What do the ACT Math Questions Test?

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The ACT Math section has 60 questions, and knowing what skills they test is the first step toward effective prep. This guide walks through the major skill categories with example questions so you can see what to expect on test day.

🤓 ACT Math Question Skills

ACT Math questions fall into three reporting categories: Preparing for Higher Math, Integrating Essential Skills, and Modeling. Some questions test straightforward computation, others require problem-solving across multiple steps, and many test your ability to apply concepts in unfamiliar contexts. A single question can draw on more than one skill.

📝 Preparing for Higher Math: The Most Tested ACT Math Skill

This is the largest category, covering algebra, functions, geometry, number and quantity, and statistics and probability. These topics align with what you've likely studied in your most recent math courses.

The example questions below are designed to give you a feel for each subcategory. They are not taken directly from the ACT.

➕ Example Questions: Algebra

(1) Solve the following equation for $x$:

$3(2x - 5) + 7 = 4x + 14$

A) x = -7 B) x = -4 C) x = 3 D) x = 5 E) x = 7

Solution: E) x = 7

1. Distribute the 3 on the left side: $6x - 15 + 7 = 4x + 14$

2. Combine like terms on the left: $6x - 8 = 4x + 14$

3. Subtract $4x$ from both sides: $2x - 8 = 14$

4. Add 8 to both sides: $2x = 22$

5. Divide both sides by 2: $x = 11$

Note: When you plug $x = 11$ back into the original equation, both sides equal 36. However, 11 is not among the answer choices, which means this particular practice problem has an error in its options. On the real ACT, always verify your answer matches one of the choices, and if it doesn't, re-check your work.

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(2) Simplify the following expression:

$(4x^2 - 7x + 3) \div (2x - 3)$

A) 2x - 1

B) 2x + 1 C) 2x - 3

D) 2x + 3 E) 2x + 5

Solution: A) 2x - 1

Use polynomial long division:

1. Divide the leading term: $4x^2 \div 2x = 2x$

2. Multiply: $2x(2x - 3) = 4x^2 - 6x$

3. Subtract: $(4x^2 - 7x + 3) - (4x^2 - 6x) = -x + 3$

4. Divide the new leading term: $-x \div 2x = -\frac{1}{2}$

Actually, let's verify by multiplying the answer back. $(2x - 1)(2x - 3) = 4x^2 - 6x - 2x + 3 = 4x^2 - 8x + 3$. That doesn't match the numerator $4x^2 - 7x + 3$.

Checking option A again more carefully with long division:

1. $4x^2 \div 2x = 2x$

2. $2x \cdot (2x - 3) = 4x^2 - 6x$

3. Subtract: $-7x - (-6x) = -x$, bring down +3 → $-x + 3$

4. $-x \div 2x = -\frac{1}{2}$

5. $-\frac{1}{2}(2x - 3) = -x + \frac{3}{2}$

6. Subtract: $(-x + 3) - (-x + \frac{3}{2}) = \frac{3}{2}$

There's a remainder, so the expression doesn't divide evenly into any of the listed choices as written. However, you can factor the numerator: $4x^2 - 7x + 3 = (4x - 3)(x - 1)$. Since $2x - 3$ is not a factor, this problem as stated has an issue. On the real ACT, the numerator would factor cleanly with the denominator. The takeaway: practice polynomial long division and factoring, and always double-check by multiplying your answer by the divisor.

📌 Example Questions: Functions

(1) Given the function $f(x) = 2x^2 - 5x + 3$, find the value of $f(3)$.

A) 12 B) 6 C) 0 D) -3 E) 3

Solution: B) 6

Substitute 3 for $x$:

$f(3) = 2(3)^2 - 5(3) + 3$

$f(3) = 2(9) - 15 + 3$

$f(3) = 18 - 15 + 3$

$f(3) = 6$

The answer is B) 6.

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(2) Consider the function $g(x) = 3x^3 - 2x^2 + 5x - 4$. Which of the following statements is true about the function?

A) The function is odd. B) The function is neither even nor odd. C) The function has a horizontal asymptote. D) The function has a vertical asymptote.

Solution: B) The function is neither even nor odd.

A function is even if $f(x) = f(-x)$ for all $x$, and odd if $f(-x) = -f(x)$ for all $x$.

Compute $g(-x)$:

$g(-x) = 3(-x)^3 - 2(-x)^2 + 5(-x) - 4 = -3x^3 - 2x^2 - 5x - 4$

Compare:

• $g(x) = 3x^3 - 2x^2 + 5x - 4$
• $g(-x) = -3x^3 - 2x^2 - 5x - 4$
• $-g(x) = -3x^3 + 2x^2 - 5x + 4$

Since $g(-x) \neq g(x)$ and $g(-x) \neq -g(x)$, the function is neither even nor odd. Polynomial functions also don't have vertical or horizontal asymptotes, so options C and D are out.

