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PMA Cadet Entrance Test study materials
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PMA Cadet Entrance Test practice questions

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Question 1Mathematics

A cadet runs 3.2 km on Monday, 2.75 km on Tuesday, and 4.05 km on Wednesday. What is the total distance run over the three days?

  1. 10.0 km Correct answer.
  2. 9.95 km
  3. 10.05 km
  4. 9.9 km

Explanation

Add the distances place by place: 3.20 + 2.75 = 5.95, and 5.95 + 4.05 = 10.00. Since the hundredths digits 0 + 5 + 5 give 10 hundredths, the tenths column gains one, so the total is exactly 10.0 km.

Question 2Mathematics

Simplify the expression 5(2x − 3) − 2(x − 4).

  1. 8x − 23
  2. 8x + 7
  3. 8x − 7 Correct answer.
  4. 12x − 7

Explanation

Distribute first: 5(2x − 3) = 10x − 15 and −2(x − 4) = −2x + 8. Combining like terms gives 10x − 2x = 8x and −15 + 8 = −7, so the result is 8x − 7.

Question 3Mathematics

A cadet's scores on four quizzes are 78, 85, 90, and 83. What is the mean score?

  1. 85
  2. 86
  3. 83
  4. 84 Correct answer.

Explanation

The mean equals the sum of the scores divided by the number of scores. The sum is 78 + 85 + 90 + 83 = 336, and 336 ÷ 4 = 84.

Question 4Mathematics

What is the value of 2³ × 2² ÷ 2⁴?

  1. 4
  2. 1
  3. 8
  4. 2 Correct answer.

Explanation

When multiplying powers with the same base, add the exponents: 2³ × 2² = 2⁵. Dividing by 2⁴ subtracts exponents, giving 2⁵⁻⁴ = 2¹ = 2.

Question 5Mathematics

A cadet leaves the barracks at 06:45 and arrives at the training ground at 08:10. How long is the journey?

  1. 1 hour 25 minutes Correct answer.
  2. 1 hour 15 minutes
  3. 1 hour 35 minutes
  4. 1 hour 45 minutes

Explanation

From 06:45 to 07:45 is one hour, and from 07:45 to 08:10 is a further 25 minutes. The total journey time is therefore 1 hour 25 minutes.

Question 6Mathematics

A rectangle has a length of 12 cm and a width of 7 cm. What is its perimeter?

  1. 42 cm
  2. 84 cm
  3. 19 cm
  4. 38 cm Correct answer.

Explanation

The perimeter of a rectangle is 2(length + width). Here 2(12 + 7) = 2 × 19 = 38 cm.

Question 7Mathematics

Which of the following fractions is equivalent to 0.375?

  1. 3/4
  2. 5/8
  3. 2/5
  4. 3/8 Correct answer.

Explanation

To convert 0.375 to a fraction, write it as 375/1000 and divide numerator and denominator by 125, giving 3/8. Checking, 3 ÷ 8 = 0.375.

Question 8Mathematics

Solve for x: 4x − 7 = 2x + 9.

  1. x = 4
  2. x = 8 Correct answer.
  3. x = 16
  4. x = 1

Explanation

Subtract 2x from both sides to get 2x − 7 = 9, then add 7 to both sides to get 2x = 16. Dividing by 2 gives x = 8.

Question 9Mathematics

A cadet's monthly allowance is 2,400 pesos. If 15% is set aside for savings, how much is saved each month?

  1. 180 pesos
  2. 240 pesos
  3. 300 pesos
  4. 360 pesos Correct answer.

Explanation

Fifteen percent means 15 per hundred, so multiply 2,400 by 0.15. Since 2,400 × 0.10 = 240 and 2,400 × 0.05 = 120, the sum is 360 pesos.

Question 10Mathematics

The angles of a triangle are in the ratio 2 : 3 : 4. What is the size of the largest angle?

  1. 90°
  2. 80° Correct answer.
  3. 60°
  4. 40°

Explanation

The angles of a triangle sum to 180°. The ratio has 2 + 3 + 4 = 9 parts, so one part is 180 ÷ 9 = 20°, and the largest angle is 4 × 20 = 80°.

Question 11Mathematics

A cadet walks 6 km due north and then 8 km due east. What is the straight-line distance from the starting point?

