2023-2024 Grade 8 Mathematics EOY Exam (PDF)

Total marks: / 50 End of Year Assessment 2023- 2024 Grade 8 Mathematic...

Total marks: / 50 End of Year Assessment 2023- 2024 Grade 8 Mathematics Time allowed: 60 minutes Instructions 1. Use black ink or black/blue ball-point pen. 2. Write your name and homeroom in the spaces provided. 3. Answer all questions. 4. Without sufficient steps shown, correct answers may be awarded no marks. 5. Answer the questions in the spaces provided. - there may be more space than you need. Information 1. The total mark for this paper is 50. 2. The marks for each question are shown in brackets. - use this as a guide as to how much time to spend on each question. Advice 1. Read each question carefully before you start to answer it. 2. Check your answers if you have time at the end. Student name: Homeroom: Subject Teacher: Ms. Chong / Ms. Muthuraman / Ms. Sing / Mr. Tsui  Mathematics International GCSE Mathematics Formulae sheet Formulae sheet – Foundation Tier DO NOT WRITE IN THIS AREA 1 Area of trapezium = (a + b)h 2 a h b Volume of prism = area of cross section length DO NOT WRITE IN THIS AREA cross section length Volume of cylinder = 2 h Curved surface area of cylinder = 2 h DO NOT WRITE IN THIS AREA 2  Answer ALL FIFTEEN questions. Write your answers in the spaces provided. You must write down all the stages in your working. 1 In a sale, normal prices are reduced by 35% The normal price of a sofa is $3800 Work out the sale price of the sofa. 35 X 3800 on or 1330 M 3800 x (1 - 35 % 100 M2 MI = 2470 3800 - 1330' 24778 Al $........................................................... (Total for Question 1 is 3 marks) 2 (a) Write 2.4 × 10−5 as an ordinary number. 0. 000024 BI........................................................... (1) (b) Work out (4.3 × 103 ) × (5.1 × 106 ) Give your answer in standard form. (4. 3 x 5. 1) x(103 x10 % = 21. 93 X109 M1 or 2. 193 x 10 X1010. 193 2 x 101 Al = 2 193............................................................ (2) (Total for Question 2 is 3 marks) 3 3 (a) Simplify (2𝑥 3 𝑦 5)3 BI for 2 correct terms as part of a product 8x9y15 B2........................................................... (2) (b) Find the value of 4𝑘 0 where 𝑘 > 0 4 BI........................................................... (1) (Total for Question 3 is 3 marks) 4 The mean of five numbers is 3.8 One of the five numbers is 4.2 Find the mean of the other four numbers. M1 for 14 8 seen.. 8 x5 3 - 4 2. MI Correct full calculation 4 which would lead to correct answer 3 7. Al........................................................... (Total for Question 4 is 3 marks) 4 5 𝐻 is inversely proportional to the square of 𝑣. Given that 𝐻 = 15 when 𝑣 = 4 , find a formula for 𝐻 in terms of 𝑣 n = M K 15 = M1 or M2 42 k = 240 240 H = Al Uz........................................................... (Total for Question 5 is 3 marks) 6 (a) Expand (𝑥 − 5)(𝑥 + 4) = X - 5x + 4X - 20 M1 for any 3 correct terms or for 4 Out of 4 correct terms ignoring signs X2 - X - 20 Al or for X * -5X.............................................................. or for... 4X-20 (2) (b) Factorise fully 20𝑥 2 𝑦 5 + 15𝑥 3 𝑦 2 M1 for any correct partial factorisation with at least 2 factors , one of which must be a letter or the correct common I error inside the more than factor with no 5x3 y 14y3 + - 3x) Al bracket............................................................ (2) (Total for Question 6 is 4 marks) 5 7 (a) Complete the table of values for 𝑦 = 𝑥 2 − 𝑥 − 4 𝑥 −3 −2 −1 0 1 2 3 𝑦 8 2 - 2 −4 - 4 - 2 2 BC for all correct values. Otherwise (2) BI for 3 or 4 correct values (b) On the grid below, draw the graph of 𝑦 = 𝑥 2 − 𝑥 − 4 for values of 𝑥 from −3 to 3 V · · & ⑳ · M1 for at (2) dep on BI scored in (a) (Total for Question 7 is 4 marks) least 5 points plotted correctly Al for a fully correct curve and correctly 6 Plotted and joined with a curve and curved between 10.-4) and (1 -4).. 8 Use ruler and compasses to construct the bisector of angle ABC. You must show all of your construction lines. - (Total for Question 8 is 2 marks) 7 9 A cylinder has diameter 8 cm and length 12 cm. Work out the curved surface area of the cylinder. Give your answer correct to 3 significant figures. M1 for circumference Sit SA 2TWh Curved = It = (4) · 12 M1 for correct expression = 96π I full SA given , then = 302 cm2 award 2 marks as long as you see on in working (M1 for Sit Des 302 Al......................................................... cm2 (Total for Question 9 is 3 marks) 8 10 𝐴𝐵𝐶 and 𝐷𝐸𝐹 are similar triangles. Work out the length of 𝐵𝐶. MI for correct scale factor AC BC - accept ratio notation DF EF 9: 5 21. 6 X Z 12 15 12x = 324 27 17 I......................................................... cm X = 27 (Total for Question 10 is 2 marks) 11 The bearing of London from Iceland is 138° Work out the bearing of Iceland from London. - 1380 270 + 48 or 1800 + 138 M/ ⑧ 3 I 480 A 48) 318 Al......................................................... ° (Total for Question 11 is 2 marks) 9 12 The diagram shows a shaded shape 𝐴𝐵𝐶𝐷 made from a semicircle 𝐴𝐵𝐶 and a right-angled triangle 𝐴𝐶𝐷. r= 4 · 𝐴𝐶 is the diameter of the semicircle 𝐴𝐵𝐶. Work out the area of the shaded shape. Give your answer correct to 3 significant figures. AC" 172-15 : = Ml AC = S M/ Area = [(42) = 8icm2 MI 2 8X15 8t = 85. 1 cm M/ 2 85 Al 1......................................................... cm2. (Total for Question 12 is 5 marks) 10 13 Mike has 8 identical rectangular tiles and 4 identical square tiles. He arranges the tiles to fit exactly round the edge of a rectangle, as shown in the diagram below. X Y X Y Y Y X Work out the area of one of Mike's rectangular tiles. Let the X be the length of the rectangle y be the width of the rectangle 2x + y = 9 1 E 2x + 3y = 192 MI 2y = 10 M/ y = 5 2X = 4 M/ X = 2 10 Al........................................................... cm2 Area = 5x2 = 10 MI (Total for Question 13 is 5 marks) 11 14 A box contains four different kinds of cookies. Dex takes at random a cookie from the box. The table shows the probability of Dex taking an Oreo or a Chocolate or a Strawberry cookie. Cookie Probability Oreo 0.2 Chocolate 0.35 Strawberry 0.15 Caramel (a) Work out the probability that Dex takes a Caramel cookie. 1 - 0. 2-0. 35-0 15. M/ 0 3 Al............................................................ (2) (b) Work out the probability that Dex takes an Oreo cookie or a Chocolate cookie. 0 2 +. 0 35. MI 0. 55 Al........................................................... (2) (Total for Question 14 is 4 marks) 12 15 𝐴𝐵𝐶 is an isosceles triangle with 𝐵𝐴 = 𝐵𝐶. 𝑁 is the point on 𝐴𝐶 such that 𝐴𝑁 = 8.5 cm and 𝐵𝑁 is perpendicular to 𝐴𝐶. Work out the perimeter of triangle 𝐴𝐵𝐶. Give your answer correct to 3 significant figures. 8 5 400. COS = MI for use of cos AB AB = 8 5. " MI for the correct solving COS40 AB = 11. 1 cm M1 for finding the perimeter p = 11 1 x. 2 + 8 5X2. 39 2 Al........................................................... cm. =. 2 39 (Total for Question 15 is 4 marks) TOTAL FOR PAPER IS 50 MARKS 13  BLANK PAGE 14 BLANK PAGE 15  BLANK PAGE 16