O-LevelMathematicsAlgebra and graphs4024/21 · May/June 2024 · Q811 Marks

Complete the table for y = 2ˣ/5. x | 0 | 1 | 2 | 3 | 4 | 5 ---|---|---|---|---|--- y | 0.2 | 0.4 | 0.8 | 1.6 | 3.2

(a)(i)Complete the table for y = 2ˣ/5. x | 0 | 1 | 2 | 3 | 4 | 5 ---|---|---|---|---|--- y | 0.2 | 0.4 | 0.8 | 1.6 | 3.2[1]
(a)(ii)On the grid, draw the graph of y = 2ˣ/5 for 0 ≤ x ≤ 5.[3]
(a)(iii)(a)2ˣ⁺³ = 100 Show that 2ˣ/5 = 5/2.[2]
(a)(iii)(b)By drawing a suitable line on the grid, solve 2ˣ⁺³ = 100. x =[2]
(b)This is a sketch of the graph y = a + bx – x². The graph crosses the x-axis at integer values of x. Find the value of a and the value of b. a = b =[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

[1] 6.4 oe cao
[3] Correct smooth curve
[3] B2FT for 5 or 6 points correctly plotted
[3] or B1FT for 3 or 4 points correctly plotted
[2] 2ˣ⁺³ = 2ˣ×2³ soi
[2] M1 May be done in stages by division by 2 three times
[2] A1 (2ˣ/5) = (100/(8×5)) leading to (2ˣ/5) = (12.5/5) = (5/2)
[2] y = 2.5 drawn
[2] M1
[2] 3.5 to 3.8
[2] A1
[3] a = 7
[3] b = 6
[3] B1 for a = 7
[3] B1 for (-1, 0) and (7, 0) soi
[3] or (-7, 0) and (1, 0) soi
[3] or (c, 0) and (d, 0) where cd = -their a soi where c and d are integer values

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