Math Reviewer for College Entrance Exams: Free Practice Questions

Mariano Luiz King

Free math reviewer for college entrance exams, with practice questions on algebra, arithmetic, geometry, statistics and probability, and trigonometry. Pick an answer to see the step-by-step solution. No sign-up needed.

Free Math reviewer: mock questions

Questions from across the question types, picked from core topics. Pick an answer to see whether you got it right, along with the full explanation.

Question 1
Algebra
Solve for $x$ : $3x - 4 = -28$
Not quite. The answer is: -8
Topic: Linear Equations.
Formula: $3x - 4 = -28$ .
Step 1: Add 4 to both sides ( $3x = -24$ ).
Result: $x = -8$ .
Question 2
Arithmetic and number sense
If $a:b = 5:8$ and $a = 25$ , what is $b$ ?
Not quite. The answer is: 40
Topic: Ratios.
Formula: $b = a \times \frac{r_2}{r_1}$ .
Result: $b = 25 \times \frac{8}{5} = 40$ .
Question 3
Geometry
A circle has radius 19. What is its circumference in terms of $\pi$ ?
Not quite. The answer is: $38\pi$
Topic: Circle Geometry.
Formula: $C = 2\pi r$ .
Result: $C = 2 \times \pi \times 19 = 38\pi$ .
Question 4
Geometry
A right triangle has legs 13 and 9. What is the length of the hypotenuse?
Not quite. The answer is: 15.81
Topic: Pythagorean Theorem.
Formula: $a^{2} + b^{2} = c^{2}$ .
Step 1: $13^{2} + 9^{2} = 169 + 81 = 250$ .
Result: $c = \sqrt{250} \approx 15.81$ .
Question 5
Statistics and probability
A standard deck has 52 cards. What is the probability of drawing a heart on one draw?
Not quite. The answer is: 1/4
Topic: Probability.
Step 1: There are 13 hearts and 52 total cards.
Result: $P = \frac{13}{52} = \frac{1}{4}$ .
Question 6
Statistics and probability
A fair coin is flipped 4 times. What is the probability of getting exactly 3 heads?
Not quite. The answer is: 4/16
Topic: Binomial Probability.
Formula: $P(k) = \binom{n}{k} \cdot p^k \cdot q^{n-k}$ .
Step 1: $n=4$ , $k=3$ , $p=0.5$ .
Step 2: $\binom{4}{3} \cdot (0.5)^4 = 4 \cdot \frac{1}{16} = \frac{4}{16}$ .
Result: $P = \frac{1}{4}$ .
Question 7
Trigonometry
In a right triangle, the side opposite angle $\theta$ is 3 and the hypotenuse is 5. What is $\sin(\theta)$ ?
Not quite. The answer is: $\frac{3}{5}$
Topic: Right Triangle Trigonometry.
Formula: $\sin(\theta) = \frac{opposite}{hypotenuse}$ .
Result: $\sin(\theta) = \frac{3}{5}$ .

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Math reviewer FAQ

What math topics come out in college entrance exams?

Mostly high school math: algebra (equations and inequalities), ratios and percents, geometry (circles, triangles, area), basic statistics and probability, and some trigonometry. The UPCAT and the USTET are reported to go deeper into algebra and geometry than the others.

Can I use a calculator in the CET?

Past takers report that calculators are not allowed in the major college entrance exams, so practice solving by hand. Check the official exam advisory for your test, since rules can change.

How do I review math for the CET in a short time?

Start with algebra and ratios, since they show up in many word problems. Memorize the few formulas that come up most (area, circumference, Pythagorean theorem, sine and cosine), then practice timed sets and review every mistake.

Can I practice math questions for free on prepPH?

Yes. The practice questions on this page are free to try without an account. prepPH also has a free plan, and a Premium plan that unlocks unlimited flashcards and weak-topic breakdowns.

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