BVSS 2024 Prelim EM Paper 1 (Marking Scheme)

Answer all the questions. 1. Evaluate 34.5 23.4 8.17 , leaving your answer correct to 4 significant figures. Answer ……………….………….. [1] ---------------------------------------------------------------------------------------------------------------- 2. Express the ratio 21 3 kg : 450 g : 300 g in its simplest form. Answer ……… : ..……. : ……… [2] ---------------------------------------------------------------------------------------------------------------- 3. The Mathematics grades of students in Class A and Class B are summarised on accurate pie charts shown below. For each statement, state whether you agree or disagree and explain your reason. Statement Agree / Disagree Reason (a) More students in Class A failed Mathematics compared to Class B. Disagree We do not know the total number of students in each class. ----- B1 (b) The percentage of students who achieved A1-A2 are the same for both classes. Agree The proportion/percentage is 90 1 360 4= for A1-A2 for both classes. ----- B1 [2] A1-A2 B3-C6 D7-F9 Class B 2.306 ----- B1 5000 3 g : 450 g : 300 g ----- M1 (convert first number to g) 5000 : 1350 : 900 100 : 27 : 18 -------- A1 ( S4E/5N EM Prelim 2024 Paper 1 Marking Scheme A1-A2 B3-C6 D7-F9 Class A

2 4. A regular polygon has n sides. The size of each interior angle is 5 times the size of each exterior angle. (a) Calculate the value of each exterior angle. Answer ………….………….. [1] (b) State the value of n. Answer n = ……….…………. [1] ---------------------------------------------------------------------------------------------------------------- 5. The radius, r, of an object is directly proportional to the square root of its surface area, A. (i) Sketch the relationship between r and A on the space below. r ------ B1 A [1] (ii) The surface area of the object is 1.21 cm2 when the radius is 0.44 cm. Find the surface area of the object when the radius is 1.2 cm. Answer ………….………….. cm2 [2] ---------------------------------------------------------------------------------------------------------------- 5x + x = 180 x = 30 ------- B1 360 30n== 12 ------- B1 r k A= 0.44 1.21k= ------- M1 0.4k = 0.4rA= 1.2 0.4 A= 3 A= 9A= cm2 ------- A1

3 6. (a) Expand and simplify 2(4 1) 2x−+ . Answer ………….………….. [1] (b) Hence, or otherwise, explain if 2(4 1) 2x−+ is always odd, given that x is an integer. Answer : ……………………………………………………………………………… ………………………………………………………………………………………... ……………………………………………………………………………….…… [2] ---------------------------------------------------------------------------------------------------------------- 7. (a) Write down the set represented by the shaded region. Answer ……………………..…………. [1] (b) It is given that 𝜉 = { x : x is an integer}, A = {x : 9x } and B {2, 4, 6, 8}. State and explain whether the following mathematical statements are true or false. (i) 𝐵 ⊂ 𝐴. This is …………….. because …………………………………………………. ……………………………………………………..……………………….. [1] (ii) 𝐵 ∈ 𝐴. This is …………….. because …………………………………………………. ……………………………………………………..……………………….. [1] 2(4 1) 2x−+ = 216 8 1 2xx− + + = 216 8 3xx−+ --- B1 16 and 18 are even numbers. Hence, 216 8xx− will be an even number. ------ B1 Adding an odd number to an even number gives an odd number. Therefore adding 3 to 216 8xx− will always be odd. ------ B1 ( ) ( )'A B A B --- B1 True all the elements in B are in A and B  A --- B1 False B is a set, not an element --- B1

4 8. Express 22 2 15 39 de d e d e −−+− as a single fraction in its simplest form Answer ……………….………….. [3] ---------------------------------------------------------------------------------------------------------------- 9. A plan of a garden is drawn to a scale 1 : 20. (a) Calculate the length of the line on the plan which represents 13 m long. Answer ………….………….. cm [1] (b) The actual area of a pond in the garden is p m2. Show, with clear working, that the area of the pond represented on the map is 25p cm2. [2] ---------------------------------------------------------------------------------------------------------------- 22 2 15 39 de d e d e −−+− = 2 15 3 ( 3 )( 3 ) de d e d e d e −−+ + − ---- M1 (factorise denominator) = 2( 3 ) ( 15 ) ( 3 )( 3 ) d e d e d e d e − − − +− ---- M1 (single fraction or better) = 2 6 15 ( 3 )( 3 ) d e d e d e d e − − + +− = 9 ( 3 )( 3 ) de d e d e + +− ----- A1 (accept 22 9 9 de de + − ) 1 cm : 20 cm 1 cm : 0.2 m ? : 13 m 13 0.2= 65 cm ------ B1 1 cm : 20 cm 1 cm : 0.2 m 1 cm2 : 0.04 m2 ------- M1 ? : p m2 4 0.04 100 p p= = 100 4p A1 (show all steps) = 25 p

5 10. x is 35% of y. 2 45xy+= . Find the value of x and of y. Answer x = ………… , y = .………… [3] ---------------------------------------------------------------------------------------------------------------- 11. The difference between simple interest and compound interest for a period of 3 years at 5% per annum is $366. Find the principal amount. Answer $………….………….. [3] ---------------------------------------------------------------------------------------------------------------- 0.35 [1]xy= −−−−− 2 45xy+= ---------- [2] Sub [1] into [2] : 2(0.35y) + 45 = y ------ M1 0.7 y + 45 = y 0.3 y = 45 y = 150 ------ A1 And x = 52.5 ------ A1 Interest (compound int) – Simple interest = 366 3 5 5 31 100 100 PPP  + − −  = 366 ------ M1 (compound interest application correct) ------ M1 (difference is compound interest – simple interest)  1.57625 0.15PP−− = 366 0.007625P = 366 P = 48000 ------ A1

6 12. The following data shows the masses of 11 parcels in kg. 1.8 2.1 2.4 2.5 2.6 3.2 3.3 3.5 3.8 4.0 4.9 (a) Calculate the mean mass. Answer ……………….………… kg [1] (b) Find the median mass. Answer ……………….……… kg [1] (c) Two parcels (the 2.4 kg and the 4.9kg) were removed from the delivery van. Explain why the median mass remains unchanged. Answer …………………………………………………………...……………………. …………………………………………………………………………………………. ……………………………………………………………………………………… [1] 2.6 3.2 2.4 3.3 1.8 4.0 4.9 3.5 3.8 2.5 2.1 11 + + + + + + + + + + = 3.1 ----- B1 Rearrange 1.8 2.1 2.4 2.5 2.6 3.2 3.3 3.5 3.8 4.0 4.9 ----- B1 The 2 weights falls on the left and right of the median value, keeping the median weight unchanged in the middle. ----- B1

7 13. (a) By completing the square, find the coordinates of the turning point of the curve y = x2 + 4x + 7. Answer (……… , .….…) [2] (b) Hence, sketch the graph of y = x2 + 4x + 7 in the space below, showing your y-intercept and turning point clearly. y x B1 (u-shaped with correct turning point) B1 (y-intercept) no ECF [2] ---------------------------------------------------------------------------------------------------------------- 22 4 7 ( 2) 4 7x x x+ + = + − + = 2( 2) 3x++ ----- M1 (this must be evident) Turning point is (– 2, 3) ----- A1 – 2 3 – 7

8 14. On the grid, OA= a and OB= b. (a) Mark clearly on the grid in the answer space, (i) the point C such that OC= 2b + a (ii) the point D such that OD= 1 2 b − 3a. Answer