# Exam-Style Question on Algebra

## A mathematics exam-style question with a worked solution that can be revealed gradually

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Question id: 129. This question is similar to one that appeared on a GCSE Higher paper (specimen) for 2017. The use of a calculator is allowed.

Rätselzeit school has an annual sports day in which the mathematics teachers are in charge of the scoring system.

The points scored for throwing the discus are worked out using the formula:

$$p = 15(d – 4.2)$$

where $$p$$ is the number of points scored when the discus is thrown a distance of $$d$$ metres.

(a) How many points does Homer score for throwing the discus a distance of 52 metres?

(b) How far did Marge throw the discus if she scored 492 points?

The points scored for running 400 metres are worked out using the formula:

$$p = 6(95 – t)^2$$

where $$p$$ is the number of points scored when the time taken is $$t$$ seconds.

(c) Lisa scores 1014 points for the 400 metres race. Work out the time, in seconds, it took Lisa.

The formula for the number of points scored in the 400 metres race should not be used for $$t\gt n$$.

(d) State the value of $$n$$ giving a reason for your answer.

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