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 car joins a motorway from a slip road. It passes the start of the slip road at time $t = 0$ .

Its velocity, $v$ m/s, for the next $12$ seconds is shown on the graph.Kwame says,

"The car travels more than $200$ metres in these $12$ seconds."

Is Kwame correct?

You must show how you get your answer.

(4 marks)
Level 5 · 4 marksTry it
2
A car is travelling along a straight road.

Its speed increases at a constant rate from $u$ m/s to $3u$ m/s in $8$ seconds.

In these $8$ seconds the car travels $160$ metres.

Work out the acceleration of the car.

You must show your working.

(4 marks)
Level 5 · 4 marksTry it
3
A lift carries a passenger up a tall building. It starts and finishes at rest.
- It speeds up at a constant rate from rest to $4$ m/s in $5$ seconds.
- It then travels at $4$ m/s for $T$ seconds.
- It then slows down at a constant rate and stops $3$ seconds later.
The average speed of the lift for the whole journey is $3.2$ $3.2$ m/s.

Find the value of $T$ $T$ .

You must show your working.

(5 marks)
Level 5 · 5 marksTry it