All Topics · 20 Questions
ACT Math
Power 20
High-difficulty questions across every ACT Math topic. Study the concepts, then test yourself.
📐 Core Concepts to Know
1. Linear Equations & Systems
Solve by substitution or elimination. For systems ax+by=c, use elimination to cancel one variable.
ax + b = cx + d → (a−c)x = d−b → x = (d−b)/(a−c)
Example
Solve: 5x − 3 = 2x + 9
→ 3x = 12 → x = 4 ✓
2. Quadratic Equations
Factor, complete the square, or use the quadratic formula. Sum of roots = −b/a, product = c/a.
x = (−b ± √(b²−4ac)) / 2a | Discriminant: b²−4ac
Example
x² − 7x + 12 = 0 → (x−3)(x−4) = 0
→ x = 3 or x = 4 ✓
3. Functions & Graphs
Vertex form: y = a(x−h)² + k, vertex at (h, k). Composition: g(f(x)) — evaluate inner first.
f∘g(x) = f(g(x)) | Vertex: (h, k) when y = a(x−h)² + k
4. Geometry Essentials
Area of sector = (θ/360)·πr². Similar triangles: area ratio = (side ratio)². Pythagorean theorem: a²+b²=c².
Sector area = (θ/360)πr² | sin θ = opp/hyp | cos θ = adj/hyp
5. Statistics & Probability
Mean = sum/count. For independent events: P(A and B) = P(A) × P(B). Median = middle value when sorted.
Mean = Σx/n | P(A∩B) = P(A)·P(B) if independent
6. Exponentials & Polynomials
f(x) = a·bˣ: a is the initial value, b is the growth factor. For polynomials, multiply term by term (FOIL extended).
f(x) = a·bˣ | (x²+px)(x+q) = x³+qx²+px²+pqx