How to Read Long Numbers
How to Subtract with Negative Numbers
Nested Parentheses in the Order of Operations

Ten Pitfalls to Avoid on Basic Maths Tests

When you’re under pressure in a maths test, you’re bound to make some mistakes. But some mistakes are avoidable when you know how; there are also some mistakes you can learn to check for and put right.

Take care with your calculator

A machine is only as good as what you tell it to do. Calculators can be amazingly helpful when you use them effectively, but you should always work out rough answers for each step of your calculation so you can check you’re doing the right thing along the way.

You’re out of line!

When you draw a line graph, you plot a series of points on graph paper and join up the dots. Normally you get a smooth or at least smooth-ish curve.

But sometimes you go to draw the line and think, ‘Hang on! That point’s miles away from the others.’ Check that dodgy point very carefully – it’s not necessarily wrong, but be suspicious of it.

Make sure your answer makes sense

In almost every sum you do, ask yourself whether your answer looks plausible. Here are a few questions to ask about your answer:

  • Adding: Is your answer bigger than what you started with?

  • Taking away: Is your answer smaller than what you started with?

  • Real-life problems: Roughly what would you expect if you just guessed?

  • Probability: Is your answer between 0 and 1?

You can probably come up with dozens of similar checks. Before you even begin a question, try to think of as many criteria as possible that your answer has to satisfy.

Distinguish ‘more than’ and ‘at least’

This is one that everyone trips up on at least once. If you have to pack ‘at least a dozen pairs of socks’, then 12 pairs is a perfectly acceptable number. If you have to ‘take more than a dozen pairs’, then 12 is no longer good. You have to take more than 12, so 13 is the smallest number you can take.

Read the question

If you don’t read the question correctly, you get the wrong answer. You may be tempted to rush through and do the first thing that comes into your head – when you do, you mess up.

Take a breath, write down all the information you have, and ponder what the question is asking. Start calculating only after you’re fairly certain what you need to do.

Fathom the phantom forty minutes when solving time problems

Almost every unit you use in maths and science works on powers of 10: 100 centimetres make a metre, 1,000 grams make a kilogram, and so on. The only real exception is time, where 60 seconds are the order of the day.

When you try to do normal maths on time, you can end up ‘missing’ the 40-minute gap between the 60 minutes in an hour and the 100 whatevers that you use in other sums.

Get the wrong percentage

A couple of things commonly go wrong when you do percentages: you work out the percentage of the wrong thing, or you add when you’re meant to take away.

You can get around the ‘wrong thing’ problem by filling in the Table of Joy. To deal with the ‘add or take away’ problem, simply read the question carefully to see whether your answer needs to be higher or lower than the original number in the question.

The Table of Joy is a technique for figuring out what sum you need to do when you have two amounts you know to be proportional – that is, if you double the size of one, you double the size of the other. The Table of Joy looks like an oversized noughts and crosses grid.

Round too early

If you want to find an answer correct to, say, two decimal places, you may be tempted to round everything as you go along. This is normally okay in day-to-day life, but in a maths test it costs you some accuracy and leaves you with a slightly wrong answer. Instead, wait until the very end to round off your numbers. If you’re only working out an approximation, round early and often.

Mix up the mean, mode and median

‘Mode’ is another word for fashion. In maths, think of the mode of a set of numbers as the most fashionable, the most popular – the number that comes up most often.

In maths, the median is the number in the middle of a set of numbers. Try remembering that median sounds a bit like ‘medium’, which means ‘middling’.

The ‘mean’ is the meanest thing an examiner can ask: you have to add up everything in a list and then divide by the number of things in the list.

Forget to convert

In 1999, one of NASA’s Mars Orbiters disintegrated as it descended through the Martian atmosphere, at a cost of hundreds of millions of dollars.

The cause was traced back to a software error: one of the control programs used imperial units such as inches, and another program used scientific units such as metres. The two programs didn’t understand each other’s numbers and the mission went catastrophically wrong.

You can take two lessons from this story:

  • Whatever happens in your exam, you won’t make a spaceship blow up.

  • Even rocket science isn’t rocket science.

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The Three Types of Average – Median, Mode and Mean
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Parentheses and Powers in the Order of Operations
The Elements of Number Sets
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