Linear equations
Isolate the unknown, keep both sides honest. Sounds trivial until a fraction or a bracketed negative shows up; that is where I watch students drop easy points.
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Topic drills
OMPT topic drills, skill by skill
Every skill the seven OMPT variants test, drilled one page at a time. I group them the way the test thinks: five strands, roughly in the order you should study them. Each drill gives you six original problems with full worked solutions.
Algebra
5 drillsThe plumbing of the whole test. Every variant leans on these five skills, and most lost points I see in sessions trace back here, not to the fancy chapters.
Quadratic equations
Factoring, completing the square, and the abc-formula, plus knowing which one saves you a minute. The discriminant question format turns up on nearly every variant.
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Inequalities
One habit decides everything here: flip the sign when you multiply or divide by a negative. Quadratic inequalities add a sketch-the-parabola step most students skip at their peril.
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Exponents and roots
Power rules, fractional exponents, and rationalising denominators. The single most-reused skill on the whole test. Get it automatic before touching anything else.
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Polynomials and factoring
Expanding brackets is mechanical; factoring is pattern recognition. Difference of squares and common-factor extraction cover most of what the OMPT actually asks.
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Functions
6 drillsWhere notation starts doing real work. Domains, graphs, logs and inverses: the middle weight of the OMPT, and the strand that decides most A and B scores.
Function basics
Domain, range, and reading f(x) notation without flinching. Domain restrictions from roots and denominators are a reliable source of test questions.
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Linear and quadratic functions
Slopes, intercepts, vertices, and intersections. If you can find where a line meets a parabola quickly, a surprising share of the test opens up.
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Exponential functions
Growth and decay, solving a^x = b, and recognising when an exponential model applies. Pairs directly with logarithms — study them back to back.
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Logarithms
Log rules, change of base, and solving logarithmic equations. In my sessions this is the topic with the widest gap between "seen it" and "can do it under time".
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Rational functions
Fractional functions: asymptotes, excluded values, and solving equations with x in the denominator, where multiplying through without checking creates phantom solutions.
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Inverse and composite functions
Chaining functions and undoing them. The mechanical part is easy; the traps are order of composition and domain after inversion.
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Trigonometry
4 drillsUnit circle first, everything else second. Only B, D and G test trig, but for those variants it is a full chapter you cannot talk your way around.
Angles and radians
Radians are the native language of the OMPT trig chapters. Converting fluently and knowing the unit-circle landmarks by heart is non-negotiable.
BDG
Trigonometric functions
Sine, cosine, tangent as functions: graphs, amplitude, period, and exact values. Learn the unit circle once, properly, and half this topic is free.
BDG
Trigonometric identities
The Pythagorean identity and the double-angle formulas do nearly all the work. The skill is spotting which rewrite turns the question into arithmetic.
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Trigonometric equations
Solving sin(x) = c means finding every solution in the interval, not just the calculator one. The forgotten second solution is the classic lost mark.
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Calculus
5 drillsDerivatives carry the load; integrals appear on B and D. The rules are few; the OMPT tests whether you apply them without a wobble under time.
Limits
Limits at infinity and around excluded points, mostly via algebraic simplification. On the OMPT this stays computational — no epsilon-delta in sight.
D
Differentiation rules
Power, product, quotient, and chain rule. Chain rule with a function inside a function inside a power is the OMPT's favourite way to separate the prepared from the hopeful.
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Applications of derivatives
Tangent lines, extreme values, and optimisation. The derivative is the tool; the question is really about translating a situation into f'(x) = 0.
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Integration basics
Antiderivatives and definite integrals as area. Reverse the power rule, mind the +c, and check by differentiating, a ten-second habit that catches most slips.
BD
Integration techniques
Substitution carries the load at OMPT level. Recognising the inner function and its derivative sitting next to each other is the entire game.
BD
Probability & statistics
4 drillsOMPT-E territory. Counting, chance and summary statistics — light arithmetic, heavy notation, and the strand with the least prep material anywhere else.
Counting and combinatorics
Permutations versus combinations: does order matter? Answer that one question correctly and the formulas pick themselves.
E
Probability basics
Sample spaces, complements, and the addition and multiplication rules. Conditional probability is where intuition fails and the formula must take over.
E
Random variables
Expected value, variance, and reading a probability distribution table. The arithmetic is light; the notation is what needs rehearsal.
E
Descriptive statistics
Mean, median, quartiles, standard deviation — and knowing which one a skewed dataset breaks. OMPT-E leans on these harder than most students expect.
E
Not sure which of these your variant covers? Each drill lists the variants that test it, and every test hub links back to its own topics.