A-level · Exponentials & logarithms

Exponential functions and eExam-style questions

Functions with the variable in the power, y = a^x — their graph shape, the asymptote and intercept — and the special exponential e^x whose gradient equals itself.

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3 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4

1
$f(x) = e^{2x} - 8e^x + 12$ .
(a) Solve the equation $f(x) = 0$ , giving your answers exactly. (4 marks)
(b) Find the exact coordinates of the stationary point of the curve $y = f(x)$ , and state its nature. (4 marks)
(c) Show that $\displaystyle\int_0^{\ln 2} f(x)\; dx = 12\ln 2 - \frac{13}{2}$ . (3 marks)
Level 4 · 11 marksTry it