AISS Prelim EMath Paper 1 Marking Scheme

3 AISS PRELIM/4052/01/2025 [Turn over Answer all the questions. 1 Expand and simplify 225 3 5pqpqr . 32 26 2 10 15 5 25pp qp rp q q q r Answer ...…………….……………. [2] 2 Lee has two pieces of string. Their lengths are in the ratio 5 : 3 and the total length of the two pieces of string is 8 x cm. Lee cuts 6 cm from each piece of string. The ratio of their lengths is now 9 : 5. Find the value of x. the first piece of string be 5x cm. The first piece of string is 5x cm. The second piece of string is 3x cm. 56 9 36 5 25 30 27 54 24 2 12 x x xx x x Answer x =…………….…………… [3] 3 A salesperson earns a fixed weekly salary of $1000 plus 8% commission on the total value of items he sells. (a) In one week, he sold items worth $1750. Calculate the total amount the salesperson earned that week. Total amount = $1000 + 8 1750100u = $1140 Answer $...…………….…………… [1] B1 B2 if all terms are correct B1 if at least 3 terms are right M1 for setting up the right equation M1 for manipulation of algebraic terms A1

4 AISS PRELIM/4052/01/2025 (b) The following week, the salesperson earned a total of $1450. Calculate the total value of items he sold that week. Commission = $1450 $1000 = $450 8% represents $450 100% represents $ 450 1008 u = $5625 4 The box-and-whisker-plot gives information about the time, in hours, that 120 adults spent on social media in one week. (a) State the median time. 15.5 hours Answer ………………………..hours [1] (b) State the range. Range = 31.5 6.5 = 25 Answer ………………………. hours [1] (c) There was an error in the collection of data. Every adult spent 2 hours less on social media in one week. Describe the effect this change would have on the box-and-whisker plot. The whole box-and-whisker plot will move to the left by 4 square units. M1 for recognising that 8% rep $450 B1 B1 all key words must be present A1 B1

5 AISS PRELIM/4052/01/2025 [Turn over 5 6 Sketch the graph of 83yx x on the axes below. Indicate clearly the values where the graph crosses the x- and y- axes. [3] Express as a single fraction in its simplest form 45 32 3 yy . 45 32 3 4 1 21 51 0 32 3 14 3 32 3 yy yy yy y yy

Answer ...…………….…………… [2] M1 for combining to a single fraction A1 B1 correct shape and y-intercept B1 correct turning point B1 correct x-intercepts Coor of turning point (2.5, 30.25)

6 AISS PRELIM/4052/01/2025 7 (a) A map has a scale of 1 : 2 500 000. The distance between Singapore and Phuket is 1314 km. Calculate the distance, in centimetres, between Singapore and Phuket on the map. 25 km represents 1 cm 1314km represents 52.56cm Answer .....…………….………...cm [2] (b) When a ball is dropped, the distance, d metres, it falls is directly proportional to h square of the time, t seconds, from when the ball is released. The distance from which the ball is dropped is increased by 44%. Calculate the percentage change in the time taken for the ball to reach the ground. d t2 1.44 d (1.2t)2=1.44 t2 1.2Percentage change = 100% = 20% tt t u Answer .....………………………% [2] 8 Simplify 2 2 9 39 x xx

Answer ...…………….……………. [3] A1, exact answer only M1 for correctly converting from cm to km M1 for getting 1.22 t2 or 1.2t as t

2 2 9 39 33 33 3 3 x xx xx xx x x

B2, factorising numerator and denominator correctly A1 A1

7 AISS PRELIM/4052/01/2025 [Turn over 9 Factorise 22 2 263 2xy x y xy x y .

22 2 263 2 61 3 2 63 1 2 32 1 2 1 31 21 xy x y xy x y xy xy x y xy xy x y xy x y y xy x y ªº¬¼ Answer ….….……………………... [3]] 10 Five positive integers have a mean of 6, a median of 7 and a mode of 10. Find the five numbers. 1, 2, 7, 10,10 Answer ………., ………., ………., ………., ……….[ 2] 11 Calculate the perimeter of the shaded area. All lengths are in centimetres. Perimeter of shaded area = 1.7 24 1.7 90uu +2(66) = 325.8 cm ….….…………………... cm [2] M1 for setting up the equation correctly A1, exact so do not accept 3 s.f ans M1 for extracting common term M1 for factorising by grouping A1 B2 for getting all the numbers correct right B1 if for getting 7, 10, 10

8 AISS PRELIM/4052/01/2025 12 (a) Calculate the distance YZ. sin 35 20 20sin 35 = 11.472 cm = 11. 5 cm (3 s.f.) YZ YZ q q Answer YZ = ……………………cm [2] (b) Calculate the area of triangle XYZ. cos35 20 20cos35 = 16.383 cm = 16. 4 cm (3 s.f.) XY XY q q Area of triangle XYZ = = 94.0 cm2 Alternative solution 2 55 1Area of triangle = 20 11.472 sin 552 = 94.0 cm XZY‘ q uq Answer ………………………... 2cm [2] M1 for setting up the correct equation A1 M1 for finding XY A1 M1 for finding angle XZY A1

9 AISS PRELIM/4052/01/2025 [Turn over 13 A group of 200 people estimated the time, t minutes, they spent at an exhibition. The cumulative frequency diagram represents their estimates. (a) Use the diagram to find the estimated interquartile range of the estimated times. Interquartile range = 72 47 = 25 minutes Answer ..….….….…………minutes [2] (b) One of these people is chosen at random. The probability that the person’s estimate is greater than t minutes is 4 5 . Find the value of t. Probability of a person’s estimate less than or equal to t minutes is 1 5 . Number of people = 40 From graph, t = 44 Answer t = ….….…………………... [2] A1 M1for finding the UQ and LQ M1 for 40 A1

10 AISS PRELIM/4052/01/2025 14 2mx y n p

, where 0pz . (a) Find n when 14m , 9p , 2x and 3y . Answer n = ….……………………… [1] (b) Rearrange the formula to make y the subject.

2 2 2 2 or mx y n p np mx my my mx np mx npy m mx pn pnyx mm

r r Answer y = ….……………………… [3] A1, exact value, hence do not accept answers corrected to 3 s.f M1 for finding y2 M1 for multiplying n by p A1, no marks if r is not seen

14 2 9 9 14 2 9 9 89 8 = 10 or 99 n n

11 AISS PRELIM/4052/01/2025 [Turn over 15 A , B and C are points on a circle, centre O. ACD is a straight line, angle BDC = 26qand angle BAO = 42q. (a) Find angle OBC. Give a reason for each step of your working. OA = OB (radii of a circle) 42OBA‘ q (base angle of isosceles triangle OAB) 90ABC‘ q (angle in a semicircle) 90 42 = 48 OBC‘ q q q (b) Explain why BD is not a tangent to the circle. 84BOC‘ q (ext angle of isosceles triangle OBC) 180 84 26 (sum of angles in a triangle) = 70 OBD‘ q q q q Since 90OBD‘z q , therefore by the conver