  1. 48 km
  2. 2 km
  3. 10 km Correct answer.
  4. 14 km

Explanation

The two legs are perpendicular, so they form a right triangle with legs 6 and 8. By the Pythagorean theorem the distance is √(6² + 8²) = √(36 + 64) = √100 = 10 km.

Question 12Mathematics

If f(x) = 3x² − 2x + 1, what is f(−2)?

  1. 17 Correct answer.
  2. −7
  3. 9
  4. 13

Explanation

Substitute x = −2: 3(−2)² − 2(−2) + 1 = 3(4) + 4 + 1. This gives 12 + 4 + 1 = 17.

Question 13Mathematics

A train travels 240 km in 3 hours and then 180 km in 2 hours. What is its average speed for the whole journey?

  1. 80 km/h
  2. 90 km/h
  3. 85 km/h
  4. 84 km/h Correct answer.

Explanation

Average speed is total distance divided by total time, not the average of the two speeds. The total distance is 240 + 180 = 420 km and the total time is 3 + 2 = 5 hours, so 420 ÷ 5 = 84 km/h.

Question 14Mathematics

What is the next term in the sequence 3, 7, 15, 31, ...?

  1. 63 Correct answer.
  2. 47
  3. 62
  4. 55

Explanation

Each term is one less than a doubling: 3 = 4 − 1, 7 = 8 − 1, 15 = 16 − 1, 31 = 32 − 1. The next term is therefore 64 − 1 = 63.

Question 15Mathematics

A circular running track has a radius of 35 m. Using π = 22/7, what is the circumference of the track?

  1. 110 m
  2. 220 m Correct answer.
  3. 154 m
  4. 770 m

Explanation

The circumference of a circle is 2πr. Substituting gives 2 × (22/7) × 35 = 2 × 22 × 5 = 220 m, since 35 ÷ 7 = 5.

Question 16Mathematics

Two cadets are chosen from a group of 5 to form a drill pair. How many different pairs are possible?

  1. 20
  2. 5
  3. 25
  4. 10 Correct answer.

Explanation

Because the order of the pair does not matter, this is a combination: C(5,2) = (5 × 4) ÷ 2 = 10. Dividing by 2 removes the double counting of each pair.

Question 17Mathematics

A cadet's score improved from 60 to 75. What is the percentage increase?

  1. 25% Correct answer.
  2. 20%
  3. 15%
  4. 30%

Explanation

Percentage increase is the change divided by the original value, multiplied by 100. The change is 75 − 60 = 15, and 15 ÷ 60 = 0.25, which is 25%.

Question 18Mathematics

If 3x + 2y = 16 and x = 2, what is the value of y?

  1. 4
  2. 7
  3. 6
  4. 5 Correct answer.

Explanation

Substitute x = 2 into the equation to get 6 + 2y = 16. Subtracting 6 from both sides gives 2y = 10, so y = 5.

Question 19Mathematics

What is the slope of the line passing through the points (2, 3) and (6, 11)?

  1. 1/2
  2. 4
  3. 8
  4. 2 Correct answer.

Explanation

Slope equals the change in y divided by the change in x. Here (11 − 3) ÷ (6 − 2) = 8 ÷ 4 = 2.

Question 20Mathematics

The sum of three consecutive even integers is 84. What is the largest of the three integers?

  1. 30 Correct answer.
  2. 28
  3. 32
  4. 26

Explanation

Let the integers be n, n + 2, and n + 4. Their sum is 3n + 6 = 84, so 3n = 78 and n = 26. The largest integer is 26 + 4 = 30.

Question 21Mathematics

A cube has a total surface area of 96 cm². What is its volume?

  1. 96 cm³
  2. 16 cm³
  3. 24 cm³
  4. 64 cm³ Correct answer.

Explanation

A cube has six congruent square faces, so each face has area 96 ÷ 6 = 16 cm² and each edge is √16 = 4 cm. The volume is 4³ = 64 cm³.

Question 22Mathematics

Simplify (x² − 9) ÷ (x − 3) for x ≠ 3.

  1. x − 3
  2. x + 3 Correct answer.
  3. x² − 3
  4. x + 9

Explanation

The numerator is a difference of squares: x² − 9 = (x + 3)(x − 3). Cancelling the common factor (x − 3) leaves x + 3, valid whenever x ≠ 3.

