What is 4/6 − 1/4?
Answer & explanation
Learn: Numbers, vectors & matrices5/12. Use denominator 12: 8/12 − 3/12.
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View coverage ACT Math Flashcards & Study Review
Read 12 sample cards from the 80-card ACT Math foundation collection. Try recalling each answer before checking the explanation.
Version 2026-10-27 · Original foundation materials · No sign-up
What this collection covers
Enhanced ACT Mathematics foundations.
The cards preview selected ideas; they do not measure readiness for the whole examination. Your personal review schedule is available in the review tool.
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.
Sample flashcards, with answers
If 5x − 9 = 2x + 15, what is x?
Answer & explanation
Learn: Equations with restrictions8. Subtract 2x from both sides and add the constant on the left.
f(x) = 2x + 4 for x < 0 and f(x) = x² − 4 for x ≥ 0. What is f(−5)?
Answer & explanation
Learn: Functions as input rules-6. The input is negative, so use the first branch.
A line has slope 4/3. What is the slope of a perpendicular line?
Answer & explanation
Learn: Coordinate geometry connections-3/4. For two nonvertical perpendicular lines, the slopes multiply to −1.
A class of 4 students has mean score 60; another class of 8 students has mean 90. What is the combined mean?
Answer & explanation
Learn: Summaries from data80. Convert each mean into a total by multiplying by its group size.
A map scale is 1 cm to 4 km. Two towns are 5 cm apart on the map. How many kilometers apart are they?
Answer & explanation
Learn: Rates, scales & mixtures20. Each map centimeter represents the stated real distance.
In matrix notation a₂₃, which index names the row?
Answer & explanation
Learn: Vectors and matrix structureThe first index: row 2, column 3.
The equations x + y = 13 and x − y = 5 hold. What is y?
Answer & explanation
Learn: Systems and practical constraints4. Subtract the second equation from the first to eliminate x.
For real x, what is the minimum value of y = 2(x − 4)² + 5?
Answer & explanation
Learn: Read quadratic structure5. The square is nonnegative for every real input.
A trapezoid has parallel bases 4 cm and 5 cm and perpendicular height 4 cm. What is its area in square centimeters?
Answer & explanation
Learn: Geometry with dimensions18. Average the two parallel base lengths.
A fair spinner has 5 equal sectors, of which 2 are green. What is the probability of not landing on green?
Answer & explanation
Learn: Count the sample space3/5. The green probability is its number of sectors divided by the total.
A code consists of one of 4 letters followed by one of 5 digits. Repetition restrictions do not apply. How many codes are possible?
Answer & explanation
Learn: Patterns, counting & reasoning20. For each possible letter, every digit is allowed.
Use the cards as a recall routine
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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.