UPCAT Math Review: Topics to Drill and a 12-Week Plan

UPCAT Math Review: Topics to Drill and a 12-Week Plan

Mathematics is one of the four UPCAT subtests, and it's where a lot of applicants lose ground — not because the math is advanced, but because they drill the wrong way and arrive on test day slow on word problems.

This post is the topic-by-topic plan that the UPCAT pillar guide hands off to. Use it to plan 12 weeks of math practice.

What UP publishes — and what it doesn't

UP lists Mathematics as one of four subtests in a paper-based test that takes about five hours, with no calculators allowed. It does not publish the number of math items, the time allotted, or a topic breakdown. Item counts and "percent per topic" tables you see online are guesses.

So build your scope from what you've been taught through Grade 10 and Grade 11 math, and train for two things the test clearly demands: working without a calculator and reading word problems quickly.

Topic scope to drill

Algebra

Algebra word problems are the classic entrance-test staple — mixture, work-rate, age and distance-rate-time problems.

• Linear equations in one and two variables, including word problems
• Quadratic equations: factoring, the quadratic formula, the discriminant, sum and product of roots
• Systems of equations by elimination and substitution
• Exponents and radicals: rules, simplification, rationalising denominators
• Polynomials: operations, special products, factoring, synthetic division
• Linear and quadratic inequalities, including absolute value
• Arithmetic and geometric sequences and series
• Functions: domain, range, composition, inverse, reading graphs
• Basic logarithms and exponential equations

Most algebra word problems need one of three setups: two linear equations, a single quadratic, or a rate equation. Practise spotting which one a problem needs before you start calculating.

Geometry

Geometry rewards people who sketch quickly and label what they know.

• Triangles: angle sums, exterior angles, similarity, congruence, 30-60-90 and 45-45-90 triangles
• Circles: inscribed and central angles, tangents and chords, arc length, sector area
• Polygons: interior and exterior angle sums, areas of regular polygons
• Coordinate geometry: distance, midpoint, slope, equations of lines, circles and parabolas
• Area and volume of prisms, cylinders, pyramids, cones and spheres
• The Pythagorean theorem and its applications
• Similar triangles in word-problem form (shadows, scale drawings)

Trigonometry

• SOH-CAH-TOA on right triangles
• Unit-circle values for 0°, 30°, 45°, 60°, 90° and related angles
• Cofunctions of complementary angles
• The Pythagorean identity and its rearrangements
• Law of sines and law of cosines on simple triangles
• Basic trigonometric equations
• Angle of elevation and depression problems

Number sense and arithmetic

Without a calculator, clean arithmetic matters more than people expect.

• Divisibility rules, prime factorisation, GCF and LCM
• Percentages: increase and decrease, reverse percentages
• Ratios and proportions, direct and inverse variation
• Rates: speed, work, mixture, density
• Basic probability and counting (factorials, permutations, combinations with small numbers)
• Mental arithmetic with fractions and decimals

Statistics and data

• Mean, median, mode, range and weighted averages
• Reading bar charts, line graphs, pie charts and frequency tables

If you're in a STEM strand and have covered pre-calculus or basic calculus, keep that knowledge fresh, but put most of your time into the blocks above — they're the foundation of every entrance-test math section.

A 12-week math drilling plan

Assume 12 weeks, five days a week, 45 minutes a day — about 45 hours of practice.

Drill items, not chapters. Re-reading a textbook feels productive but doesn't build speed. Do the items, check them, and re-attempt the wrong ones a week later.

Guessing

UP's current bulletin doesn't state any deduction for wrong answers, and it doesn't publish a scoring formula either. Don't build a strategy around a penalty rule nobody can confirm. What does help: never leave an item blank because you ran out of time. Pace yourself, mark hard items, and come back to them.

Where Super Tutor fits

Super Tutor's UPCAT reviewer has a full mathematics subject — nine chapters, each in 11 study formats (summaries, study notes, flashcards, cheat sheets and more) — with practice quizzes at three difficulty levels and full UPCAT mock exams. When you get stuck on a problem, the AI tutor explains it step by step. Start free — 5-day trial, no card needed.

What to read next

Read the UPCAT pillar guide for the full review plan across all four subtests, then pair this math plan with the UPCAT Science review and the UPCAT Language and Reading review.