The eight OMPT algebra mistakes I see on every 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 exhibits; this year it has grown from five rooms to eight. These errors appear on every variant, because algebra is the shared spine from OMPT-A to OMPT-G, and the format is unforgiving of them. On the A, C and E the system scores the final answer only, so one mechanical slip erases an otherwise perfect solution. On the D and F your written notes can rescue partial credit, but the rubric pays a fraction for the step, never the whole question.

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: students get standalone inequality questions right and 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 term is 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 downstairs 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 accept your single answer without complaint, and the grading guidelines give partial scores when an exercise has several answers, so you get part of the point at best and none of it if the question was built around the root you dropped. 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.

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). An invented law here corrupts the exponential and logarithm chapters downstream, so drill exponents and roots first. Ten minutes of law-drills daily for a week rebuilds this completely, and since the basic on-screen calculator has no power key, the laws have to live in your head anyway.

Exhibit six: the log law that does not exist

This is exhibit five wearing a logarithm. The genuine laws turn products into sums, quotients into differences and powers into multipliers in front. The moment a student writes log(x² + 9) = 2 log x + 2 log 3, the rest of the question is dead. I see the mirror error just as often: log a + log b written as log a · log b. On the OMPT-A the exponential and logarithm chapter is worth 10%, and the F goals name logarithmic equations explicitly. The logarithms drills are the fix, and the check needs no calculator: try a = 10 and b = 100 in your head, since log 110 is not 3.

Exhibit seven: the forgotten domain

The algebra above is fine right up to the last comma, and the last comma is where the point is. A logarithm needs a positive argument and a square root a non-negative one, so x = -2 was never a candidate: log(-2) does not exist. Students who nail exhibit four and keep both roots then lose the point by keeping one the equation forbids. The same trap sits under √(x-2) = x-4, where squaring produces x = 3 as a false extra. Before you touch the equation, write the domain in the margin (x > 3 here), and after you solve, cross out anything outside it. On the D, domain and asymptote questions sit inside a block worth 30%. Drill it in function basics.

Exhibit eight: the minus that stops at the first term

A negative sign in front of a bracket multiplies every term inside, and the second term is the one that gets forgotten. The wrong version, 3 - 2x - 5, is what happens when the minus reaches 2x and then runs out of energy. It appears most often at the very end of an otherwise correct solution, where the final line comes out wrong by twice the second term. My fix is mechanical: during practice, rewrite -(2x - 5) as (-1)(2x - 5) and distribute the -1 like any other number, writing both products before simplifying. It slows you down for a week and then becomes invisible; the linear equations drills supply the brackets.

The eight exhibits side by side

The 30-second checking pass

Whenever a question leaves you spare seconds, spend them on a structured check rather than a vague re-read. Students hear "check your work" their whole lives and nobody shows them what it means. It means this, in this order.

1. Read the stem once more and underline what it asks for: a value, a set of values, an expression, or a decimal. "Solve" means every solution and only the legal ones.
2. Substitute your answer into the original equation, not into your second line, and watch it balance. This catches lost roots, sign slips and domain violations in ten seconds.
3. If the answer is an expression, test it with small numbers: a = 1 and b = 2 for brackets, x = 0 for a subtracted bracket. One disagreement means the algebra is wrong.
4. Look at every fraction you simplified and ask whether you cancelled a factor or a term. If the word "term" comes up, undo it.
5. Look at the form. The help centre expects exact answers unless a decimal is asked for: -2/17 scores and -0.12 does not. The calculator rules post covers how to type each form.
6. If a step failed, fix the line where it failed rather than the final answer, then run steps two and three again.

Where algebra bites on each OMPT variant

The official learning-assessment pages give a weight to each chapter, and they show why "it is only algebra" is a dangerous sentence. On some variants algebra is the biggest block on the paper; on the others it hides inside calculus questions, where the slip costs a differentiation point instead.

If you are sitting the C, sort the eight exhibits and you have sorted most of the paper. If you are sitting the B or the D, do not skip algebra drilling because the weight looks small: the marking does not care whether the calculus step or the simplification step went wrong.

Two students, two error logs

Student one is applying to International Business at Maastricht, where the OMPT-A bar is 75% and a score between 70 and 74% goes to an individual review. Her timed mock came back at 71%. The error log across three mocks showed nothing wrong in differentiation and nine wrong answers spread over exhibits two, four and eight, plus two decimals where the question wanted a fraction: a student who knows the maths and is throwing away roughly ten points on mechanics. The prescription was a week on notable products and quadratics, the checking pass drilled until automatic, and no new content. Her fourth mock scored 82%.

Student two is sitting the OMPT-D for a computer science programme with a 60% cutoff and two attempts at most. His notes are good and the D graders pay partial credit per step, so exhibits three and eight cost him fractions of questions. Exhibit seven was the expensive one: on an asymptote question he found the vertical asymptote correctly and then reported a domain that included the very value he had just excluded, a wrong final answer with credit for the working. On a 21-question paper, one full question is close to 5% of the score. His fix was the margin habit: domain first, every time. Both students used the score estimator to price each exhibit before choosing where to spend the week.

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, at a tenth of the time. It is not glamorous, but neither is a 73% against a 75% cutoff; the passing scores post lists how thin those margins are, and the sample questions walkthrough shows the exhibits inside real question shapes.