GED and HiSET maths — the arithmetic of ordinary life

A formula sheet is provided on both papers, which tells you where the marks are not. They are not in remembering that the area of a rectangle is length times width. They are in deciding what to work out, and in finishing the job — rounding the right way, taking the fee off before dividing, noticing that a percentage has changed its base.

Ten questions in the shapes both exams use, all of them from adult life. A coat cut by twenty per cent and then raised by twenty per cent, which does not return to its old price and is worth understanding rather than memorising. A length of timber in feet and eighths. A taxi fare with a flat charge in it, where three of the four answers are the three ways the two steps go wrong. A painter's budget written as an inequality. A draining tank, where the question is what one number in the equation means in litres and minutes. A ladder against a wall. A floor and a tin of paint that covers six square metres. Five days of profits where the median and the mean are sixty dollars apart. And ten pens in a box.

Every explanation does the arithmetic step by step and names the mistake behind each wrong answer — the wrong base, the fee not subtracted, the fraction subtracted without a common denominator, the quotient rounded down when paint is being bought, the mean given when the median was asked for. That last pair is worth a moment on its own: in the profits question the mean is 210 and the median is 150, and knowing which one the question asked for is the entire difference between the two answers.

Nothing here needs a calculator, though one is allowed on both papers. There are no diagrams: every shape is described in words, and for anything that depends on reading a drawn figure or a graph, use the free practice tests both organisations publish.

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• Apply a percentage change to the correct base, and explain why a cut and a rise of the same percentage do not cancel
• Add and subtract mixed numbers by finding a common denominator first
• Write a linear equation or inequality from a described situation and solve it, handling a fixed fee correctly
• Say what the coefficient in a linear model means in the units of the thing being measured
• Use the Pythagorean theorem in a practical situation, and work out an area and convert it into whole units bought
• Find a median and know when it differs from a mean and by how much
• Compute a simple probability, including the probability of an event not happening

A shop sells a coat for 100 dollars. During a sale, the price is reduced by 20 percent. The following week, the shop increases the new price by 20 percent. What is the final price of the coat?