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A-LevelMathematicsNumerical methods9709/31 · Oct/Nov 2024 · Q57 Marks

By sketching a suitable pair of graphs, show that the equation 2+e-0.2x = ln(1+x) has only one root.

(a)By sketching a suitable pair of graphs, show that the equation 2+e-0.2x = ln(1+x) has only one root.[2]

Mark scheme

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

[B1] Sketch a relevant graph, e.g. y = 2 + e⁻⁰·²ˣ For the sketches: Correct curvature Intersections with the y-axis approximately correct Horizontal asymptote approximately correct – need not draw in Allow scale not marked and implied by their sketch
[B1] Sketch a second relevant graph, e.g. y = ln(1+ x) and justify the given statement

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About this question

Topic: Numerical methods, A-Level Mathematics (syllabus 9709). Structured question, 7 marks.
Source: A-Level Mathematics, Oct/Nov 2024 Paper 3 Variant 1, question 5.

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