Question 23Mathematics

A cadet invests 5,000 pesos at 4% simple interest per year. After how many full years will the investment first exceed 5,600 pesos?

  1. 5 years
  2. 4 years
  3. 2 years
  4. 3 years Correct answer.

Explanation

Simple interest is I = Prt, so each year earns 5,000 × 0.04 = 200 pesos. The target gain is 600 pesos, and 600 ÷ 200 = 3 years, at which point the balance reaches exactly 5,600 and the following year exceeds it.

Question 24Mathematics

The roots of a quadratic equation are 2 and −5. Which equation has these roots?

  1. x² − 3x − 10 = 0
  2. x² − 7x + 10 = 0
  3. x² + 3x + 10 = 0
  4. x² + 3x − 10 = 0 Correct answer.

Explanation

If the roots are r and s, the equation is x² − (r + s)x + rs = 0. Here r + s = 2 + (−5) = −3 and rs = −10, giving x² + 3x − 10 = 0.

Question 25Mathematics

A bag contains 4 red and 6 blue marbles. Two marbles are drawn without replacement. What is the probability that both are red?

  1. 2/15 Correct answer.
  2. 8/45
  3. 1/5
  4. 4/25

Explanation

The probability the first marble is red is 4/10, and given that, the second is red with probability 3/9. Multiplying gives (4/10) × (3/9) = 12/90 = 2/15.

Question 26Mathematics

A cadet's canteen bill is 850 pesos. A 12% value-added tax is applied to the bill. How much is the total amount payable?

  1. 102 pesos
  2. 862 pesos
  3. 952 pesos Correct answer.
  4. 748 pesos

Explanation

The tax is 12% of 850, which equals 102 pesos, and the total payable is the original bill plus the tax: 850 + 102 = 952 pesos. Multiplying directly by 1.12 gives the same result.

Question 27Mathematics

A cadet platoon forms a square drill formation with 196 cadets arranged in equal rows and columns. How many cadets stand in each row?

  1. 24
  2. 18
  3. 14 Correct answer.
  4. 16

Explanation

A square formation has the same number of rows and columns, so the number per row is the square root of 196. Since 14 × 14 = 196, each row holds 14 cadets.

Question 28Mathematics

A cadet's water container holds 2.5 liters. How many milliliters is this?

  1. 250 mL
  2. 2,500 mL Correct answer.
  3. 25 mL
  4. 25,000 mL

Explanation

One liter equals 1,000 milliliters, so you multiply the number of liters by 1,000. Thus 2.5 × 1,000 = 2,500 milliliters.

Question 29Mathematics

During inspection, a cadet's height is recorded as 1.68 meters. Which value shows this height correctly rounded to the nearest tenth of a meter?

  1. 1.6 m
  2. 2.0 m
  3. 1.7 m Correct answer.
  4. 1.60 m

Explanation

Rounding to the nearest tenth means keeping one digit after the decimal point and checking the hundredths digit. The hundredths digit is 8, which is 5 or more, so the tenths digit rounds up from 6 to 7, giving 1.7 m.

Question 30Mathematics

A cadet is issued a rectangular locker whose length is 3 cm more than twice its width. If the width is w cm, which expression gives the perimeter of the locker?

  1. 6w + 6 Correct answer.
  2. 2w + 3
  3. 4w + 3
  4. 3w + 3

Explanation

The length is 2w + 3, and the perimeter of a rectangle is 2(length + width). Substituting gives 2((2w + 3) + w) = 2(3w + 3) = 6w + 6.

Question 31Mathematics

A cadet needs to mix a cleaning solution in the ratio of 3 parts water to 1 part concentrate. How much concentrate is needed to make 20 liters of the mixture?

  1. 15 liters
  2. 5 liters Correct answer.
  3. 6.67 liters
  4. 3 liters

Explanation

The ratio 3 : 1 means the mixture has 4 equal parts in total. Each part is 20 ÷ 4 = 5 liters, and the concentrate is 1 part, so 5 liters are needed.

Question 32Mathematics

A cadet's daily schedule allots time for training, study, and rest in the ratio 5 : 3 : 2. If the total scheduled time is 10 hours, how many minutes are allotted to study?

  1. 300 minutes
  2. 120 minutes
  3. 60 minutes
  4. 180 minutes Correct answer.

