Unit 3

The distance–time graphs of two runners, Helen and Marco, show Helen's graph as a straight line and Marco's as a curve starting steeper and becoming less steep.

What can you say about the speed of each runner during their run? Explain your answer.

Two cyclists, Jay and Lisa, travel towards each other from towns A and B, which are 48 km apart. Jay leaves A at 09:00 and cycles at a constant speed of 16 km/h. Lisa leaves B at 09:30 and cycles at a constant speed of 12 km/h towards A.

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.

A straight road runs up a hill at a constant angle with the horizontal. The road makes an angle of 18° with the horizontal and is 120 m long.

Calculate the height gained, correct to 3 significant figures.

Write down the value of tan 60°. Give your answer correct to 3 significant figures.

In the right-angled triangle below, which side is adjacent to angle ?

A mobile phone mast is 48 m tall. From a point on level ground, the angle of elevation to the top of the mast is 40°.

Work out the value of x in the triangle below. Give your answer correct to 3 significant figures.

PQ = 7 cm, angle R = 35°.

A triangle has a tangent ratio of 1.0 at one of its angles. Write down the value of that angle to the nearest degree.