GCSE · Graphs of functions

Rates of change from graphs (tangents, chords and the area under a graph)Exam-style questions

Read a rate off a curved graph: the gradient of a chord is the average rate of change over an interval, the gradient of a tangent is the rate at one instant, and the units on the axes say what that rate is (a speed, an acceleration, litres per minute). Then the other half: the area under a speed–time graph is the distance travelled, found exactly from straight pieces or estimated with strips, with a reason why the estimate is too big or too small.

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20 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 2 Level 3 Level 4 Level 5

1
A curve is drawn on the grid for values of $x$ from $0$ to $7$ .(a) Find the average rate of change of $y$ from $x = 2$ to $x = 6$ .

(2 marks)
(b) Is the rate of change of $y$ at $x = 6$ greater than or less than your answer to part (a)?

Give a reason for your answer.

(1 mark)
Level 2 · 3 marksTry it
2
Ella rides an e-scooter along a straight path.

The graph shows her speed during a journey of $24$ seconds.Work out the total distance Ella travels.

(3 marks)
Level 2 · 3 marksTry it
3
A skateboarder rolls down a slope.

The graph shows the distance, $s$ metres, she has travelled $t$ seconds after a timer is started.

The tangent to the curve at the point $P$ , where $t = 4$ , has been drawn.Use the tangent to work out an estimate of the speed of the skateboarder when $t = 4$

(2 marks)
Level 2 · 2 marksTry it
4
Priya cycles along a straight road.

The table gives information about her speed, $v$ m/s, $t$ seconds after she passes a lamp post.
$t$ (seconds) $0$ $2$ $4$ $6$
$v$ (m/s) $2$ $5$ $7$ $8$
Her speed–time graph is a smooth curve through these points.

Estimate how far Priya travels in the $6$ seconds after she passes the lamp post.

Use $3$ strips of equal width.

(3 marks)
Level 2 · 3 marksTry it