Chapter 5: Review

Resolve the chapter problem

The garden path is 18 m long. At 1 cm for each metre, its drawing length is 18 cm, so it fits on a 30 cm page. If the page uses a different scale, convert metres to centimetres first, then apply the scale factor. The drawing and real path keep the same length ratio.

Mixed practice

Choose a method before calculating. Say why it fits.

1. Simplify $21:35$. Which common factor do you use?
2. Share £84 in the ratio $2:5$. How many ratio parts represent the total?
3. $y$ is directly proportional to $x$. If $y=24$ when $x=6$, find $y$ when $x=11$.
4. Higher only. $y$ is inversely proportional to $x$. If $y=15$ when $x=4$, find $y$ when $x=10$.
5. A map uses scale $1:100\,000$. Work out the real distance represented by 6.5 cm.
6. Higher only. Similar shapes have length scale factor 4. Work out the area and volume scale factors.
7. A temperature rises from $-3^\circ$C by $8^\circ$C. Work out the new temperature. Which earlier number method applies?

Look back

Write one method you can now use with confidence. Name one question type you want to practise again. Return to your connection from the chapter opener: did you notice another use for ratios?