Math

For many students, the Mathematics subtest is one of the most challenging parts of the UPCAT. The good news is that the exam emphasizes fundamental concepts rather than advanced mathematics. If you have a solid grasp of your high school lessons, you’ll already have a strong foundation.

Algebra

A large portion of the Math subtest focuses on algebra. Be prepared to answer questions involving the real number system, solving linear equations and inequalities, exponents, radicals, sets and set notation, graphing linear equations, factoring, quadratic equations, functions, and mathematical word problems.

Occasionally, you may also encounter questions about sequences, series, progressions, and logarithms. However, these topics appear much less frequently, so it’s more practical to spend most of your review time mastering the core algebra concepts.

Statistics and Probability

The UPCAT also includes questions on introductory statistics and probability. Common topics include the Fundamental Counting Principle, permutations and combinations, probability, measures of central tendency (mean, median, and mode), and basic data interpretation.

These questions often test your ability to analyze information rather than simply memorize formulas, so make sure you understand when and how each concept is applied.

Geometry

Geometry questions cover the essential concepts you’ve learned throughout junior and senior high school. Expect topics such as points, lines, planes, angles, parallel lines, triangles, congruence, polygons, circles, perimeter, area, surface area, and volume.

Many problems require you to apply geometric theorems and postulates to solve practical situations or analyze diagrams. Since the UPCAT is a multiple-choice exam, you won’t be asked to write formal proofs. However, strong logical and deductive reasoning skills are still important when solving geometry questions.

Trigonometry

Trigonometry appears only occasionally on the UPCAT. When it does, the questions are usually limited to basic trigonometric ratios (sine, cosine, and tangent) and simple applications involving right triangles.

There’s no need to spend excessive time on advanced trigonometry unless you’ve already mastered the more common topics.

Should You Study Calculus?

Not really. Calculus has little to no presence on the UPCAT. Instead of reviewing advanced topics, focus your efforts on strengthening your understanding of basic algebra, geometry, statistics, and problem-solving techniques. Mastering these fundamentals will give you a much better chance of earning a high score on the Mathematics subtest.

Math Subtest Review Tips

Preparing for the UPCAT Math subtest isn’t about mastering advanced mathematics—it’s about building a strong foundation. Most questions are based on concepts you’ve already learned in junior and senior high school. Here are some practical tips to help you review effectively:

• Master the fundamentals. Focus on the core concepts of arithmetic, algebra, geometry, and statistics before moving on to more advanced topics. A solid understanding of the basics will make solving complex problems much easier.

• Practice the four basic operations. Addition, subtraction, multiplication, and division should become second nature. Since calculators are not allowed during the UPCAT, you’ll need to perform calculations quickly and accurately on your own.

• Improve your mental math skills. Memorize multiplication tables, practice long division, and work on performing calculations without a calculator. Strong mental computation skills can save valuable time during the exam.

• Become comfortable with fractions, decimals, and percentages. Make sure you can add, subtract, multiply, and divide fractions, convert between fractions, decimals, and percentages, and simplify your answers correctly. These concepts appear frequently in UPCAT questions.

• Review basic trigonometry. Although trigonometry isn’t a major focus of the exam, it’s worth studying the basic trigonometric ratios (sine, cosine, and tangent) and their simple applications. Advanced trigonometry and calculus are generally unnecessary.

• Understand formulas instead of memorizing them. Rather than trying to memorize every mathematical formula, learn why each formula works and when it should be applied. A deeper understanding will help you solve unfamiliar problems more effectively.

• Strengthen your English comprehension. Many Math questions are presented as word problems. Improving your reading comprehension will help you identify the information being asked and avoid careless mistakes.

• Practice with mock exams and review questions. Regular practice is one of the best ways to prepare. Taking timed practice tests will help you become familiar with the exam format, improve your speed, and identify topics that need more attention.

• Use reliable learning resources. If you need extra help, supplement your review with quality textbooks, review centers, or educational platforms such as Khan Academy, PatrickJMT, and other reputable math tutorial channels.

• Study consistently instead of cramming. Mathematics is a skill that improves with regular practice. Solving a few problems every day is far more effective than trying to review everything in a single weekend.

Remember, the UPCAT Math subtest rewards students who have mastered the fundamentals and know how to apply them in different situations. Consistent practice, conceptual understanding, and strong problem-solving skills will give you the confidence to perform well on exam day.

Reading Comprehension

The Reading Comprehension subtest measures more than just your ability to read—it evaluates how well you understand, interpret, and analyze written and visual information. Strong reading skills are essential not only for this section but also for succeeding in many of the other UPCAT subtests.

What Topics Are Covered?

Expect questions that test your ability to identify the main idea, understand context clues, make inferences, draw logical conclusions, recognize the author’s purpose, and interpret figurative language such as similes, metaphors, and other figures of speech.

Rather than focusing on memorized facts, this section challenges you to think critically about the information presented in a passage.

Types of Reading Materials

The passages used in the UPCAT come in different formats and writing styles. You may be asked to read short stories, essays, news articles, poems, speeches, excerpts from plays, comic strips, or other informational and literary texts.

In some cases, you’ll also encounter graphs, tables, charts, or diagrams. These require you to interpret visual information and answer questions based on the data presented.

Because every passage is different, it’s important to adapt your reading strategy depending on the type of material you’re given.

Reading Comprehension Review Tips

One of the most effective test-taking strategies is to read the questions before reading the passage. Doing this gives you an idea of what information to look for, allowing you to read with a clear purpose instead of trying to memorize every detail.

As you read, pay close attention to the author’s main point, supporting details, tone, and the relationships between ideas. Avoid getting stuck on unfamiliar words—use the surrounding sentences as context to infer their meaning whenever possible.

To improve your reading speed and comprehension, make it a habit to read a variety of materials, such as books, newspapers, feature articles, editorials, and academic essays. Challenge yourself by summarizing what you’ve read and explaining the main idea in your own words.

Finally, practice answering comprehension questions under timed conditions. The more you expose yourself to different passage types, the more confident and efficient you’ll become on exam day.