1. Write the ratio $3:8$ as a fraction of the total for the first part.

Answer: $3/11$.

2. In the ratio $2:5$, what fraction of the total is the second part?

Answer: $5/7$.

3. For the ratio $y:x=4:3$, complete $y$ when $x=9$.

Answer: $y=12$.

4. For $y=6x$, find the constant of proportionality.

Answer: The constant is $6$.

5. A printer makes 18 labels in 3 minutes at a constant rate. How many labels in 7 minutes?

Answer: 42 labels.

6. A sum is shared in the ratio $3:7$. What fraction goes to the smaller share?

Answer: $3/10$.

7. A straight-line graph passes through $(0,0)$ and $(4,20)$. Find the multiplier from $x$ to $y$.

Answer: The multiplier is $5$, so $y=5x$.

8. If $y=2.5x$, find $y$ when $x=12$.

Answer: $30$.

9. If $y=7x$ and $y=63$, find $x$.

Answer: $x=9$.

10. If $a:b=5:2$ and $b=14$, find $a$.

Answer: $a=35$.

11. A taxi fare is £3 plus £1.80 for each kilometre. Work out the fare for 4 km.

Answer: The fare is £10.20.

12. Explain why $y=3x+2$ is not directly proportional to $x$.

Answer: When $x=0$, $y=2$, so the graph does not pass through the origin.