There is a new book focused on hardest ACT math questions, much of which is available for free here . Since there is limited material online that truly targets hard ACT math problems, this collection was created specifically to fill that gap. The problems are based on the study of thousands of real ACT math questions. Some problems combine multiple concepts commonly tested on the ACT, while others are real ACT math problems that have been intentionally made harder.
This resource is designed to help high-achieving students prepare for top ACT math scores using hard ACT math problems that closely reflect real exam difficulty but push beyond standard practice material. It is important to note that this content should not be used to predict or estimate an expected ACT score. Instead, it serves as targeted ACT math prep for students aiming to master the most difficult problem types.Â
The test included here is intentionally short. In addition, there are multiple full-length ACT math practice tests composed entirely of extremely challenging and realistic hard ACT math problems. These full-length tests make this one of the strongest ACT math preparation resources available for advanced students seeking top scores.
These hard ACT math problems should not be taken under timed conditions and should not be used for score prediction. Every problem is meant to challenge advanced reasoning, accuracy, and problem-solving skills. They are intentionally difficult yet realistic, making them ideal for students preparing for the highest ACT math score ranges.
1. Suppose you can pick exactly 
 of 
 ice creams and 
 of 
toppings. How many possible sundaes can you have?
A. 
B. 
C. 
D. 
E. 
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2. What is the equation of the perpendicular bisector of the line segment between 
 and 
?
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B. 
C. 
D. 
E. 
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3. A cube has a volume of 
 cubic feet. What is its surface area in square feet?
A. 
B.
C. 
D. 
E. 
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4. What is the equation of 
 reflected about the 
-axis?
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B. 
C. 
D. 
E. 
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5. 
, 
, 
. What is 
?
A. 
B. 
C. 
D. 
E. 
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6. What is the slope of the line 
?
A. 
B. 
C. 
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7. What is 
?
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8. 
 ?
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9. Simplify 
A. 
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10. 
A. 
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11. What is 
?
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B. 
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12. The 
term in a geometric sequence is 16 and the 
 term is 
. What is the 
 term?
A. 
B. 
C. 
D. 
E. 
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13. The 
 term in a geometric sequence is 
 and the 
 term is 
. What is the 
 term?
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B. 
C. 
D. 
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14. The  term in an arithmetic series is 
 and the last is 
. The sum of the series is 
. What is the 
 term?
A. 
B. 
C. 
D. 
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15. What is the area of the circle having 
 and 
 as endpoints of the diameter?
A. 
B. 
C. 
D. 
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16. 
. What is a positive solution?
A.
B.
C.
D. 
E.
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17. Which fraction is equal to 
?
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18. 
, 
. For what value of 
 does 
?
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B.
C.
D.
E.
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19. 
. What is 
?
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B. 
C. 
D. 
E. 
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20. You roll a die and flip 2 coins. What is the probability you roll a 6 and both coins come up heads?
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B. 
C. 
D. 
E. 
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21. 
 of hexagon 
 has measure 
. What is the average of the measures of the other  angles?
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B. 
C. 
D. 
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22. 
. What is 
?
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B. 
C. 
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23. Which of the following is equivalent to 
?
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B. 
C. 
D. 
E. 
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24. A cube with sides of length 6 is inscribed in a sphere. What is the surface area of the sphere (surface area of a sphere =Â 
)?
A. 
B. 
C. 
D. 
E. 
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Answer key: 1D, 2A, 3C, 4B, 5E, 6C, 7A, 8B, 9D, 10D, 11A, 12C, 13C, 14B, 15A, 16C, 17E, 18D, 19E, 20E, 21C, 22A, 23A, 24D
By completing these ACT math questions, students have worked through some of the hardest ACT math questions designed to strengthen advanced problem-solving skills and mathematical reasoning. These challenging hard ACT math problems and realistic ACT math hard questions help build the confidence needed to handle difficult exam scenarios. Consistent practice with high-level ACT math problems like these is one of the most effective ways to prepare for the ACT math hardest questions and continue improving overall performance on future ACT exams.
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