AS & A Level Mathematics (9709) — May–June 2023, Paper 23

7 questions · every question answerable online with instant point-by-point AI marking against the official mark scheme.

Start with Question 1 →
Question 1 · 5 marks · Trigonometry (identities and solution of equations)

Solve the equation sec²θ + 5 tan²θ = 9 + 17 sec θ for 0° < θ < 360°.

Answer this question and get it marked →
Question 2 · 5 marks · Logarithmic and exponential functions (reduction to linear form)

The variables x and y satisfy the equation y = Ae^((A−B)x), where A and B are constants. The graph of ln y against x is a straight line passing through the points (0.4, 3.6) and…

Answer this question and get it marked →
Question 3 · 5 marks · Integration (area, integration to a logarithmic function)

The diagram shows part of the curve y = 6 / (2x + 3). The shaded region is bounded by the curve and the lines x = 6 and y = 2. Find the exact area of the shaded region, giving…

Answer this question and get it marked →
Question 4 · 7 marks · Numerical solution of equations (location of roots by graph); the modulus function

The diagram shows the graph of y = 3 − e^(−½x). On the diagram, sketch the graph of y = 5x − 4 , and show that the equation 3 − e^(−½x) = 5x − 4 has exactly two real roots.

Answer this question and get it marked →
Question 5 · 9 marks · Differentiation (product rule, exponential functions)

The diagram shows the curve with equation y = e^(−½x)(x² − 5x + 4). The curve crosses the x-axis at the points A and B, and has a maximum at the point C. Find the exact gradient…

Answer this question and get it marked →
Question 6 · 10 marks · Trigonometry (compound and double angle formulae, identities)

Show that 4 sin(θ + ⅓π) cos(θ − ⅓π) ≡ √3 + 2 sin 2θ.

Answer this question and get it marked →
Question 7 · 9 marks · Differentiation (parametric equations)

A curve has parametric equations x = (2t + 3) / (t + 2), y = t² + at + 1, where a is a constant. It is given that, at the point P on the curve, the gradient is 1. Show that the…

Answer this question and get it marked →

← May–June 2023 Paper 31 · May–June 2023 Paper 22 →

← All AS & A Level Mathematics (9709) past papers