A-level · Algebra & functions

Algebraic fractionsExam-style questions

Fractions with letters in them, handled by the rules of number fractions. What may cancel and why; factorising before cancelling; adding and subtracting over a common denominator, with the minus sign kept on the whole top; multiplying, and dividing by the reciprocal; solving equations with fractions and rejecting answers that make a denominator zero; and writing a top-heavy fraction as a quotient plus a remainder.

Start practising Read the lesson

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

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
The function f is defined by

$\text{f}(x) = \dfrac{x^2 + 7x + 12}{2x^2 + 5x - 3} - \dfrac{1}{2x - 1} \qquad x \in \mathbb{R},\ x > 1$
(a) Show that $\text{f}(x) = \dfrac{x + 3}{2x - 1}$

(3 marks)
(b) Show, using calculus, that f is a decreasing function. You must make your reasoning clear.

(3 marks)

The function g is defined by

$\text{g}(x) = 1 + 3\ln(2x) \qquad x \geqslant \dfrac{1}{2}$
(c) Find $\text{g}^{-1}$

(3 marks)
(d) Find the exact value of $a$ such that

$\text{gf}(a) = 4$

(Solutions relying on calculator technology are not acceptable.)

(4 marks)
Level 5 · 13 marksTry it