A-level · Algebra & functions

Sketching curvesExam-style questions

Drawing a curve from its equation without plotting points. Where it meets the axes, read from the factors; which way the ends go, from the leading term; whether it crosses or touches at each root; reciprocal curves and their asymptotes; finding where two curves meet; and counting meeting points from a sketch or with the discriminant.

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17 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 curve $C_1$ has equation

$y = -\dfrac{8}{x} \qquad x \neq 0$
(a) Sketch $C_1$ .

(2 marks)

The curve $C_2$ has equation

$y = -\dfrac{8}{x + 2} \qquad x \neq -2$
(b) Describe fully the single transformation that maps $C_1$ onto $C_2$ .

(2 marks)

The line $l$ has equation $y = kx + 2$ , where $k$ is a constant. The point $P$ lies on $C_2$ and has $x$ coordinate $2$ . The line $l$ passes through $P$ .
(c) Show that $k = -2$

(2 marks)

The line $l$ meets $C_2$ at $P$ and at one other point, $Q$ .
(d) Use algebra to find the coordinates of $Q$ .

(Solutions relying entirely on calculator technology are not acceptable.)

(4 marks)
Level 5 · 10 marksTry it