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80 multiple-choice questions and 250 flashcards, written to the ACT Math content categories: Pre-Algebra; Elementary Algebra; Intermediate Algebra; Coordinate Geometry; Plane Geometry; Trigonometry blueprint. Every question carries a full rationale.
ACT Math content categories: Pre-Algebra; Elementary Algebra; Intermediate Algebra; Coordinate Geometry; Plane Geometry; Trigonometry (60 questions, 60 minutes)
CoStudy's ACT Math bank holds 330 items. Every multiple-choice question carries a written rationale explaining why the correct answer is correct and why each distractor is tempting but wrong.
A sample of 8 multiple-choice questions from the bank, with the full rationale shown.
30-60-90 right triangle has side ratios:
Answer: C — 1 : √3 : 2 (shortest leg : longer leg : hypotenuse)
30-60-90: 1 : √3 : 2. 45-45-90: 1 : 1 : √2 (isoceles right). Memorize both; ACT tests heavily. 3-4-5 and 5-12-13: Pythagorean triples — useful for shortcuts.
If 30% of a number is 24, what is the number?
Answer: D — 80
Set 0.30 × N = 24, so N = 24 / 0.30 = 80. Quick mental math: 24 ÷ 0.3 = 24 × (10/3) = 80.
Equation of line through (0, 2) with slope 3:
Answer: A — y = 3x + 2 (slope-intercept form: y = mx + b)
Slope-intercept: y = mx + b. m = 3, b = 2 (y-intercept). Point-slope alternative: y − 2 = 3(x − 0). General form: ax + by = c.
Express 0.0001275 in scientific notation:
Answer: C — 1.275 × 10⁻⁴
C) Move the decimal 4 places right; coefficient between 1 and 10. A) Wrong exponent. B) Coefficient must be < 10. D) Wrong sign on exponent.
The interior angles of a regular hexagon sum to:
Answer: C — 720°
Sum of interior angles = (n − 2) × 180°. For hexagon (n = 6): (6 − 2)(180) = 4 × 180 = 720°. Each interior angle = 720/6 = 120°.
If f(x) = 2x² − 3, then f(−2) =
Answer: D — 5 (2(4) − 3 = 8 − 3)
Substitute x = −2: f(−2) = 2(−2)² − 3 = 2(4) − 3 = 5. Note (−2)² = +4 (parens square the negative). Functions notation: f(input) → output.
Solve the system: 2x + 3y = 12 and x − y = 1.
Answer: A — x = 3, y = 2
From eq 2: x = y + 1. Substitute: 2(y + 1) + 3y = 12 → 5y + 2 = 12 → y = 2. Then x = 3. Verify: 2(3) + 3(2) = 12 ✓ and 3 − 2 = 1 ✓.
Solve: 3(x − 2) = 2x + 1
Answer: C — x = 7 (3x − 6 = 2x + 1 → x = 7)
Distribute: 3x − 6 = 2x + 1. Subtract 2x: x − 6 = 1. Add 6: x = 7. Check: 3(7−2) = 15; 2(7)+1 = 15 ✓.
6 sample cards from the 250 in the bank.
Perimeter of rectangle?
2(L + W).
Item $80 with 25% off. Sale price?
$80 × 0.75 = $60.
Composition: f(g(x)) when f(x) = x+2, g(x) = 3x?
f(3x) = 3x + 2.
Discriminant < 0 means?
Two complex/imaginary solutions; no real.
Standard parabola: y = x². Vertex form: y = (x-h)² + k.
Use to graph any parabola.
Right triangle: angle 45°, leg 7. Hypotenuse?
7√2.
These samples are a small slice. The full bank runs flashcards, multiple choice and timed mock exams with per-chapter progress tracking, on the web and in the iOS app.
The ACT Math bank holds 330 items: 80 multiple-choice questions, 250 flashcards. 14 of them are on this page to read free, with no signup.
Yes. Every multiple-choice item carries a written rationale that states the controlling principle behind the correct answer and then addresses each wrong option in turn — why it tempts and precisely where it fails. Knowing why the plausible answer was wrong is worth more than knowing which letter was right.
ACT Math content categories: Pre-Algebra; Elementary Algebra; Intermediate Algebra; Coordinate Geometry; Plane Geometry; Trigonometry (60 questions, 60 minutes)
The samples on this page are free to read in full, rationales included, with no account. The complete 330-item bank, the timed mock exams and per-chapter progress tracking are part of CoStudy on the web and in the iOS app.
Last reviewed 2026-08-22. Banks are written against the certifying body's published exam outline and re-checked when that outline changes — exams get renumbered, retired and reweighted, and a bank written to a superseded outline teaches the wrong proportions. Figures that are re-indexed annually are deliberately not asserted as rules; the questions test the governing principle instead.
This bank is written against ACT's published exam material. Check ACT's test descriptions for the current outline, fees and eligibility rules — those change, and the certifying body is the only authority on them. CoStudy is not affiliated with ACT.