Converting between units

How many centimetres are there in 4·58 m?

Circle the correct answer.

45·8 cm 0·458 cm 46 cm 458 cm 4580 cm

Write 3729 grams in kilograms.

A mass is shared in the ratio 3: 5.

The larger share is 44 lb (pounds).

Calculate the total mass.

Give your answer in kilograms (kg).

You must show all your working.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

A mass is shared in the ratio 3: 5. The larger share is 44 lb (pounds).

Calculate the total mass.

Give your answer in kilograms (kg).

You must show all your working.

Which of the following is the nearest value to 488 grams?

Circle the correct answer.

0·5 kg 500 kg 50 kg 5 tonnes 0·05 kg

Circle the correct answer for the following. 15 miles is approximately equal to

1500 m 24 km 15 km 2·4 km 3000 m

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?

Which of the following is the nearest value to 488 grams?

Circle the correct answer.

0·5 kg 500 kg 50 kg 5 tonnes 0·05 kg

Circle the correct answer for the following. 15 miles is approximately equal to

1500 m 24 km 15 km 2·4 km 3000 m

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?

The diagram below shows a water container.

It is formed from an open rectangular tank with a solid cylinder attached to its base inside the tank.

The base radius of the cylinder is 10 cm. The height of the cylinder is 30 cm.

How many litres of water can the container hold?

You must show all your working.

The container can hold_{…........ ……........ ……} litres.

Solve the following equations.

52 − n = 38

How many centimetres are there in 24·8 metres?

Give your answer in metres.

Express 25 minutes as a percentage of 2 hours 5 minutes.

What is 32 km approximately equal to?

Circle your answer.

16 miles 20 miles 32 miles 51 miles 64 miles

Give your answer in metres.

Express 25 minutes as a percentage of 2 hours 5 minutes.

What is 32 km approximately equal to?

Circle your answer.

16 miles 20 miles 32 miles 51 miles 64 miles

Find the volume of the solid prism shown above.

The solid prism is made of gold. Gold has a density of 19∙3 g/cm³. Calculate the mass of the prism.

Give your answer in kilograms.

Find the volume of the solid prism shown above.

The solid prism is made of gold. Gold has a density of 19∙3 g/cm³. Calculate the mass of the prism.

Give your answer in kilograms.

Which of the following is equal to 0·5 kg?

Circle the correct answer.

50 mg 500 g 500 mg 5 mg 50 g

Which of the following is equal to 700 cm?

Circle the correct answer.

7 m 7 km 0·7 m 0·07 km 70 m

Which of the following is nearest in mass to 5 kg?

Circle the correct answer.

7 lb 11 lb 15 lb 19 lb 23 lb

Which of the following is nearest in mass to 5 kg?

Circle the correct answer.

7 lb 11 lb 15 lb 19 lb 23 lb

Write 0·034 35 correct to two significant figures.

Circle your answer.

0·03 0·033 0·0344 0·034 0·034 00

Convert 6∙7 m² into cm².

Circle your answer.

670 6700 67 000 670 000 6 700 000

Factorise 12e 15.

Circle your answer.

27e 34e 5 12e 15 5(12e + 3) 150 8e 3

Two similar shapes have perimeters of 241 cm and 719 cm. The area of the smaller shape is 2063 cm².

Calculate the area of the larger shape.

Give your answer in m².

A sack contains 5·4 kg of potatoes. A second sack contains 3·08 kg of potatoes. A third sack contains 2·2 lb (pounds) of potatoes.

Calculate the total mass of these potatoes.

Give your answer in kilograms.

Circle the correct answer for each of the following statements.

7·2 m³ is equal to

720 cm³ 72 000 cm³ 7·2 10⁵cm³ 7·2 10³cm³ 7·2 10⁶cm³

Circle the correct answer for each of the following statements.

7·2 m³ is equal to

720 cm³ 72 000 cm³ 7·2 10⁵cm³ 7·2 10³cm³ 7·2 10⁶cm³

The mass of 1 litre of water is 1 kg. What is the mass of 4·3 litres of water?

Write your answer in grams.

A rope is 3 m long. It is cut into 6 equal pieces.

What is the length of each piece of rope?

Write your answer in centimetres.

A camera was switched on at

21:45 on 20th March, 2021.

