Philippine Military Academy Entrance Examination (PMAEE) Study Guide

Algebra: translate the situation before solving

The PMA entrance examination includes algebra, and this guide treats algebra as a skill area for practice rather than as a complete official blueprint. A strong approach is to turn words into equations, keep units visible, and check whether the final value makes sense. For more administration-related information, use the PMAEE exam overview; for timed drills, use PMAEE practice.

Original worked example: A cadet candidate jogs 3 kilometers more than twice the distance walked during a warm-up. The total distance is 15 kilometers. How far did the candidate walk?

Let w be the walking distance. The jogging distance is 2w + 3. Total distance: w + 2w + 3 = 15. Combine like terms: 3w + 3 = 15. Subtract 3: 3w = 12. Divide by 3: w = 4. The candidate walked 4 kilometers and jogged 11 kilometers; together they total 15.

Common error: Many students write 2(w + 3) instead of 2w + 3. That changes “3 more than twice the distance” into “twice the distance plus 3 before doubling.” Read the phrase in chunks.

Action drill: Write one equation for each sentence: “five less than three times a number is 22,” “a number increased by 15 percent becomes 46,” and “two consecutive integers total 57.” Solve, then substitute your answer back into the original wording.

Geometry: use angle facts, not visual guessing

The PMA entrance examination includes geometry. For preparation, prioritize relationships you can prove from the information given: angle sums, right angles, parallel-line clues if supplied, perimeter, area, and basic coordinate movement. Do not trust a drawing unless the problem states the measurement; a sketch may be only approximate.

Original worked example: A quadrilateral has angles of 88 degrees, 104 degrees, and 79 degrees. What is the fourth angle?

A quadrilateral’s interior angles sum to 360 degrees. Add the known angles: 88 + 104 + 79 = 271. Subtract from the total: 360 - 271 = 89. The fourth angle is 89 degrees.

Second quick check: If a triangle has one right angle and another angle of 35 degrees, the third angle is 180 - 90 - 35 = 55 degrees because a right angle is 90 degrees and a triangle’s interior angles sum to 180 degrees.

Common error: Students often assume a shape is a rectangle because it “looks like one.” Unless the item says there are right angles, equal sides, or parallel sides, use only the stated facts.

Action drill: Create five angle questions on index cards: two triangle sums, two quadrilateral sums, and one equilateral triangle question. Solve without a calculator, then explain each answer in one sentence using the rule you applied.

Grammar and composition: make the sentence clean and controlled

PMA English coverage includes grammar and composition. Prepare by practicing sentence correction, paragraph order, concise wording, subject-verb agreement, pronoun reference, verb tense, modifiers, and punctuation. The goal is not to memorize fancy terms; it is to choose the version that communicates the idea clearly and correctly.

Original worked example: Choose the best revision: “The applicants submits their forms early, and the officer check the list.”

Best revision: “The applicants submit their forms early, and the officer checks the list.” The subject applicants is plural, so the verb should be submit. The subject officer is singular, so the verb should be checks. The pronoun their correctly refers to plural applicants.

Composition angle: If asked to improve a paragraph, look for the sentence that gives the topic, then place supporting details in a logical order. For example: “The team inspected the route. They assigned roles. They began the march.” This is clearer than jumping from the march back to planning.

Common error: Do not choose the longest option just because it sounds formal. Extra words can introduce errors or weaken the sentence.

Action drill: Each day, rewrite five sentences from your notes. Check one issue at a time: agreement, tense, pronouns, punctuation, then concision. Read the final sentence aloud to catch awkward structure.

Reading comprehension: prove every answer from the passage

PMA English coverage includes reading comprehension. Practice by separating what the passage says from what you already believe. A correct answer should be supported by a line, phrase, contrast, or overall pattern in the text.

Original passage: “At dawn, the patrol reached a narrow bridge after a night of rain. The river below was louder than usual, but the bridge posts stood firm. Instead of crossing immediately, the team leader sent two members to inspect the planks while the rest checked the equipment. Ten minutes later, they crossed one at a time, keeping distance between each person.”

Original question: What is the best inference about the team leader?

A. The leader feared all bridges. B. The leader acted cautiously because conditions had changed. C. The leader wanted to delay the mission for no reason. D. The leader knew the bridge would collapse.

Answer reasoning: Choice B is best. The passage says there had been rain, the river was louder than usual, and the leader ordered an inspection before crossing. That supports caution due to changed conditions. The passage does not say the leader feared all bridges, delayed without reason, or knew a collapse would happen.

Common error: Avoid answers that are more dramatic than the passage. “Possible” is not enough; the answer must be supported.

Action drill: Read one short article daily. Write the main idea in one sentence, underline two supporting details, and label one inference that is reasonable but not directly stated.

Verbal and numerical reasoning: find the relationship first

The PMA page lists verbal and numerical reasoning as part of its reasoning coverage. These items often test whether you can identify a relationship quickly, not whether you know a rare fact. For verbal reasoning, define the relationship between words. For numerical reasoning, identify the operation pattern before calculating.

Original verbal example: “Compass is to direction as thermometer is to ____.” Options: A. pressure, B. temperature, C. distance, D. weight. A compass is an instrument used to determine direction. A thermometer is an instrument used to determine temperature. The answer is B.

Original numerical example: Find the next number: 4, 9, 19, 39, 79, __. Each term is doubled, then 1 is added: 4 x 2 + 1 = 9, 9 x 2 + 1 = 19, and so on. Therefore 79 x 2 + 1 = 159.

Common error: Students sometimes force a familiar rule, such as “add the same number,” even when the differences are changing. Check at least two transitions before deciding.

Action drill: Make a two-column page. On the left, write 10 analogies using everyday tools and functions. On the right, write 10 number sequences using addition, multiplication, alternating operations, or squared numbers. For each item, write the relationship in words before the answer.

Pattern analysis: test the rule against every position

The PMA page lists pattern analysis as part of its reasoning coverage. Pattern items may use numbers, letters, symbols, rotations described in words, or grids. A safe method is to compare positions, identify what changes, and reject any rule that works only once.

Original pattern: Row 1: A3, C6, F10. Row 2: J15, O21, U28. What comes next if the same pattern continues?

Answer reasoning: Look at the letters by alphabet position: A is 1, C is 3, F is 6, J is 10, O is 15, U is 21. The letter jumps are +2, +3, +4, +5, +6, so the next jump is +7. U is the 21st letter; 21 + 7 = 28. Since the alphabet has 26 letters, wrap around: 28 becomes B. Now check the numbers: 3, 6, 10, 15, 21, 28. The differences are +3, +4, +5, +6, +7, so the next number is 36. The next term is B36.

Common error: Do not solve only the letters or only the numbers when both are changing. Mixed patterns may have two simultaneous rules.

Action drill: Build six patterns of your own: two letter sequences, two number sequences, and two mixed sequences. For each, write three wrong answers that follow only part of the rule.

Suggested 14-day PMAEE study plan

This is an unofficial study suggestion, not an official PMA requirement. Use it to organize the preparation areas above: algebra, geometry, grammar and composition, reading comprehension, verbal and numerical reasoning, and pattern analysis. For a compact review, use the PMAEE cheat sheet. For exam administration topics, use the PMAEE exam overview.

How to adapt after diagnostics

• If algebra and geometry are below your English scores, spend the next two study sessions on worked solutions rather than speed.
• If reading errors come from unsupported inferences, require yourself to quote the exact phrase that proves each answer.
• If reasoning errors come from rushing, reduce the number of items per drill and write the rule before answering.
• If careless errors are common, add a final 60-second review of signs, units, copied numbers, and answer choice letters.