ACT practice test

ACT Geometry and Statistics Practice Test

Angles, triangles, circles, area, probability, mean and median. Here are 10 ACT geometry and statistics questions, each with the answer and the reason.

Updated 2026-11-14 by the Tigertest team. Original passages and questions written to the enhanced ACT format (2025): four choices, 50/45/36/40 questions, Science optional. Not affiliated with ACT, Inc. Score estimates are unofficial.

1. 1.

   Two angles are supplementary. One angle measures $(2x + 10)^\circ$ and the other measures $50^\circ$. What is the value of $x$?

   • A.

     $20$

   • B.

     $40$

   • C.

     $60$

   • D.

     $85$

   Answer: C.

   Supplementary angles add to $180^\circ$, so $2x + 10 + 50 = 180$. Subtract $60$ from both sides to get $2x = 120$, so $x = 60$. The choice $20$ comes from setting the two angles equal to each other ($2x + 10 = 50$), and $40$ comes from setting the first angle alone equal to $90^\circ$ ($2x + 10 = 90$).

2. 2.

   A bag contains $5$ red marbles, $3$ blue marbles, and $4$ green marbles. If one marble is drawn at random, what is the probability that it is NOT red?

   • A.

     $\frac{1}{3}$

   • B.

     $\frac{5}{12}$

   • C.

     $\frac{7}{12}$

   • D.

     $\frac{5}{7}$

   Answer: C.

   There are $5 + 3 + 4 = 12$ marbles in all, and $3 + 4 = 7$ of them are not red, so the probability is $\frac{7}{12}$. Equivalently, $1 - \frac{5}{12} = \frac{7}{12}$. The choice $\frac{5}{12}$ is the probability of drawing a red marble, and $\frac{5}{7}$ compares red marbles to non-red marbles instead of to the whole bag.

3. 3.

   The circumference of a circle is $16\pi$ centimeters. What is the area of the circle, in square centimeters?

   • A.

     $8\pi$

   • B.

     $16\pi$

   • C.

     $64\pi$

   • D.

     $256\pi$

   Answer: C.

   Circumference is $2\pi r$, so $2\pi r = 16\pi$ gives $r = 8$. Area is $\pi r^2 = \pi \cdot 8^2 = 64\pi$ square centimeters. The choice $256\pi$ comes from squaring the diameter $16$ instead of the radius, and $8\pi$ comes from using $\pi r$ instead of $\pi r^2$ for area.

4. 4.

   An isosceles triangle has a perimeter of $36$ inches, and each of its two equal sides is $13$ inches long. What is the area of the triangle, in square inches?

   • A.

     $60$

   • B.

     $65$

   • C.

     $78$

   • D.

     $120$

   Answer: A.

   The third side is $36 - 13 - 13 = 10$ inches. The height to that side splits the triangle into two right triangles with hypotenuse $13$ and one leg $5$, so the height is $\sqrt{13^2 - 5^2} = \sqrt{144} = 12$. The area is $\frac{1}{2}(10)(12) = 60$ square inches. The choice $65$ comes from using a side of $13$ as the height ($\frac{1}{2} \cdot 10 \cdot 13$), and $120$ forgets the $\frac{1}{2}$ in the area formula.

5. 5.

   A fair coin is flipped and a fair six-sided die is rolled. What is the probability that the coin shows heads and the die shows a number greater than 4?

   • A.

     $\dfrac{1}{12}$

   • B.

     $\dfrac{1}{6}$

   • C.

     $\dfrac{1}{3}$

   • D.

     $\dfrac{5}{6}$

   Answer: B.

   The two events are independent, so multiply their probabilities. The coin shows heads with probability $\frac{1}{2}$, and the die shows a 5 or a 6 with probability $\frac{2}{6} = \frac{1}{3}$, so the probability of both is $\frac{1}{2} \cdot \frac{1}{3} = \frac{1}{6}$. Choice D adds the two probabilities instead of multiplying them, and choice A counts only the 6 as greater than 4.

6. 6.

   In a right triangle, one acute angle measures $30^\circ$ and the longer leg has length 9. What is the length of the hypotenuse?

   • A.

     $3\sqrt{3}$

   • B.

     $6\sqrt{3}$

   • C.

     $9\sqrt{3}$

   • D.

     18

   Answer: B.

   In a 30-60-90 triangle the sides are in the ratio $1 : \sqrt{3} : 2$ (shorter leg, longer leg, hypotenuse). The longer leg is $9 = s\sqrt{3}$, so the shorter leg is $s = \dfrac{9}{\sqrt{3}} = 3\sqrt{3}$, and the hypotenuse is twice that, $6\sqrt{3}$, about 10.4. Choice D treats 9 as the shorter leg and doubles it. Choice A is the shorter leg, not the hypotenuse.

7. 7.

   A school committee will consist of exactly 2 teachers chosen from 5 teachers and exactly 3 students chosen from 6 students. How many different committees are possible?

   • A.

     30

   • B.

     200

   • C.

     330

   • D.

     462

   Answer: B.

   Order does not matter within a committee, so use combinations. There are $\binom{5}{2} = 10$ ways to choose the teachers and $\binom{6}{3} = 20$ ways to choose the students, and by the counting principle the two choices multiply: $10 \times 20 = 200$. Choice D, $\binom{11}{5} = 462$, chooses any 5 people from all 11 and ignores the requirement of exactly 2 teachers and 3 students. Choice A multiplies 5 by 6 as if only one of each were chosen.

8. 8.

   Dana's scores on 7 quizzes were 72, 86, 94, 70, 85, 77, and 90. What is the median of Dana's quiz scores?

   • A.

     $24$

   • B.

     $70$

   • C.

     $82$

   • D.

     $85$

   Answer: D.

   Order the scores from least to greatest: $70, 72, 77, 85, 86, 90, 94$. With $7$ values, the median is the 4th value, which is $85$. The choice $82$ is the mean ($574 \div 7$), $70$ is the middle value of the list before it is sorted, and $24$ is the range.

9. 9.

   In the standard $(x, y)$ coordinate plane, a circle has the equation $x^2 + y^2 - 6x + 4y - 12 = 0$. What is the radius of the circle?

   • A.

     $\sqrt{12}$

   • B.

     5

   • C.

     13

   • D.

     25

   Answer: B.

   Complete the square in each variable: $(x^2 - 6x + 9) + (y^2 + 4y + 4) = 12 + 9 + 4$, which gives $(x - 3)^2 + (y + 2)^2 = 25$. The right side is $r^2$, so the radius is $\sqrt{25} = 5$. Choice D is $r^2$ rather than $r$, and choice A takes the square root of the constant 12 without completing the squares first.

10. 10.

    In triangle $PQR$, $PQ = 7$, $QR = 9$, and the measure of angle $Q$ is $60^\circ$. What is the length of $\overline{PR}$?

    • A.

      8

    • B.

      $\sqrt{67}$

    • C.

      $\sqrt{130}$

    • D.

      $\sqrt{193}$

    Answer: B.

    Angle $Q$ is included between the known sides, so use the law of cosines: $PR^2 = 7^2 + 9^2 - 2(7)(9)\cos 60^\circ = 49 + 81 - 126 \cdot \dfrac{1}{2} = 130 - 63 = 67$, so $PR = \sqrt{67}$, about 8.2. Choice C omits the cosine term, which would only be correct for a right angle at $Q$, and choice D adds $63$ instead of subtracting it.