UPCAT Mathematics Reviewer
9 Mathematics practice questions for the University of the Philippines College Admission Test, each with the correct answer and an explanation of why it's right.
Mathematics Practice Questions with Answers
- 1medium
If n is an odd integer, which one of the following is an even integer?
- A.n³
- B.n/4
- C.2n + 3
- D.2n(n + 3)
Show answer & explanation
Answer: D. 2n(n + 3)
2n is always even; multiplying by any integer keeps it even. So 2n(n+3) is even regardless of n.
- 2medium
What should be multiplied to the binomial x - y so that the product is a trinomial?
- A.10y
- B.3x - 5y
- C.x + y
- D.3x² + 5y + 4y²
Show answer & explanation
Answer: B. 3x - 5y
(x - y)(3x - 5y) = 3x² - 5xy - 3xy + 5y² = 3x² - 8xy + 5y², a trinomial with 3 terms.
- 3medium
A particular carmaker sells four models of cars, and each model comes with 5 options. How many different types of cars does this carmaker sell?
- A.10
- B.15
- C.20
- D.35
Show answer & explanation
Answer: C. 20
By the counting principle: 4 models × 5 options = 20 different car types.
- 4medium
Bowl Z contains only marbles. If 1/4 of the marbles were removed, the bowl would be filled to 1/2 of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl Z?
- A.120
- B.200
- C.250
- D.300
Show answer & explanation
Answer: B. 200
Let max capacity = M. Current marbles × 3/4 = M/2 (removing 1/4 leaves 3/4, equaling 1/2 capacity). So current = 2M/3. Adding 100 fills it: 2M/3 + 100 = M → M = 300. Current marbles = 200.
- 5medium
Let f(x) = 2x - 1 and g(x) = x² + 3. What is (f∘g)(2)?
- A.5
- B.7
- C.12
- D.13
Show answer & explanation
Answer: D. 13
First compute g(2) = 4 + 3 = 7, then f(7) = 2(7) - 1 = 13.
- 6medium
A pyramid has a base area of 9m² and an altitude of 200cm. What is its volume?
- A.6m³
- B.60cm³
- C.18m³
- D.180cm³
Show answer & explanation
Answer: A. 6m³
Convert 200cm = 2m. Volume = (1/3) × base area × height = (1/3) × 9 × 2 = 6m³.
- 7medium
Oble runs at least 10km everyday on a circular track. If the track has a diameter of 1km, approximately how many rounds does Oble jog everyday?
- A.2
- B.3
- C.5
- D.7
Show answer & explanation
Answer: B. 3
Circumference = π × d = π × 1 ≈ 3.14 km per round. 10 ÷ 3.14 ≈ 3.18, so approximately 3 rounds.
- 8medium
Ann invested Php 80,000 into a venture that pays 3.5% annual simple interest. How much will she earn after a year?
- A.Php 77,200
- B.Php 2,800
- C.Php 5,600
- D.Php 82,000
Show answer & explanation
Answer: B. Php 2,800
Simple interest = Principal × Rate × Time = 80,000 × 0.035 × 1 = Php 2,800.
- 9medium
If you roll two six-sided dice simultaneously, which of the following would be the most likely outcome?
- A.Exactly one die is even.
- B.At least one die is even.
- C.Both dice are even.
- D.The sum is even.
Show answer & explanation
Answer: B. At least one die is even.
P(at least one even) = 1 - P(both odd) = 1 - (1/2)² = 3/4 = 0.75, the highest among all options.
Practise the full Mathematics set
Super Tutor has 134 Mathematics questions for the UPCAT, each with an explanation, plus full timed UPCAT mock exams. Start free — 5-day trial, no card.