PSAT Data and Geometry — units, bases and figures in words

This is the half of the Math section where the arithmetic is easiest and the reading is hardest. Ten questions across both of its domains, and in most of them the calculation takes ten seconds once you have decided what is being asked.

Four are about quantities and what they are quantities of. A cyclist's speed, where the whole question is that 24 minutes is not 24 hours. A price rise, where the whole question is which number goes on the bottom. Seven test scores with one very high one, where the median stays at 15 and the mean climbs past 25 — the clearest demonstration available of what "resistant" means. And a line of best fit given as an equation with units attached, where the slope has to be read back as a sentence about hours and marks.

Two are the statistical ideas that are examined here without any arithmetic at all. A poll with a margin of error, where the tempting wrong answer is the confident one — that a candidate on 55 per cent "definitely" leads. And an observational study of green tea and blood pressure, where the tempting wrong answer is the causal one. Both come up on the real test, both are three sentences to learn, and both are routinely skipped by students revising formulas.

The rest is geometry, all of it described in words because there are no figures here: a 3-4-5 triangle scaled up, a right triangle where the three wrong answers are the sine, the cosine and the reciprocal of the tangent asked for, and a circle whose distractors include the circumference formula and the classic diameter-for-radius error, which always gives exactly four times the right area.

A formula sheet is provided in the real test, so nothing here rewards memorising an area formula. What it rewards is knowing which one the situation calls for.

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• Convert units before computing a rate, and recognise a correct ratio attached to the wrong unit
• Identify the correct base for a percentage change and reject the answer that divides by the new value
• Predict how one extreme value moves a mean and leaves a median unchanged
• Read the slope of a line of best fit back as a statement about the quantities being measured
• Compute a conditional probability by restricting to the right group
• State what a margin of error licenses and what it does not, and why an observational study cannot establish cause
• Use a scale factor between similar triangles, choose the right trigonometric ratio, and apply the area formula for a circle

A cyclist rides 9 kilometres in 24 minutes, keeping the same speed throughout. What is that speed in kilometres per hour?