Adding ± to a square root
From \(\sqrt{x}=3\), conclude \(x=9\), not \(x=\pm9\). The symbol \(\sqrt{x}\) is the principal non-negative root.
TMUA TRAP BANK
20 mistakes that cost marks even when the mathematics is known.
Strong students often lose TMUA marks through a logical or structural slip rather than lack of content. Use this list as a pre-mock checklist.
Forgetting the logarithm domain
Solve the algebra only after recording that every logarithm argument is positive and every base is valid.
Squaring without checking
A squaring step can create extraneous roots. Final substitution is part of the solution.
Cancelling a zero factor
If you divide by \(x-a\), record \(x=a\) first. It may be a genuine solution or a crucial excluded case.
Confusing roots with distinct roots
A repeated root counts once when the question asks for distinct solutions.
Ignoring endpoints
A strict inequality, a closed interval and a tangency boundary can change a count by one.
Using a discriminant without the leading-coefficient condition
For a quadratic positive for all real \(x\), you need both an upward opening parabola and no real roots.
Assuming a graph transformation acts on the output
In \(f(|x|)\), the absolute value changes the input. Only the non-negative input side of \(f\) is sampled.
Solving a recurrence by brute force
Check fixed points, reciprocals, telescoping, invariants and cycles before calculating dozens of terms.
Using the GP sum formula without convergence
For a sum to infinity, verify \(|r|<1\) before applying \(a/(1-r)\).
Treating area as signed integral
If the graph crosses the axis and the question asks for area, split at the roots and use positive contributions.
Applying the trapezium rule to the wrong ordinates
For a modulus graph, sample the modulus values themselves, not the signed polynomial values.
Differentiating before simplifying
Rational powers often turn a difficult-looking expression into a one-line derivative after simplification.
Finding stationary points but not classifying sign changes
A derivative equal to zero is not automatically a maximum or minimum.
Counting polynomial roots without turning heights
For parameter equations, differentiate first, evaluate the original polynomial at turning points, then compare the horizontal level.
Using a trig identity outside its useful direction
Choose the form that exposes a bounded variable such as \(\sin x\), \(\cos x\) or \(\sin2x\).
Forgetting the ambiguous sine-rule case
\(SSA\) data can give zero, one or two triangles. A single calculator-style inverse sine is not enough.
Reversing necessary and sufficient
‘A only if B’ means \(A\Rightarrow B\). Write the arrow before reasoning.
Proving the converse
A correct proof of \(B\Rightarrow A\) does not establish \(A\Rightarrow B\). Paper 2 tests this constantly.
Trying to disprove a universal claim with algebra alone
One valid counterexample is enough. Search for boundary values, zero, one, negative values or a small integer first.
Turn traps into an error log.
After every mock or diagnostic, label each miss by cause: content gap, recognition delay, algebra slip, domain error, root-count error, or logic direction. Patterns are more useful than a raw percentage.
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Use free resources first. If they expose a gap, move into the full lecture notes, the 20-question diagnostics or timed mock papers.