UPCAT Math Review: The Topics That Actually Show Up

UPCAT Math Review: The Topics That Actually Show Up

The UPCAT Math sub-test is where most applicants lose the percentile points that move them out of contention for UP Diliman programmes. Not because the math is hard — it isn't, by international standards — but because applicants drill the wrong topics and arrive on test day with shallow coverage of what UP actually asks.

This post is the topic-by-topic breakdown that the UPCAT 2026 pillar guide hands off to. Use it to plan your 12 weeks of math drilling.

What UP actually tests

The Math sub-test runs roughly 60 items in 75 minutes — a pace of one item per 75 seconds. That's faster than most SHS final exams, and the pace is the first thing that breaks people who have only practised untimed. The items skew applied: word problems with a small bit of arithmetic dressed up in an unfamiliar context.

The five major topic blocks, in rough order of how often they appear:

Topic shares move 2–4% cycle to cycle. The block ordering above has been stable across the last five UPCAT releases including the 2023 computer-based pilot.

Topic-level scope (what to drill)

Algebra — the workhorse

UP loves algebra word problems. Mixture problems, work-rate problems, age problems, distance-rate-time. The math is grade-9 — the trap is reading speed.

Drill list:

• Linear equations in one and two variables, including word problems
• Quadratic equations: factoring, quadratic formula, discriminant, sum/product of roots
• Systems of equations (2×2 and 3×3 by elimination/substitution)
• Exponents and radicals: rules, simplification, rationalising denominators
• Polynomial operations and factoring (special products, grouping, synthetic division)
• Linear and quadratic inequalities, including absolute value
• Arithmetic and geometric sequences and series
• Functions: domain, range, composition, inverse, basic graph reading
• Logarithms and exponential equations (basic only)

UP's algebra word problems usually need one of three setups: a system of two linear equations, a single quadratic, or a rate equation. If you can recognise which of the three is being asked within 20 seconds, you've solved 80% of the algebra block before touching the math.

Geometry — the visual one

Geometry items reward people who sketch fast. Most items can be solved by drawing a clear figure and labelling what's known.

Drill list:

• Triangle properties: angle sums, exterior angle, similarity, congruence, special right triangles (30-60-90, 45-45-90)
• Circle theorems: inscribed angle, central angle, tangent-chord, arc length, sector area
• Polygon properties: interior/exterior angle sums, regular polygon area
• Coordinate geometry: distance, midpoint, slope, line equations, conics (circle and parabola)
• Area and volume of standard solids (prisms, cylinders, pyramids, cones, spheres)
• Pythagorean theorem and its applications
• Similar/congruent triangles in word-problem form (shadow problems, scale drawings)

The 30-60-90 and 45-45-90 ratios appear nearly every cycle. Memorise them cold.

Trigonometry — narrower than you think

UPCAT trig is mostly right-triangle ratios and unit-circle values. Identities show up but rarely the deep ones.

Drill list:

• SOH-CAH-TOA on right triangles
• Unit circle values for 0°, 30°, 45°, 60°, 90° and their reflections
• Sine and cosine of complementary angles
• Pythagorean identity (sin²θ + cos²θ = 1) and its rearrangements
• Law of sines and law of cosines on simple triangles
• Basic trig equations (one or two solutions per cycle)
• Angle of elevation / depression word problems

Skip the deep identity proofs (sum-to-product, product-to-sum). They almost never appear and the time you'd spend learning them is better spent on algebra word problems.

Number theory & arithmetic — the easy points

This block is where prepared candidates pick up nearly free items.

Drill list:

• Divisibility rules (especially for 3, 4, 6, 9, 11)
• Prime factorisation, GCD, LCM
• Percentages: increase/decrease, percent of, reverse percent
• Ratios and proportions, including direct and inverse variation
• Rates: speed, work, mixture, density
• Basic probability (single event, mutually exclusive, simple combinations)
• Basic counting (factorials, permutations, combinations on small n)

If you're scoring under 70% on this block in a mock, your math review hasn't started yet. Fix this first.

Statistics & basic calculus — keep it light

UP's statistics block is descriptive only — mean, median, mode, range, basic data table reading. Calculus appears in 2–4 items per cycle and is always a single concept asked at a single point.

Drill list:

• Mean, median, mode, range, simple weighted average
• Reading bar charts, line graphs, pie charts, simple frequency tables
• Limits at a point (algebraic substitution; the indeterminate-form trick on simple cases)
• Derivative as a slope at a point (no chain rule, no implicit differentiation)
• Tangent line at a point on a polynomial

If you're not in a STEM strand and calculus is unfamiliar, learn the derivative-as-slope intuition only. That single concept covers two of the four typical calculus items per cycle. The other two you can leave blank without dropping below your target percentile.

A 12-week math drilling plan

Assume 12 weeks before the test, 5 days a week of math work, 45 minutes per day. That's 45 hours of drilling — enough to move from the 50th to the 80th percentile if you start at the median.

Drill items, not concepts. The trap people fall into is "studying" the topic by re-reading textbook chapters. UPCAT items are pattern-recognition under time pressure. Pattern recognition is built by doing items, scoring them, and re-attempting the wrong ones a week later.

The negative-marking math

UPCAT deducts a fractional value for wrong answers (historically about one-third of a point per wrong answer; UP publishes the exact value each cycle in the bulletin). Practical consequence on the math sub-test:

• If you can eliminate two of four options, guess. The expected value is positive.
• If you can eliminate one option, guess only if you have a leaning toward one of the remaining three. Pure 1-in-3 guessing is roughly break-even after the deduction.
• If you can eliminate none, leave it blank.

Five blank items hurt less than five random fills. Build the discipline in your mocks.

Where Super Tutor fits

Super Tutor's UPCAT Math track follows the 12-week structure above, surfaces the topics you're slowest on, and runs the mocks for you. The Free tier covers algebra and number theory in full; the Focused plan (₱49/week, ₱249/month, ₱1,999/year) opens the geometry, trig, and calculus blocks plus the full-length mocks.

What to do next

Read the UPCAT 2026 pillar guide for the full review plan across all four sub-tests, then pair this math plan with the UPCAT Science review and UPCAT Language and Reading review. When you're ready, start a free UPCAT mock on Super Tutor to baseline where your math currently sits.