It was left continuously filming until the battery ran out.

The battery lasted for exactly 2 days and 10 hours.

At what time and on which date did the battery run out?

Battery ran out at_{……........ …}:_{……........ …} on_{……........ …} March 2021.

Helen says,

Is she correct?

You must show all your working.

A camera was switched on at

21:45 on 20th March, 2021.

It was left continuously filming until the battery ran out.

The battery lasted for exactly 2 days and 10 hours.

At what time and on which date did the battery run out?

Battery ran out at_{……........ …}:_{……........ …} on_{……........ …} March 2021.

Helen says,

Is she correct?

You must show all your working.

Identical rods can be placed end to end, as shown below.

Each rod is 17·5 cm long.

How many of these rods can be placed, in this way, between two points 4 metres apart?

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

Identical rods can be placed end to end, as shown below.

Each rod is 17·5 cm long.

How many of these rods can be placed, in this way, between two points 4 metres apart?

What is the total mass when 534 g is added to 3·5 kg?

Circle the correct answer.

4·034 g 4·034 kg 537·5 g 537·5 kg 884 g

What is the total length when 35 cm is added to 7·8 m?

Circle the correct answer.

113 cm 42·8 m 42·8 cm 815 cm 815 m

How many mm³ are there in 4 cm³?

Circle the correct answer.

What is the total mass when 534 g is added to 3·5 kg?

Circle the correct answer.

4·034 g 4·034 kg 537·5 g 537·5 kg 884 g

What is the total length when 35 cm is added to 7·8 m?

Circle the correct answer.

113 cm 42·8 m 42·8 cm 815 cm 815 m

How many mm³ are there in 4 cm³?

Circle the correct answer.

A solid object is made by drilling a cylindrical hole of radius 4 cm through a cuboid measuring

20 cm by 15 cm by 10 cm as shown below.

Calculate the volume of the object.

Give your answer in cm³.

The object is made from a material which has a density of 2·4 g/cm³. Calculate the mass of the object.

Give your answer in kg, correct to the nearest kg.

Circle either TRUE or FALSE for each statement given below.

Circle the longest time period from the list given below.

180 minutes 4·5 hours 4 hours 45 minutes 4 hours th of a day

Circle the longest distance from the list given below.

30 000 mm 250 m 2 km 70 m 4 000 cm 2·4 km

Circle either TRUE or FALSE for each statement given below.

Write 312 cm in metres.

Write 9·07 km in metres.

Convert an area of 4 m² into cm². (b)

The diagram below shows an empty cylinder, with radius 10 cm and height 20 cm.

Using = 3.14, calculate the volume of the cylinder. (a)

What is the greatest whole number of litres that this cylinder can hold?

Convert an area of 4 m² into cm². (b)

The diagram below shows an empty cylinder, with radius 10 cm and height 20 cm.

Using = 3.14, calculate the volume of the cylinder. (a)

What is the greatest whole number of litres that this cylinder can hold?

Circle the correct answer for each of the following.

16 km is approximately equal to

5 miles 8 miles 10 miles 16 miles 32 miles

4 litres is approximately equal to

4 pints 5 pints 6 pints 7 pints 8 pints

Circle the correct answer for each of the following.

16 km is approximately equal to

5 miles 8 miles 10 miles 16 miles 32 miles

4 litres is approximately equal to

4 pints 5 pints 6 pints 7 pints 8 pints

Calculate the volume of a pyramid with a base area of 13 200 cm² and a perpendicular height of 460 cm.

Give your answer in m³.

How many cubic centimetres (cm³) are there in 2·5 litres?

2.5 litres =_........ cm³

A triangular prism of length 2 metres is shown below.

AC = 21 cm, BC = 35 cm and BAC = 90°.

In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing. Calculate the area of triangle ABC. Give your answer in cm².

You must show all your working.

Calculate the volume of the prism.

You must give the units of your answer.

In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

The diagram shows part of a rectangle and some identical circles drawn inside the rectangle. The circles touch each other or the sides of the rectangle, as shown in the diagram.

The rectangle measures 30 cm by 1 m. The diameter of every circle is 5 cm.

What is the largest number of circles that will fit into this rectangle? The circles must be arranged in the way shown above.

You must show all your working.