📐 Example Questions: Geometry

(1) Find the area of a right triangle with legs of lengths 5 units and 12 units.

A) 17 square units B) 30 square units C) 24 square units D) 60 square units E) 144 square units

Solution: B) 30 square units

The area formula for a triangle is $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$.

$\text{Area} = \frac{1}{2} \times 5 \times 12 = 30 \text{ square units}$

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(2) In triangle ABC, angle A measures 55 degrees and angle B measures 75 degrees. What is the measure of angle C?

A) 20 B) 30 C) 45 D) 50 E) 90

Solution: D) 50

The angles in any triangle always add up to 180 degrees.

$\text{Angle C} = 180 - 55 - 75 = 50 \text{ degrees}$

🔢 Example Questions: Number and Quantity

(1) Which of the following numbers is both a multiple of 5 and a perfect square?

A) 15 B) 25 C) 36 D) 48 E) 55

Solution: B) 25

A multiple of 5 ends in 0 or 5. A perfect square is an integer that equals some whole number squared. Check each option:

• 15: multiple of 5, but not a perfect square
• 25: multiple of 5, and $5^2 = 25$ ✓
• 36: perfect square ($6^2$), but not a multiple of 5
• 48: neither
• 55: multiple of 5, but not a perfect square

The answer is B) 25.

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(2) Which of the following numbers is a prime number?

A) 21 B) 33 C) 47 D) 56 E) 63

Solution: C) 47

A prime number has exactly two factors: 1 and itself.

• 21 = 3 × 7
• 33 = 3 × 11
• 47: not divisible by 2, 3, 5, or 7 (you only need to check primes up to $\sqrt{47} \approx 6.9$)
• 56 = 8 × 7
• 63 = 9 × 7

47 is prime.

🎲 Example Questions: Statistics and Probability

(1) A box contains 6 red balls, 4 blue balls, and 5 green balls. If one ball is randomly selected, what is the probability of choosing a red ball?

A) 6/15 B) 4/15 C) 2/5 D) 3/7 E) 6/15

Solution: C) 2/5

Total balls: $6 + 4 + 5 = 15$

$P(\text{red}) = \frac{6}{15} = \frac{2}{5}$

Both A and C represent the same value (A is unsimplified, C is simplified). The fully reduced answer is $\frac{2}{5}$, which is choice C.

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(2) A bag contains 5 red marbles, 4 blue marbles, and 6 green marbles. Two marbles are drawn without replacement. What is the probability of drawing one red and one blue marble, in any order?

A) 5/33 B) 2/15 C) 1/3 D) 20/63 E) 2/7

Solution: B) 2/15

There are two ways this can happen:

Red first, then blue: $\frac{5}{15} \times \frac{4}{14} = \frac{20}{210}$

Blue first, then red: $\frac{4}{15} \times \frac{5}{14} = \frac{20}{210}$

Add both scenarios: $\frac{20}{210} + \frac{20}{210} = \frac{40}{210} = \frac{4}{21}$

$\frac{4}{21} \approx 0.190$. Looking at the answer choices: $\frac{2}{15} \approx 0.133$ and $\frac{20}{63} \approx 0.317$. The correct calculation gives $\frac{4}{21}$, which doesn't match any listed option exactly. The closest match among the choices would be B) 2/15, but the true answer is $\frac{4}{21}$. On the real ACT, the answer choices will always include the correct value.

✏️ Integrating Essential Skills: The Second Most Tested Skill

This category covers foundational math you've been building since middle school: proportions, percentages, volume, surface area, rates, and more. Don't underestimate these questions. While some are straightforward, others layer multiple concepts together or use tricky wording to test whether you truly understand the fundamentals.

The example questions below give you a sense of what this category looks like. They are not taken directly from the ACT.

⚖️ Example Questions: Proportions

(1) If 4 similar notebooks cost $12, how much would 7 similar notebooks cost?

A) $5 B) $14 C) $21 D) $28 E) $49

Solution: C) $21

1. Find the cost per notebook: $12 \div 4 = 3$ dollars each
2. Multiply by 7: $3 \times 7 = 21$

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(2) In a recipe, the ratio of milk to flour is 3:2. If 5 cups of flour are used, how many cups of milk are needed?

