O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2023 · Q412 Marks

(a) Complete the table of values for y = 2ˣ/5. x | -1 | 0 | 1 | 2 | 3 | 4 y | 0.1 | 0.2 | 0.4 | 0.8 | 1.6 | (b) Draw the graph of y = 2ˣ/5 for -1 ≤ x ≤ 4.

(a)Complete the table of values for y = 2ˣ/5.[1]
(b)Draw the graph of y = 2ˣ/5 for -1 ≤ x ≤ 4.[3]
(c)By drawing a suitable line on the grid, solve 2ˣ = 6.[2]
(d)(i)Complete the table of values for 4y = 2x+1. x | -1 | 2 | 4 y | | 2.25 |[1]
(d)(ii)On the grid on page 8, draw the graph of 4y = 2x+1 for -1 ≤ x ≤ 4.[1]
(d)(iii)Find the x-coordinates of the points where the line 4y = 2x+1 crosses the graph of y = 2ˣ/5.[1]
(d)(iv)The x-coordinates in part (d)(iii) are the solutions of the equation A×2ˣ+Bx+C = 0, where A, B and C are all integers. Use the equations 4y = 2x+1 and y = 2ˣ/5 to find the exact value of each of A, B and C.[3]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[1] 3.2 oe
[3] B2FT for 5 or 6 points correctly plotted
or B1FT for 3 or 4 points correctly plotted
Correct smooth curve
[B1] Ruled line y = 1.2
[B1] 2.5 to 2.7
After 0 scored, SC1 for y = 1.2 soi
[1] -0.25, 1.25 oe
[1] Ruled line from (-1, -0.25) to (4, 2.25)
[1] FT two x-coordinates where their ruled line and their curve cross
x-coordinates where ruled line 4y = 2x + 1 crosses y = 2x/5
[M1] 2x/5 = (2x+1)/4 oe seen
[A2] A = 4, B = −10, C = −5 OR A = -4, B = 10, C = 5
A1 for A correct and either B or C correct or 4×2x-10x-5 [=0] or -4×2x+10x+5 [=0] or Ak, Bk and Ck where k is not an integer

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