------------------------------------------------------------------------------------------------------------9.In the diagram, ABC is straight line, angle BAD = 90, AD = 3 cm and BD = 7 cm.(a)Write sin x as a fraction.sin x = sin (180 – x) = 37 ----- B1 Answer ………………………… [1](b)Find y. cos y = 37 13cos7y = 64.6----- M1 (O.E, students may use sin ratio to find other angle first before using angle sum of triangle to find y)----- A1 Answer ………………………… [2] ABCD37xy

510.A solid cylinder has radius 8 cm and height h cm.Given that the total surface area of the cylinder is 650 cm2, calculate h.Total surface area of cylinder = 222rrh 22(8)2(8)h = 650 12816650h 16650128h 65012816h 65012816h = 4.93133 = 4.93 cm (3 sf)----- M1 (correct application of formula)----- M1 (isolating h correctly)----- A1 Answer h = .…….………...…… cm [3]-------------------------------------------------------------------------------------------------------------------------11.Simplify 23525xxx.23525xxx= 35(5)(5)xxxx= )(5)(53(5)(5)(5)xxxxxx= 315(5)(5)xxxx= 415(5)(5)xxx----- M1 (factorization)----- M1 (making single fraction)----- A1 Answer ……………….….……… [3] 8 cmh cm

612. The diagram (not drawn to scale) shows a circle divided into sectors of different colours. Given than 29 of the circle is red, find b. Red = 23609 = 80b = 360 – 80 – 130 – 90 = 60-- M1-- M1-- A1130902536036096 511661360606----- M1----- M1 ----- A1 Answer b = ……………….……… [3]-------------------------------------------------------------------------------------------------------------------------13.The equation of a straight line is 3122yx.Find the coordinates of the point where the line cuts the y–axis.3122yxLet x = 0, 3120y 4y (0 , 4)----- M1 (accept rearranging to make y the subject to find c )----- A1 / B2Answer ( ………… , ….….….. ) [2] BlueOrangeGreenRed130b

714.Jenny travelled from Singapore to Thailand. She exchanged 800 dollars ($) into Thai Baht (THB) when the exchange rate is $1 = 25 THB. While in Thailand, she spent 10 800 THB. On her return, she exchanged the remaining Thai Baht into dollars when the exchange rate was $1 = 24 THB. How many dollars ($) did she receive? Leave your answer correct to the nearest dollar.$1 = 25 THB$800  800 × 25 = 20 000 THBBalance = 20 000 – 10 800 = 9200 THB$1 = 24 THB 9200 THB  920024 = $383.33 = $383 (nearest dollar)----- M1 ----- M1 (using their balance)----- A1 Answer $ …………….….……… [3]-------------------------------------------------------------------------------------------------------------------------15.(a)Which one of the following is a possible equation for the graph?y = 4x  16 y = x(4  x) y = x(x  4)y = x2y = x(x  4) ----- B1Answer ……………….….……… [1](b)Write down the equation of line of symmetry.042x 2x----- B1 Oyx4

8Answer ……………….….……… [1]16.(a)Rearrange this equation to make a the subject of the formula. 23dca23dca 32acd32adc23dca----- M1 ----- A1 Answer a = ………...….….……… [2](b) Hence or otherwise, find the value of a if 5c and 8d.2(8)(5)3a = 7----- M1 ----- A1 Answer a = ………...….….……… [2]-------------------------------------------------------------------------------------------------------------------------

917.The diagram below shows a trapezium, where AB = BC = CD, BC is parallel to AD and angle ABC = 150. (a)Find angle ACD.angle BCA = 1801502 (base angle isosceles triangle) = 15angle ACD = 150 – 15 = 135 ----- M1 ----- A1 Answer ….……………………… [2](b)Explain why AC bisects angle BAD. Show working and/or reasons clearly.Answerangle CAD = 15 (alternate angles) = 15angle BAC = 15 (base angle isosceles triangle)Since angle CAD = angle BAC, AC bisects angle BAD,----- M1 (with reason)----- M1 (with reason)(give 1m for 15 if both reasons not given)----- A1 (conclusion) [3]------------------------------------------------------------------------------------------------------------------------- ABCD 150

1018.The diagram below shows the layout of a garden. (a)Measure angle QRS. 77 ----- B1(+/- 1)Answer angle QRS = ………….……… [1](b)Construct the angle bisector of angle RQP. ----- B1[1](c)Construct the perpendicular bisector of PS. ----- B1[1]-------------------------------------------------------------------------------------------------------------------------