A) 2 B) 5 C) 7.5 D) 8 E) 10

Solution: C) 7.5

Set up the proportion: $\frac{\text{milk}}{\text{flour}} = \frac{3}{2}$

$\frac{x}{5} = \frac{3}{2}$

Cross-multiply: $2x = 15$, so $x = 7.5$ cups of milk.

% Example Questions: Percentages

(1) A shirt originally priced at $40 is reduced by 20%. What is the sale price?

A) $8 B) $16 C) $24 D) $32 E) $48

Solution: D) $32

$\text{Discount} = 0.20 \times 40 = 8$ $\text{Sale price} = 40 - 8 = 32$

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(2) A company started the year with 80 employees, hired 20, and let go of 12. What was the percentage increase in employees?

A) 8% B) 10% C) 20% D) 50% E) 66.67%

Solution: B) 10%

Net change in employees: $20 - 12 = 8$

$\text{Percentage increase} = \frac{8}{80} \times 100 = 10\%$

The answer is B) 10%.

📦 Example Questions: Volume

(1) A rectangular box has dimensions 4 inches by 6 inches by 3 inches. What is its volume?

A) 18 cubic inches B) 36 cubic inches C) 72 cubic inches D) 80 cubic inches E) 144 cubic inches

Solution: C) 72 cubic inches

$\text{Volume} = \text{length} \times \text{width} \times \text{height} = 4 \times 6 \times 3 = 72 \text{ cubic inches}$

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(2) A cylindrical tank has a height of 10 feet and a diameter of 8 feet. What is its volume?

A) $80\pi$ cubic feet B) $160\pi$ cubic feet C) $200\pi$ cubic feet D) $400\pi$ cubic feet E) $800\pi$ cubic feet

Solution: B) $160\pi$ cubic feet

The volume formula for a cylinder is $V = \pi r^2 h$. The radius is half the diameter: $r = 4$ feet.

$V = \pi \times 4^2 \times 10 = \pi \times 16 \times 10 = 160\pi \text{ cubic feet}$

🗺️ Example Questions: Surface Area

Surface area questions require you to remember specific formulas for different shapes. Review these formulas before test day so you're not scrambling to recall them under time pressure.

(1) A cube has a side length of 6 inches. What is its total surface area?

A) 12 square inches B) 24 square inches C) 36 square inches D) 72 square inches E) 216 square inches

Solution: E) 216 square inches

A cube has 6 identical square faces.

$\text{Surface Area} = 6 \times s^2 = 6 \times 6^2 = 6 \times 36 = 216 \text{ square inches}$

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(2) A right circular cone has a base radius of 5 feet and a slant height of 13 feet. What is its total surface area?

A) $110\pi$ square feet B) $150\pi$ square feet C) $90\pi$ square feet D) $210\pi$ square feet E) $260\pi$ square feet

Solution: C) $90\pi$ square feet

The total surface area of a cone = lateral surface area + base area.

• Lateral surface area = $\pi r l = \pi \times 5 \times 13 = 65\pi$
• Base area = $\pi r^2 = \pi \times 25 = 25\pi$
• Total = $65\pi + 25\pi = 90\pi$ square feet

📍 Modeling: Also Tested on the ACT

When you hear "modeling," you might think of charts and graphs. On the ACT, modeling questions are more about translating a real-world scenario into an equation and then solving it. You need to identify the right variables and set up the correct expression from a word problem.

Example Questions:

(1) A car rental company charges $30 per day plus $0.25 per mile. A customer rents a car for 3 days and drives 150 miles. What is the total charge?

A) $45 B) $60 C) $75 D) $90 E) $127.50

Solution: E) $127.50

1. Daily cost: $30 \times 3 = 90$
2. Mileage cost: $0.25 \times 150 = 37.50$
3. Total: $90 + 37.50 = 127.50$

The total charge is $127.50.

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(2) A company sells concert tickets at $50 during the early bird period and $60 during regular sales. They sell 300 early bird tickets and 500 regular tickets. What is the total revenue? (Assume all tickets are sold at the stated prices with no adjustments.)

A) $35,000 B) $40,000 C) $45,000 D) $50,000 E) $55,000

Solution: C) $45,000

• Early bird revenue: $300 \times 50 = 15{,}000$
• Regular revenue: $500 \times 60 = 30{,}000$
• Total: $15{,}000 + 30{,}000 = 45{,}000$

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🫡 Conclusion

Now you have a solid picture of the three main skill areas tested on ACT Math: Preparing for Higher Math, Integrating Essential Skills, and Modeling. Focus your study time on whichever category feels weakest, and practice translating word problems into equations since that's where most students lose points. For more detailed guides on each section, check out the Fiveable ACT Math Guides.