O-LevelMathematicsAlgebra and graphs4024/21 · Oct/Nov 2021 · Q711 Marks

7 (a) On the grid below, draw the graph of y = 2ˣ for 0 ≤ x ≤ 4. [Figure grid for plotting graph] (b) [Figure graph of y = 1/(2x²) + 3x for -1 ≤ x ≤ 3] The diagram shows the graph of y = 1/(2x²) + 3x for -1 ≤ x ≤ 3. (i) By drawing a tangent, estimate the gradient of the curve at x = 0.5 . (ii) Use the graph to estimate the solution of the equation 1/(2x²) + 3x = 2. x = (iii) By drawing a suitable line on the grid, estimate the solutions of the equation 1/(2x²) = 7-4x . x = , x = , x =

(a)On the grid below, draw the graph of y = 2ˣ for 0 ≤ x ≤ 4.[4]
(b)(i)By drawing a tangent, estimate the gradient of the curve at x = 0.5 .[2]
(b)(ii)Use the graph to estimate the solution of the equation 1/(2x²) + 3x = 2.[1]
(b)(iii)By drawing a suitable line on the grid, estimate the solutions of the equation 1/(2x²) = 7-4x .[4]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.

[4] (a) Correct smooth curve
[4] B3 for 4 or 5 correct points or B2 for 2 or more correct pairs of values soi or B1 for one correct pair of values soi
[2] (b)(i) Tangent drawn at x = 0.5
[2] B1 Dependent on close attempt at tangent
[2] -5.5 to -2.8
[1] (b)(ii) -0.45 to -0.35
[4] (b)(iii) Line y = 7 – x ruled
[4] M2
[4] M1 for 1/(2x²) + 3x = 7 – x or for line y = k − x or y = 7 + mx drawn, m≠0
[4] -0.2 to -0.3, 0.2 to 0.4, 1.6 to 1.8
[4] A2 Aldep for one correct, dep on at least M1
[4] After A0 scored SC1 for all 3 correct with no or wrong working

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