Explanation

The ratio has 5 + 3 + 2 = 10 parts, so each part equals 10 hours ÷ 10 = 1 hour. Study is 3 parts, which is 3 hours, and 3 × 60 = 180 minutes.

Question 33Mathematics

A cadet's savings account earns compound interest at 5% per year. If 10,000 pesos is deposited and no withdrawals are made, what is the balance after 2 years?

  1. 10,500 pesos
  2. 11,000 pesos
  3. 11,025 pesos Correct answer.
  4. 12,100 pesos

Explanation

Compound interest applies each year's interest to the growing balance. After year one the balance is 10,000 × 1.05 = 10,500, and after year two it is 10,500 × 1.05 = 11,025 pesos.

Question 34Mathematics

A cadet stands at the top of a 12-meter tower and spots a target on level ground at a horizontal distance of 16 meters from the base. What is the straight-line distance from the cadet to the target?

  1. 14 meters
  2. 4 meters
  3. 28 meters
  4. 20 meters Correct answer.

Explanation

The tower height and horizontal distance form the legs of a right triangle, so the straight-line distance is the hypotenuse. By the Pythagorean theorem, 12² + 16² = 144 + 256 = 400, and the square root of 400 is 20 meters.

Question 35Mathematics

A cadet's performance score is modeled by the function g(x) = 2x + 5, where x is the number of practice sessions. If the cadet wants a score of 27, how many sessions are required?

  1. 11 Correct answer.
  2. 13
  3. 22
  4. 16

Explanation

Set g(x) equal to 27 and solve: 2x + 5 = 27, so 2x = 22 and x = 11. This means 11 practice sessions produce a score of 27.

Question 36Mathematics

A cadet records the number of push-ups completed each day: 18, 22, 25, 21, 24. What is the median of these values?

  1. 22 Correct answer.
  2. 21
  3. 24
  4. 25

Explanation

Arrange the values in order: 18, 21, 22, 24, 25. With five values, the median is the middle one, which is 22.

Question 37Mathematics

A cadet's map uses a scale of 1 cm to 2.5 km. If two landmarks are 6.4 cm apart on the map, what is the actual distance between them?

  1. 6.4 km
  2. 2.56 km
  3. 15 km
  4. 16 km Correct answer.

Explanation

Each centimeter on the map represents 2.5 km, so multiply the map distance by the scale factor. Thus 6.4 × 2.5 = 16 km.

Question 38Mathematics

A cadet's exam scores in four subjects are 82, 76, 90, and 88. What score must be earned in a fifth subject so that the average of all five scores is exactly 85?

  1. 85
  2. 92
  3. 89 Correct answer.
  4. 90

Explanation

An average of 85 over five subjects requires a total of 5 × 85 = 425. The four known scores sum to 336, so the fifth score must be 425 − 336 = 89.

Question 39Mathematics

A cadet's monthly allowance of 3,600 pesos is split so that 40% goes to meals, 25% to transport, and the rest to savings. How much is saved each month?

  1. 1,800 pesos
  2. 1,260 pesos Correct answer.
  3. 1,440 pesos
  4. 900 pesos

Explanation

Meals and transport together take 40% + 25% = 65% of the allowance, leaving 35% for savings. Then 0.35 × 3,600 = 1,260 pesos.

Question 40Mathematics

A cadet solves the inequality 3x − 4 < 2x + 6. Which description gives all solutions?

  1. x < 10 Correct answer.
  2. x > 2
  3. x > 10
  4. x < 2

Explanation

Subtract 2x from both sides to get x − 4 < 6, then add 4 to both sides to obtain x < 10. No sign reversal is needed since no multiplication or division by a negative number occurred.

Question 41English

In a cadet entrance essay, choose the sentence that uses the correct form of the verb to complete the report: 'The squad ____ scheduled to march at dawn.'

  1. is Correct answer.
  2. are
  3. be
  4. were

Explanation

The subject 'squad' is a collective noun treated as a single unit here, so it takes the singular verb 'is'. 'Were' would require a plural subject or a past-tense context, and 'be' is not a finite verb form in this sentence.

Question 42English

Which word in the sentence 'Each of the cadets must submit their own written report before the inspection' creates an agreement problem in formal written English?

