A cuboid measuring 3 cm by 5 cm by 2 cm is enlarged by a ratio of 2:1, a) What is the volume of: i) the original cuboid? ii) the enlarged cuboid? b) By what ratio has the volume been increased?

A rectangle measuring 7 cm by 4 cm is enlarged by a ratio of 2:1 a) What is the area of: i) the original rectangle? ii) the enlarged rectangle? b) By what ratio has the area been enlarged?

A banner needs to be enlarged from its original format. The dimensions of the original are 4 cm tall by 25 cm wide. The enlarged banner needs to be at least 8 m wide but no more than 1.4 m tall. Calculate the minimum and maximum ratios of enlargement possible.

A drawing measuring 10 cm by 16 cm needs to be enlarged. The dimensions of the enlargement need to be 25 cm by 40 cm. Calculate the enlargement needed and express it as a ratio.

The angles of a triangle are in the ratio 2:5:8. Find the size of each of the angles.

If $f(x)=2 x+1,$ write the following in their simplest form: a) $\mathrm{f}(x+1)$ b) $f(2 x-3)$ c) $\mathrm{f}\left(x^{2}\right)$ d) $\mathrm{f}\left(\frac{x}{2}\right)$ e) $f\left(\frac{x}{4}+1\right)$ f) $\mathrm{f}(x)-x$

A photocopier enlarges in the ratio 7:4. What would be the new size of a diagram measuring 16 cm by 12 cm?

The triangle is to be reduced by a ratio of 1: 2

A swimming pool is filled in 30 hours by two identical pumps. How much quicker would it be filled if five similar pumps were used instead?

The scale of a map is 1:10000. a) Two rivers are 4.5 cm apart on the map, how far apart are they in real life? Give your answer in metres. b) Two towns are 8 km apart in real life. How far apart are they on the map? Give your answer in centimetres.

A marathon race is 42 195 m in length. The world record in 2016 was 2 hrs, 2 mins and 57 seconds held by Dennis Kimetto of Kenya.

a How many seconds in total did Kimetto take to complete the race?

b Calculate his average speed in m/s for the race, giving your answer to 2 decimal places.

c What average speed would the runner need to maintain to complete the marathon in under two hours?

A worker in a sugar factory packs 24 cardboard boxes with 15 bags of sugar in each. If he had boxes which held 18 bags of sugar each, how many fewer boxes would be needed?

A photograph measuring 8 cm by 6 cm is enlarged by a ratio of 11: 4. What are the dimensions of the new print?

The table below represents the relationship between the speed and the time taken for a train to travel between two stations.

$$\begin{matrix} \text{Speed (km/h)} & \text{60} & \text{ } & \text{ } & \text{120} & \text{90} & \text{50} & \text{10}\\ \text{Time (h)} & \text{2} & \text{3} & \text{4} & \text{ } & \text{ } & \text{ } & \text{ }\\ \end{matrix}$$

Copy and complete the table.