Here are 25 ACT math bell ringers: original, ACT-style multiple-choice problems with four labeled answer choices and a fully worked solution under each one. They’re arranged in five mixed sets of five, so one set covers a school week and students practice switching between topics the way the real test makes them.
Each problem should take a prepared student about a minute, which makes them a good fit for a quick warm-up. These are not real ACT items; they were written for this page and cover percents, algebra, functions, geometry, trigonometry, and basic statistics and probability.
ACT math timing and test-taking strategy
Before you start, it helps for students to know what they’re practicing for. According to ACT’s enhanced ACT FAQ, the mathematics section has 45 questions in 50 minutes. ACT’s student blog notes that math questions now have four answer choices instead of five, and ACT’s math test description says students may use a calculator on the math section (within ACT’s calculator policy).
That works out to a little over a minute per question. Strategy points worth teaching during bell ringer time:
- Answer every question. ACT’s own test-taking tips say there is no penalty for guessing. A blank is a guaranteed miss.
- Skip and return. If a problem stalls you, mark a guess, circle it, and come back if time allows. Don’t let one hard problem eat the time you need for three easier ones.
- Eliminate first. Crossing out even one wrong choice raises the odds on a guess.
- Back-solve. When choices are numbers, plug them in. Starting with a middle choice tells you whether to go higher or lower.
- Estimate. Rounding often rules out two choices before you calculate anything.
- Read the last line twice. Many wrong choices are the right answer to a different question (the width instead of the area, x instead of 6x + 1).
ACT math bell ringers: Set 1
1. A jacket costs $80. It’s on sale for 25% off, and 6% sales tax is added to the sale price. What is the total cost?
A. $60.00
B. $63.60
C. $64.80
D. $84.80
Answer and teacher notes
B. Sale price: 80 × 0.75 = $60. With tax: 60 × 1.06 = $63.60.
Teacher note: C comes from subtracting 6% from 25% and taking 19% off. Percents applied one after another don’t combine that way.
2. If 3x − 7 = 11, what is the value of 6x + 1?
A. 19
B. 25
C. 37
D. 43
Answer and teacher notes
C. 3x = 18, so x = 6. Then 6(6) + 1 = 37.
Shortcut: 3x = 18 means 6x = 36, so 6x + 1 = 37. Students who stop at x = 6 fall for a trap; always answer the question asked.
3. The average of 5 test scores is 84. Four of the scores are 78, 90, 85, and 80. What is the fifth score?
A. 83
B. 85
C. 87
D. 89
Answer and teacher notes
C. Total of all 5 scores: 5 × 84 = 420. Sum of the four: 78 + 90 + 85 + 80 = 333. Fifth score: 420 − 333 = 87.
4. What is the slope of the line through (−2, 3) and (4, −9)?
A. −2
B. −1/2
C. 1/2
D. 2
Answer and teacher notes
A. (−9 − 3) ÷ (4 − (−2)) = −12 ÷ 6 = −2.
Teacher note: B is rise and run flipped. The line falls from left to right, so C and D can be eliminated right away.
5. If f(x) = 2x2 − 3x, what is f(−3)?
A. −27
B. 9
C. 18
D. 27
Answer and teacher notes
D. 2(−3)2 − 3(−3) = 2(9) + 9 = 18 + 9 = 27.
Set 2
6. The ratio of boys to girls in a class of 32 students is 3:5. How many girls are in the class?
A. 12
B. 15
C. 20
D. 24
Answer and teacher notes
C. 3 + 5 = 8 parts. 32 ÷ 8 = 4 students per part. Girls: 5 × 4 = 20.
7. A rectangle has a perimeter of 46 and a length of 15. What is its area?
A. 69
B. 105
C. 120
D. 135
Answer and teacher notes
C. 2(15 + w) = 46, so 15 + w = 23 and w = 8. Area: 15 × 8 = 120.
8. A right triangle has legs of length 9 and 12. What is the length of the hypotenuse?
A. 10.5
B. 12
C. 13
D. 15
Answer and teacher notes
D. 92 + 122 = 81 + 144 = 225, and √225 = 15.
Teacher note: It’s a 3-4-5 triangle scaled by 3. Also, the hypotenuse must be longer than either leg, so A and B are out.
9. What is the solution set of |2x − 5| = 9?
A. {7}
B. {−2, 7}
C. {−7, 2}
D. {2, 7}
Answer and teacher notes
B. 2x − 5 = 9 gives x = 7. 2x − 5 = −9 gives 2x = −4, so x = −2.
Teacher note: Back-solving is fast here. Test −2: |−4 − 5| = |−9| = 9. ✓
10. For x ≠ −3, which expression is equivalent to (x2 − 9) ÷ (x + 3)?
A. x − 3
B. x + 3
C. x − 9
D. x2 − 3
Answer and teacher notes
A. x2 − 9 = (x + 3)(x − 3). Cancel (x + 3) to get x − 3.
Teacher note: Or plug in x = 5: (25 − 9) ÷ 8 = 2, and only A gives 2.
Set 3
11. A bag holds 4 red, 6 blue, and 5 green marbles. One marble is picked at random. What is the probability it is NOT blue?
A. 2/5
B. 3/5
C. 1/3
D. 2/3
Answer and teacher notes
B. Total marbles: 15. Not blue: 4 + 5 = 9. Probability: 9/15 = 3/5.
Teacher note: A is the probability of picking blue (6/15). The word NOT is the whole question.