  1. their Correct answer.
  2. before
  3. must
  4. own

Explanation

'Each' is singular, so formal written English requires the singular pronoun 'his' or a rewording such as 'his or her'. 'Their' is plural and does not agree with the singular antecedent 'each'. The other words are grammatically neutral here.

Question 43English

Identify the sentence in which the colon is used correctly according to standard punctuation rules for a cadet's formal letter.

  1. The duty roster: lists three items rifle, canteen, and helmet.
  2. The duty roster lists three items, rifle, canteen, and helmet.
  3. The duty roster lists: rifle, canteen, and helmet.
  4. The duty roster lists three items: rifle, canteen, and helmet. Correct answer.

Explanation

A colon must follow a complete independent clause and introduce what comes after it. Only the first sentence has a full clause before the colon and a list after it. Placing a colon directly after a verb or between a subject and its verb breaks the rule.

Question 44English

A cadet writes, 'The commander, together with his aides, ____ inspecting the barracks.' Which verb correctly completes the sentence?

  1. have been
  2. were
  3. is Correct answer.
  4. are

Explanation

The subject is 'the commander', singular; the phrase 'together with his aides' is parenthetical and does not change the number of the subject. Therefore the singular present verb 'is' is correct. The plural forms wrongly treat the parenthetical phrase as part of the subject.

Question 45English

Choose the option that correctly identifies the part of speech of the underlined word in: 'The cadets marched briskly across the parade ground.'

  1. conjunction
  2. adjective
  3. adverb Correct answer.
  4. preposition

Explanation

'Briskly' modifies the verb 'marched', telling how the action was performed, which makes it an adverb. Adjectives modify nouns, prepositions show relationships, and conjunctions join clauses or words.

Question 46English

Which sentence correctly uses the apostrophe in a sentence about cadet equipment?

  1. The cadets rifles' were stacked neatly in the armory.
  2. The cadet's rifles were stacked neatly in the armory, and all cadets were present.
  3. The cadets' rifles were stacked neatly in the armory. Correct answer.
  4. The cadets's rifles were stacked neatly in the armory.

Explanation

'Cadets' is a regular plural ending in -s, so the possessive is formed by adding only an apostrophe after the s. The first option correctly shows that the rifles belong to multiple cadets. The other options misplace the apostrophe or use a nonstandard plural possessive form.

Question 47English

In the sentence 'Although the drill was exhausting, the cadets completed it with precision,' what is the grammatical function of the clause 'Although the drill was exhausting'?

  1. It is a subordinate adverbial clause expressing concession. Correct answer.
  2. It is a relative clause modifying 'cadets'.
  3. It is an independent clause expressing a result.
  4. It is a noun clause acting as the subject.

Explanation

The clause begins with the subordinating conjunction 'although', which signals concession, and it cannot stand alone as a sentence. It therefore functions as a subordinate adverbial clause modifying the main clause.

Question 48English

Select the word that best completes the sentence in a formal report: 'The cadet's conduct was ____ and earned him a commendation.'

  1. exemplar
  2. exemplary Correct answer.
  3. exemplify
  4. exemplarily

Explanation

The blank follows the linking verb 'was' and must be an adjective describing 'conduct'. 'Exemplary' is the adjective form. The other options are an adverb, a noun, and a verb, none of which fits the predicate adjective slot.

Question 49English

Which sentence uses the correct comparative form when comparing two cadet platoons?

  1. Platoon A is more disciplined then Platoon B.
  2. Platoon A is most disciplined than Platoon B.
  3. Platoon A is the most disciplined than Platoon B.
  4. Platoon A is more disciplined than Platoon B. Correct answer.

Explanation

When comparing exactly two things, English uses the comparative form 'more disciplined' plus 'than'. The superlative 'most' is reserved for three or more items, and 'then' is a time word, not a comparison word.

Question 50English

Identify the sentence that correctly uses the passive voice in a military context.

  1. The duty officer issued the orders at 0600 hours.
  2. The orders issued the duty officer at 0600 hours.
  3. The orders were issued by the duty officer at 0600 hours. Correct answer.
  4. The duty officer was issued the orders at 0600 hours by himself.

Explanation

In passive voice, the object of the active sentence becomes the subject and the verb takes the form 'be + past participle'. 'The orders were issued by the duty officer' follows this pattern correctly. The other options either use active voice or scramble the roles of subject and object.