Measuring lengths & angles, bearings

In the space below, draw an angle of 134° at point P.

The diagram below shows two towns, A and B, on a map.

The scale of the map is 1 cm represents 4·5 km.

Find the straight-line distance from town A to town B.

Give your answer in kilometres.

Find the bearing of town A from town B.

Find the straight-line distance from town A to town B.

Give your answer in kilometres.

Find the bearing of town A from town B.

On the map, shade the region containing all the points that are: • closer to town A than to town B, and

• less than 27 km from town B.

A B C is a large triangle, where A C = 16 m and B C = 13 m.

Draw a scale drawing of this triangle using the following scale:

1 cm represents 2 m.

The side A B has already been drawn accurately.

What is the size of A C B ?

How many minutes are there in 1 day and 5 hours?

1 day and 5 hours =_{……........ …………………} minutes

The diagram below shows part of a measuring tape used in a long-jump competition.

The arrow indicates the distance jumped by the competitor who came second. The winning jump was 676 cm long.

What was the difference between the lengths of these jumps?

A B C is a large triangle, where A C = 16 m and B C = 13 m.

What is the actual length of A B in the large triangle?

How many minutes are there in 1 day and 5 hours?

1 day and 5 hours =_{……........ …………………} minutes

The diagram below shows part of a measuring tape used in a long-jump competition.

The arrow indicates the distance jumped by the competitor who came second. The winning jump was 676 cm long.

What was the difference between the lengths of these jumps?

Point O is the centre of the circle below. Measure and write down the length of the diameter of the circle.

Write your answer in centimetres.

Measure and write down the size of angle x.

The diagram below shows the positions of three points A, B and C on a map.

The diagram is drawn to scale.

Find the bearing of B from A.

Find the bearing of A from C.

Measure and write down the size of angle y.

Draw a line through the point C that is perpendicular to AB.

What is the bearing of point B from point A?

What is the bearing of point A from point B?

Points P, Q, R and S are all 5 km from point X.

P is on a bearing of 005° from X. Q is on a bearing of 100° from X. R is on a bearing of 240° from X. S is on a bearing of 355° from X.

Which two of the four points P, Q, R and S are closest to each other?

The two points closest to each other are_........ and_........ .

Point A and point B are shown in the scale drawing below.

Point C is 35 km from point B on a bearing of 300°.

Complete the scale drawing to show the position of point C.

Use your scale drawing to calculate • the actual length of AC, in kilometres,

• the bearing of point C from point A.

Point A and point B are shown in the scale drawing below.

Point C is 35 km from point B on a bearing of 300°.

Complete the scale drawing to show the position of point C.

Use your scale drawing to calculate • the actual length of AC, in kilometres,

• the bearing of point C from point A.

Measure and write down the size of angle x.

Measure the length of the side AB of this triangle.

Write your answer in millimetres.

Measure and write down the size of XYZ.

Two sides of a parallelogram ABCD are drawn accurately below. Using only a ruler and a pair of compasses, complete an accurate drawing of the parallelogram.

You must show all your construction arcs.

The line XY below forms part of a scale drawing of a garden. The scale drawing has a scale of 1:200.

What is the actual distance between point X and point Y in the garden?

Give your answer in metres.

Actual distance between point X and point Y =_{……………........ ….…………} metres

Write your answer as a decimal.

A number line is shown below.

To which number is the arrow pointing?

Two sides of a parallelogram ABCD are drawn accurately below. Using only a ruler and a pair of compasses, complete an accurate drawing of the parallelogram.

You must show all your construction arcs.

The line XY below forms part of a scale drawing of a garden. The scale drawing has a scale of 1:200.

What is the actual distance between point X and point Y in the garden?

Give your answer in metres.

Actual distance between point X and point Y =_{……………........ ….…………} metres

Measure and write down the size of angle x.

Calculate the size of angle x.

Hence, give the bearing of point B from point A.

Calculate the size of angle x.

Hence, give the bearing of point B from point A.

Mark the midpoint of AB with a ×.

Draw a line parallel to AB that passes through point C.

Measure BAC.

BAC =_........ °

One of the angles below is a reflex angle.

Circle the correct answer.

45° 90° 135° 180° 225°

The diagram below shows two angles on a straight line. The large angle is 5 times the size of the small angle.

Find the size of each angle.

Measure the length of a diagonal of this rectangle.

Write down your answer in the space provided.

Draw an accurate scale drawing of the triangle shown above.

Use your scale drawing to calculate the actual length of side BC.

Give your answer in metres.

Actual length of BC =_{………........ ……..} metres

What is the bearing of X from point P?

Circle the correct answer.

146° 326° 214° 034° 234°

The diagram below shows 6 points on a map. The diagram is drawn to scale.

A ship sails from point P on a bearing of 107°. It sails towards one of the five points A, B, C, D or E. Which of the five points is the ship sailing towards?

Circle the correct answer.

A B C D E

A second ship sails from point P for a number of miles on a bearing of 070°. It then changes direction and sails on a bearing of 270°. It is possible for the ship to reach only one of the five points A, B, C, D or E. Which point can the ship reach?

Circle the correct answer.

A B C D E

Draw an accurate scale drawing of the triangle shown above.

Use your scale drawing to calculate the actual length of side BC.

Give your answer in metres.

Actual length of BC =_{………........ ……..} metres

What is the bearing of X from point P?

Circle the correct answer.

146° 326° 214° 034° 234°

The diagram below shows 6 points on a map. The diagram is drawn to scale.

A ship sails from point P on a bearing of 107°. It sails towards one of the five points A, B, C, D or E. Which of the five points is the ship sailing towards?

Circle the correct answer.

A B C D E

A second ship sails from point P for a number of miles on a bearing of 070°. It then changes direction and sails on a bearing of 270°. It is possible for the ship to reach only one of the five points A, B, C, D or E. Which point can the ship reach?

Circle the correct answer.

A B C D E

Measure the length of the line AB.

Write your answer in centimetres.

In the space below, draw a circle with a radius of 6 cm.

Measure and write down the size of PQR.

On the diagram, mark the point P with a cross so that

Circle the correct answer in each of the following.

Which of the following values cannot be an external angle of a regular polygon?

10° 18° 30° 48° 72°

Point A is on a bearing of 100° from point B.

What is the bearing of point B from point A?

260° 100° 280° 180° 80°

Circle the correct answer in each of the following.

Which of the following values cannot be an external angle of a regular polygon?

10° 18° 30° 48° 72°

Point A is on a bearing of 100° from point B.

What is the bearing of point B from point A?

260° 100° 280° 180° 80°

How would the direction due west be written as a three-figure bearing?

Circle your answer.

360° 180° 090° 270° 000°

What is the bearing of point P from point A?

Circle your answer.

220° 040° 140° 320° 230°

Use a ruler and a protractor to make an accurate drawing of this triangle.