UPCAT Practice Test 2026

About the UPCAT exam

The University of the Philippines College Admission Test (UPCAT) is a university entrance examination administered in Philippines. It is designed to assess candidates' knowledge and proficiency across 4 key subject areas including Language Proficiency, Mathematics, Science, Reading Comprehension. This exam is widely recognized as an essential benchmark for students and professionals.

Use short UPCAT practice sets to identify topics to revisit. Choose a subject and difficulty, answer questions, then review the explanations. New accounts get 30 question credits; further new questions use paid credits. Retaking previously seen questions is free.

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8 free UPCAT practice questions (2026)

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1. If x = 2^a and y = 2^b, what is the value of log_2 (x^3 * y^2) in terms of a and b?

   • 3a + 2b
   • a^3 + b^2
   • 6ab
   • 3a - 2b
   Show answer & explanation

   Answer: A. 3a + 2b

   Using logarithmic properties, log_2 (x^3 * y^2) = log_2(x^3) + log_2(y^2) = 3*log_2(x) + 2*log_2(y). Since x = 2^a and y = 2^b, log_2(x) = a and log_2(y) = b. Substituting these gives 3a + 2b.

   Topic: Mathematics · medium

2. Pipes A and B can fill a pool in 6 hours together. If Pipe A alone takes 5 hours less than Pipe B alone to fill the pool, how many hours would it take Pipe A alone to fill the pool?

   • 15 hours
   • 12 hours
   • 10 hours
   • 8 hours
   Show answer & explanation

   Answer: C. 10 hours

   Let x be the time for Pipe A, so Pipe B takes x + 5. The work equation is 1/x + 1/(x + 5) = 1/6. Solving this yields 6(2x + 5) = x(x + 5), which simplifies to x^2 - 7x - 30 = 0. Factoring gives (x - 10)(x + 3) = 0. Since time must be positive, x = 10 hours.

   Topic: Mathematics · hard

3. What is the equation of the line perpendicular to 3x - 4y = 8 and passing through the point (3, -1)?

   • 4x - 3y = 15
   • 4x + 3y = 9
   • 3x + 4y = 5
   • 3x - 4y = 13
   Show answer & explanation

   Answer: B. 4x + 3y = 9

   The slope of 3x - 4y = 8 is 3/4. The slope of a line perpendicular to it is the negative reciprocal, which is -4/3. Using the point-slope form with (3, -1): y - (-1) = -4/3(x - 3) which simplifies to 3y + 3 = -4x + 12, or 4x + 3y = 9.

   Topic: Mathematics · medium

4. What is the remainder when 3^100 is divided by 5?

   • 1
   • 2
   • 3
   • 4
   Show answer & explanation

   Answer: A. 1

   The remainders of powers of 3 divided by 5 repeat in a cycle of four: 3^1 = 3 (rem 3), 3^2 = 9 (rem 4), 3^3 = 27 (rem 2), and 3^4 = 81 (rem 1). Since the exponent 100 is a multiple of 4, the remainder is 1.

   Topic: Mathematics · hard

5. What is the domain of the real-valued function f(x) = sqrt(9 - x^2) + 1/(x - 1)?

   • [-3, 3]
   • (-infinity, -3] U [3, infinity)
   • [-3, 1) U (1, 3]
   • [-3, 1] U [1, 3]
   Show answer & explanation

   Answer: C. [-3, 1) U (1, 3]

   For the radical expression to be real, 9 - x^2 >= 0, which means -3 <= x <= 3. For the rational term to be defined, the denominator cannot be zero, meaning x != 1. Combining these conditions gives [-3, 1) U (1, 3].

   Topic: Mathematics · medium

6. An angle theta is subtended by an arc of length 8*pi cm on a circle of radius 12 cm. What is the measure of the angle in degrees?

   • 60 degrees
   • 120 degrees
   • 150 degrees
   • 240 degrees
   Show answer & explanation

   Answer: B. 120 degrees

   The arc length formula is s = r * theta, where theta is in radians. Here, 8*pi = 12 * theta, so theta = 2*pi/3 radians. Converting 2*pi/3 radians to degrees gives (2*pi/3) * (180/pi) = 120 degrees.

   Topic: Mathematics · easy

7. A bag contains 4 red marbles, 5 blue marbles, and 6 green marbles. If two marbles are drawn at random without replacement, what is the probability that both marbles are blue?

   • 2/21
   • 1/9
   • 5/21
   • 4/15
   Show answer & explanation

   Answer: A. 2/21

   The total number of marbles is 4 + 5 + 6 = 15. The probability of drawing a blue marble first is 5/15. Since there is no replacement, the probability of drawing a second blue marble is 4/14. The combined probability is (5/15) * (4/14) = (1/3) * (2/7) = 2/21.

   Topic: Mathematics · medium

8. If the sum of the roots of a quadratic equation ax^2 + bx + c = 0 is 5 and the product of the roots is -6, what is the value of b + c if a = 1?

   • -1
   • -11
   • 1
   • 11
   Show answer & explanation

   Answer: B. -11

   By Vieta's formulas, the sum of the roots is -b/a = 5, and since a = 1, b = -5. The product of the roots is c/a = -6, so c = -6. Thus, b + c = -5 + (-6) = -11.

   Topic: Mathematics · easy

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UPCAT Exam Subjects

Available practice subjects: Language Proficiency, Mathematics, Science, Reading Comprehension. Select a subject for focused preparation. Coverage is not a guarantee of the complete official syllabus.

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Read our comprehensive How to Pass the UPCAT in 2026 — Complete Study Guide for expert preparation tips, study plans, and strategies.

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