act math practice questions and solutions

here, you’ll find act math practice questions for three of the main areas tested on act math: algebra, geometry, and trigonometry. they range in difficulty from easy to very hard, but these practice questions test many essential skills you’ll need on test day.

act math practice questions (with answer explanations)

after you’ve worked through each question, click on the link for the video answer and explanation! you can also do them in a row and check your answers later, as a mini-practice test in math.

we’ve included buttons for you to click to save your answers as you work through these problems, but keep in mind that these are just for your use. they don’t submit or save your answers, so you may want to take notes as you go. and now, without further ado, here’s are 15 act sample math questions to test your knowledge and sharpen your test-taking skills!

act algebra sample questions

difficulty: medium

1. if $\frac{x}{3}+\frac{x}{4}+15=\text{x}$, then $\text{x}= $

click here for the answer and video explanation for problem 1!

difficulty: medium

2. given that f(x) = 3x – 5 and g(x) = x^3 – x, what is f(g(2))?

click here for the answer and video explanation for problem 2!

difficulty: medium

3. a, b, and c are consecutive odd integers such that a<b<c.

if a + b + c = 81, then a + c =

click here for the answer and video explanation for problem 3!

difficulty: medium

4. five lemonades and two cookies cost $1.50. two lemonades and five cookies cost $2.70. how much does one cookie and one lemonade cost?

click here for the answer and video explanation for problem 4!

difficulty: medium

5. if x > x², which of the following must be true about x?

click here for the answer and video explanation for problem 5!

act geometry sample questions

difficulty: medium

6.
in trapezoid abcd, bc = ef = 6, af = de = 3, and

ab = cd = 5. if the area of a trapezoid is given by

$\text{a}=(\frac{{\text{b}_1}+{\text{b}_2}}{2})\text{h}$

then which of the following is the area of trapezoid abcd?

click here for the answer and video explanation for problem 6!

difficulty: hard

7. in the diagram below, chord df is parallel to the diameter ac. the length of df is 20 cm and the length of ac is 28 cm. what is the distance, in centimeters, from b, the center of the circle, to e, the midpoint of df?

click here for the answer and video explanation for problem 7!

difficulty: easy

8. tony plans to put a rectangular perimeter of fencing around his backyard pool. the area to be sectioned off for the pool area measures 22 feet by 30 feet. one long side of the pool area is along the house, so he only needs to fence off 3 sides. how many feet of fencing will he need?

click here for the answer and video explanation for problem 8!

difficulty: hard

9. circle b below has a radius of 4 and arc ac has a central degree measure of 145°. what is the approximate length of arc ac?

click here for the answer and video explanation for problem 9!

difficulty: very hard

10. △abc and △def are both equilateral. given de is 50% greater than ab, by what percentage is the area of △def greater than the area of △abc?

click here for the answer and video explanation for problem 10!

act trigonometry sample questions

difficulty: very hard

11. whenever cos(θ) = 0, and π ≤ θ ≤ 2π, the value of sin(θ) =

click here for the answer and video explanation for problem 11!

difficulty: hard

12.

which of the following is the value of

(sin(30°) – cos(30°))2 ?

click here for the answer and video explanation for problem 12!

difficulty: hard

13. which of the following angles has the same terminal side as 1,105°?

click here for the answer and video explanation for problem 13!

difficulty: hard

14. the tree below casts a shadow that is 24 feet long, and the angle of elevation from the tip of the shadow to the top of the tree has a cosine of $\frac{4}{5}$. what is the height of the tree?

click here for the answer and video explanation for problem 14!

difficulty: medium

15. which of the following is the value of 240° in radians?

click here for the answer and video explanation for problem 15!

more resources for act math

want more act math practice questions and resources? impressive! so what are your next steps? check out these posts to get a better understanding of all the question types you’ll see on the act math test, from categories of questions to basic formulas to geometric figures and systems of equations. these resources will help your act math prep by letting you get a better sense of all the different kinds of act math questions you’ll see on the actual test! take a look.

authors

rachel kapelke-dale

rachel is a magoosh content creator. she writes and updates content on our high school and gre blogs to ensure students are equipped with the best information during their test prep journey. as a test-prep instructor for more than five years in there different countries, rachel has helped students around the world prepare for various standardized tests, including the sat, act, toefl, gre, and gmat, and she is one of the authors of our magoosh act prep book. rachel has a bachelor of arts in comparative literature from brown university, an ma in cinematography from the université de paris vii, and a ph.d. in film studies from university college london. for over a decade, rachel has honed her craft as a fiction and memoir writer and public speaker. her novel, the ballerinas, is forthcoming in december 2021 from st. martin’s press, while her memoir, graduates in wonderland, co-written with jessica pan, was published in 2014 by penguin random house. her work has appeared in over a dozen online and print publications, including vanity fair hollywood. when she isn’t strategically stringing words together at magoosh, you can find rachel riding horses or with her nose in a book. join her on twitter, instagram, or facebook!

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brendan henrique

brendan henrique is a gre content expert for magoosh. brendan has been helping students with the sat, act and gre for over six years and has been a middle school science teacher for the past two years. he attended uc berkeley (b.a.) for cognitive science and loyola marymount (m.a.) for urban education. he is currently pursuing his ph.d. of learning sciences at uc berkeley where he will focus on building a framework for equitable stem education. his master’s thesis analyzed differing labor practices and their effects between charter schools and public schools. he has mentored hundreds of students domestically from boston to minneapolis to oakland. he has also been able to teach students remotely in international locations ranging from china to spain. brendan is a proud board member of love.learn.success, a nonprofit organization that runs after school programs in the bay area. connect with him and magoosh on linkedin!

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