The algebra mistakes I see on every OMPT mock

I mark a lot of mocks. After a while the wrong answers stop looking random and start looking like a small museum with the same five exhibits. These errors appear on every variant, because algebra is the shared spine from OMPT-A all the way to OMPT-G, and the test format is unforgiving of them: a mock exam scores the final answer, so one mechanical slip erases an otherwise perfect solution.

Exhibit one: the unflipped inequality

Multiplying or dividing an inequality by a negative number reverses the sign. Everyone knows this rule in the abstract; under time pressure, hands are faster than rules. The tell is that students get standalone inequality questions right and then miss the same move buried in step three of a longer problem. The cure is a habit, not knowledge: every time you touch an inequality with a negative, say "flip" out loud during practice. Saying it feels silly, and it works. The inequalities drills are built to trip exactly this reflex until it holds.

Exhibit two: the squared bracket illusion

Writing (a+b)² = a² + b² is the single most common error in my marking, and it is sneaky because it feels like a distributive law. It is not. Squaring means multiplying the bracket by itself, and the cross terms are where the mathematics lives. The same illusion produces √(a²+b²) = a+b, equally wrong for the same reason. If you catch yourself doing either, spend an evening in polynomials and factoring expanding brackets the long way until the middle term stops feeling optional.

Exhibit three: cancelling across a sum

You may only cancel factors of the whole numerator and whole denominator. The x in the denominator divides the x² term happily, but it must divide the 3 as well, and it cannot. Correct is x + 3/x, a different object entirely. This error clusters in rational functions questions and in the simplification steps of calculus problems on the B and D. My test: before cancelling anything, ask "is this a factor of everything upstairs and everything downstairs?" If the answer involves the word "term", stop.

Exhibit four: the lost negative root

Both roots. The OMPT interface will happily accept your single answer and mark the question wrong, because half an answer set is a wrong answer. This one hurts because the student did the hard part correctly. Related and worse: dividing both sides of x² = 3x by x, which silently throws away the solution x = 0. Factor instead of dividing by things that might be zero. The quadratic equations drills hammer both habits.

Why smart students make dumb slips

A short detour, because students beat themselves up over these errors as if they signalled weak mathematics. They do not. Every one of the five is a plausible-looking overgeneralisation of a real rule, applied at speed: distribution stretched to squaring, cancelling stretched across addition. Your brain is pattern-matching exactly as trained, one pattern too far. That is also why "be more careful" fails as a fix. Care is a finite resource that runs out at question 40; a corrected reflex costs nothing forever. Train the reflex, spend the care elsewhere.

Exhibit five: invented exponent laws

The real laws cover products, quotients and powers of powers. There is no law for sums, and there is no law that turns (a+b)ⁿ into aⁿ+bⁿ (exhibit two in a different coat). Since exponents and roots feed the exponential and logarithm chapters where most OMPT points concentrate, an invented law here corrupts everything downstream. Ten minutes of law-drills daily for a week rebuilds this completely.

The checking pass that catches all five

Whenever a question leaves you spare seconds, spend them on a structured check rather than a vague re-read. Substitution is the workhorse: push your solution back into the original equation and watch it balance, which catches lost roots and sign slips in ten seconds flat. For expansions, test with small numbers: if your expansion of (a+b)² disagrees with a=1, b=2, the algebra is wrong, no eyesight required. Students hear "check your work" their whole lives and nobody shows them these two moves; they are the entire toolkit, and they run in well under thirty seconds.

A closing thought on why this matters more than hard topics. On a 52-question OMPT-A, suppose the last five questions are genuinely difficult for you and these mechanical slips cost you four points across the easy forty-seven. Fixing the slips is worth almost as much as mastering the hard tail, and it takes a tenth of the time. Cheap points first. It is not glamorous, but neither is a 73% against a 75% cutoff.