Unit 3

The distance–time graph for a motorbike shows the following points: at 0 minutes, 0 km; at 15 minutes, 18 km; at 20 minutes, 18 km; at 40 minutes, 54 km.

a) Calculate the speed of the motorbike during the first 15 minutes.

b) Explain what the graph shows between 15 and 20 minutes.

c) Calculate the average speed for the whole journey.

On a distance–time graph, a line slopes downward from left to right. What does this mean about the object's movement? Explain your answer.

Below is an extract from a distance–time graph that describes part of Rob's run:

Describe what Rob does between each of these time intervals: (a) 0–6 min, (b) 13–18 min, (c) 18–25 min, and (d) 25–30 min.

Olivia walks from her home to the post office and back. Her journey is shown on this distance–time graph.

a) Work out Olivia's speed on her journey from home to the post office.

b) Explain why Olivia takes more time to return home compared to her outward journey.

A distance–time graph for two people, Amira and Ben, is shown below. Both walk from the same starting point to the same destination.

a) Compare the journey times for Amira and Ben to reach the destination.

b) Find the time interval during which Ben is stationary and work out how far he is from the start during this time.

c) Calculate the speed (in km/h) for Amira over her whole journey.

In a right-angled triangle, which side is always opposite the right angle?

Calculate the value of tan 45°. Give your answer to 3 significant figures.

In the triangle below, calculate the length of side x.

Which of the following ratios represents the 'tangent' of an angle θ in a right-angled triangle?

A lamp post stands vertically. From a point 6 metres away from the base of the lamp post, the angle of elevation to the top of the lamp post is 35°.