What is 3/6 − 1/4?
- 1/4
- 3/4
- 1/3
- 2/5
Read the answer and explanation
Answer: 1/4
- Use denominator 12: 6/12 − 3/12.
- Subtract the numerators and reduce the fraction.
- The requested value is 1/4.
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View coverage ACT Math Practice Worksheets & Answer Key
Download an 8-question ACT Math worksheet with a separate answer and explanation section. The selected text questions work without a screen or an account.
Version 2026-10-27 · Original foundation materials · No sign-up
What this collection covers
Enhanced ACT Mathematics foundations.
This fixed sample includes one question per selected skill before additional families. Questions requiring a separate diagram are excluded from this text worksheet. It is an untimed study resource with working space, rather than an official mock examination.
Author-reviewed learning materials. Independent educator review is pending; question difficulty has not been calibrated with learner results. Check coverage and gaps before planning your preparation.
Inside the printable worksheet
8 original questionsSeparate explanationsUS Letter · PDF · Version 2026-10-27
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Questions included in this PDF
If 5x − 9 = 2x + 15, what is x?
- 24/5
- 2
- 8
- 24
Read the answer and explanation
Answer: 8
- Subtract 2x from both sides and add the constant on the left.
- Divide by the remaining coefficient.
- The requested value is 8.
f(x) = 2x + 5 for x < 0 and f(x) = x² − 5 for x ≥ 0. What is f(−6)?
- 31
- -17
- -41
- -7
Read the answer and explanation
Answer: -7
- The input is negative, so use the first branch.
- Substitute the negative input into the linear rule.
- The requested value is -7.
A line has slope 6/3. What is the slope of a perpendicular line?
- -2
- 1/2
- 2
- -1/2
Read the answer and explanation
Answer: -1/2
- For two nonvertical perpendicular lines, the slopes multiply to −1.
- Take the reciprocal and change its sign.
- The requested value is -1/2.
A class of 3 students has mean score 60; another class of 6 students has mean 90. What is the combined mean?
- 75
- 70
- 80
- 50
Read the answer and explanation
Answer: 80
- Convert each mean into a total by multiplying by its group size.
- Add the totals and divide by the total number of students.
- The requested value is 80.
A map scale is 1 cm to 4 km. Two towns are 5 cm apart on the map. How many kilometers apart are they?
- 2000
- 5/4
- 20
- 4
Read the answer and explanation
Answer: 20
- Each map centimeter represents the stated real distance.
- Multiply map distance by kilometers per centimeter; centimeters cancel.
- The requested value is 20.
Vectors u=(4,−2) and w=(3,6) are given. What is the second component of 2 u−w?
- -8
- -10
- 5
- -16
Read the answer and explanation
Answer: -10
- Compute the second component only: 2(−2) minus the second component of w.
- Apply the scalar before subtracting the vector.
- Substitute the given numbers: 2 × (-2)-6 = -10.
- Therefore the requested value is -10.
The equations x + y = 19 and x − y = 7 hold. What is y?
- 6
- 7
- 13
- 12
Read the answer and explanation
Answer: 6
- Subtract the second equation from the first to eliminate x.
- The resulting equation has 2y on the left; divide by 2.
- The requested value is 6.
Sources and preparation route
These prompts and explanations are the site's original learning materials. The reference links below support the selected skills; they are not endorsements or official examination questions.