Common mistakes in TMUA Paper 1

Doing more algebra than the options need

TMUA Paper 1 asks you to apply mathematical knowledge in new situations. Writing out long algebra doesn't earn anything extra. If the options differ by sign, by a factor, by an interval or by rough size, a full expansion may be time you don't get back.

Get into the habit of reading the options before you choose a method. Using them this way is fair: they tell you what the question actually needs you to decide.

An example: a quadratic you don't need to expand

Suppose a question asks for all the solutions of (x − 2)(x + 5) = (x − 2)(3x − 1). The options are 'x = 2 only', 'x = 3 only', 'x = 2 or x = 3', 'x = −2 or x = 3' and 'no real solutions'.

The long way is to expand both sides: x² + 3x − 10 = 3x² − 7x + 2. Collecting terms gives 2x² − 10x + 12 = 0, so x² − 5x + 6 = 0, which factorises to (x − 2)(x − 3) = 0. It works, but there are several lines where a sign could go wrong.

The short way is to notice that (x − 2) appears on both sides. Move everything to one side and take it out as a factor: (x − 2)((x + 5) − (3x − 1)) = 0, which is (x − 2)(6 − 2x) = 0. So x = 2 or x = 3, in one line.

Now look at the option 'x = 3 only'. That's what you get if you divide both sides by (x − 2), which throws away the solution x = 2. Wrong options are often built from a mistake like this one. If an answer comes very easily, check you haven't lost something on the way.

Graph questions that look easy

Graph questions can look gentle and still cost you a mark. The usual places to go wrong are intercepts, asymptotes, turning points, transformations and restricted domains.

For example, y = f(x − 2) is the graph of y = f(x) moved 2 to the right. Moving it to the left is an easy mistake to make. The graph of y = 1/(x − 2) + 3 has a vertical asymptote at x = 2 and a horizontal one at y = 3. If you sketch quickly and put the vertical asymptote at x = −2, there may well be an option drawn that way.

When you review, write down the feature you didn't check. 'Graph error' is too vague to practise. 'Moved the graph the wrong way for f(x − 2)' or 'ignored the restricted domain' gives you something specific to work on.

Correct answers that took too long

Paper 1 gives you 75 minutes for 20 questions. A correct answer that took you six minutes still scores one mark, but it uses time you needed for later questions, and on a harder paper it might have been a wrong answer.

Go through slow correct answers as carefully as wrong ones. Ask what the quickest method would have been: substituting a value, using symmetry, finding a counterexample, testing the options, or a standard identity.

Keeping a log of your mistakes

TMUA papers are short, so vague feedback doesn't help much. Keep a log where each mistake gets a name, and read it back once a week.

One wrong answer on its own doesn't tell you much. If the same mistake turns up in two mocks, such as dividing by a factor that could be zero, make it the next thing you practise.