12. What are the center and radius of the circle (x − 2)2 + (y + 5)2 = 49?
A. Center (2, −5), radius 7
B. Center (−2, 5), radius 7
C. Center (2, −5), radius 49
D. Center (−2, 5), radius 49
Answer and teacher notes
A. The form is (x − h)2 + (y − k)2 = r2. So h = 2, k = −5, and r = √49 = 7.
13. In right triangle ABC, angle C is the right angle and sin A = 5/13. What is cos A?
A. 5/12
B. 12/13
C. 13/12
D. 12/5
Answer and teacher notes
B. Sine is opposite over hypotenuse, so the opposite side is 5 and the hypotenuse is 13. The adjacent side is √(169 − 25) = √144 = 12. Cos A = adjacent ÷ hypotenuse = 12/13.
Teacher note: The cosine of an acute angle in a right triangle is always less than 1, which rules out C and D.
14. Two angles of a triangle measure 47° and 68°. What is the measure of the exterior angle at the third vertex?
A. 65°
B. 105°
C. 115°
D. 125°
Answer and teacher notes
C. Third interior angle: 180 − 47 − 68 = 65°. The exterior angle is 180 − 65 = 115°, which also equals 47 + 68.
Teacher note: A is the interior angle, a classic “answered the wrong question” choice.
15. If x + y = 10 and x − y = 4, what is the value of xy?
A. 21
B. 24
C. 28
D. 40
Answer and teacher notes
A. Add the equations: 2x = 14, so x = 7. Then y = 3. xy = 7 × 3 = 21.
Set 4
16. If 2x + 1 = 32, what is x?
A. 3
B. 4
C. 5
D. 16
Answer and teacher notes
B. 32 = 25, so x + 1 = 5 and x = 4.
Teacher note: C is the exponent before subtracting 1. D comes from dividing 32 by 2.
17. A car travels 225 miles in 3.75 hours. What is its average speed in miles per hour?
A. 45
B. 50
C. 55
D. 60
Answer and teacher notes
D. 225 ÷ 3.75 = 60. Check: 60 × 3.75 = 225. ✓
Teacher note: Estimate first: 225 ÷ 4 is about 56, and the time is under 4 hours, so the speed is a bit more than 56.
18. What is the median of this data set: 12, 7, 19, 7, 15, 10?
A. 7
B. 10
C. 11
D. 11.67
Answer and teacher notes
C. In order: 7, 7, 10, 12, 15, 19. With six values, the median is the average of the middle two: (10 + 12) ÷ 2 = 11.
Teacher note: A is the mode and D is the mean (rounded). Good chance to review all three.
19. What is the product of the solutions of x2 − 3x − 10 = 0?
A. −10
B. −3
C. 3
D. 10
Answer and teacher notes
A. (x − 5)(x + 2) = 0, so the solutions are 5 and −2. Product: 5 × (−2) = −10.
Teacher note: For x2 + bx + c = 0, the product of the solutions equals c. That’s a fast check.
20. A cylinder has a radius of 3 and a height of 10. What is its volume?
A. 30π
B. 45π
C. 60π
D. 90π
Answer and teacher notes
D. V = πr2h = π(32)(10) = 90π.
Teacher note: C is the lateral surface area (2πrh), and A comes from forgetting to square the radius.
Set 5
21. What is the 20th term of the arithmetic sequence 7, 11, 15, 19, …?
A. 80
B. 83
C. 87
D. 91
Answer and teacher notes
B. The common difference is 4. a20 = 7 + (20 − 1)(4) = 7 + 76 = 83.
Teacher note: C comes from using 20 × 4 instead of 19 × 4.
22. The point (3, −4) is reflected across the y-axis. What are the coordinates of its image?
A. (3, 4)
B. (−3, 4)
C. (−4, 3)
D. (−3, −4)
Answer and teacher notes
D. Reflecting across the y-axis changes the sign of the x-coordinate only: (−3, −4).
Teacher note: A is a reflection across the x-axis.
23. Which of the following is equal to √72?
A. 6√2
B. 6√3
C. 8√2
D. 36√2
Answer and teacher notes
A. 72 = 36 × 2, so √72 = √36 × √2 = 6√2.
24. For what value of x is g(x) = (x + 4) ÷ (x − 2) undefined?
A. −4
B. −2
C. 2
D. 4
Answer and teacher notes
C. A fraction is undefined when the denominator is 0. x − 2 = 0 when x = 2.
Teacher note: A makes the numerator 0, which makes g(x) equal 0, not undefined.
25. A stock’s price falls from $50 to $40. What is the percent decrease?
A. 10%
B. 20%
C. 25%
D. 80%
Answer and teacher notes
B. Change ÷ original = 10 ÷ 50 = 0.20 = 20%.
Teacher note: C divides by the new price (10 ÷ 40). Going from $40 up to $50 would be a 25% increase, so the “original” value matters.
How to fit ACT prep into bell ringer time
Run one set per week, one problem a day, on a visible one-minute timer. When you review, ask “What was the fastest way?” so back-solving, estimation, and elimination become habits. Have students record their work on a weekly bell ringer sheet and note which traps caught them. For more high school warm-ups, see our algebra bell ringers, geometry bell ringers, and the bell ringers for high school guide.
FAQ
Are these real ACT questions?
No. All 25 are original problems written in an ACT style. For official practice, use the free practice materials on ACT’s website.
When should students start ACT math bell ringers?
Sophomore year works well, so pacing feels familiar before a junior-year test. They also make good spiral review in Algebra 2 or precalculus.
Should students use a calculator on these bell ringers?
Yes, since one is allowed on the ACT math section. But review the by-hand shortcut too; many are faster without it.
How many ACT problems should a bell ringer include?
One or two. Save full timed sections for practice-test days.
Keep the daily routine going
Once students finish these 25, keep the warm-up habit alive with our daily bell ringers, especially the grades 9–12 sets. The free bell ringer creator can also build extra math practice by topic in a few seconds.