ACT Math

Full practice tests

Timed like the real digital test, with a score estimate. Every answer is solved step by step.

• ACT Math Practice Test 1 · 45 questions, 50 minutes, score 1-36 · answer key · print it
• ACT Math Practice Test 2 · 45 questions, 50 minutes, score 1-36 · answer key · print it

What the ACT math test asks, and where we teach it

The ACT math test: 45 questions in 50 minutes, 4 choices each, calculator allowed, no formula sheet, score 1-36. Each skill below links to its lesson, with every step written out.

Number and Quantity

• Integers, fractions, decimals: Integers, Fractions, Decimals
• Roots and powers: Powers, square roots, absolute value, Simplifying square roots, Rational exponents
• Scientific notation: Scientific notation
• Complex numbers: Complex numbers, Dividing complex numbers
• Matrices: Matrices, Multiplying matrices, Determinants
• Vectors: Adding, subtracting, × a number, Dot product, angle between two vectors
• Repeating patterns: ACT: Repeating patterns

Algebra

• Linear equations: Linear equations, Linear equations
• Inequalities: Inequalities, Compound inequalities
• Absolute value: Absolute value equations
• Systems: Systems of equations, Solving by substitution
• Factoring and quadratics: Factoring, Solving by factoring, Quadratic equations, Completing the square
• Slope and lines: Slope from two points, Equation of a line through two points, Parallel and perpendicular lines
• Word problems: Word problems part 1, Word problems part 2, Work-rate

Functions

• f(x), composition, inverse: Functions, Composition and inverse functions
• Domain and range: Domain and range
• Sequences: Sequences
• Exponents and logs: Exponential models from words, Exponential equations and logarithms, Compound and continuous interest
• Graphs and shifts: Graph transformations, Piecewise functions, Polynomial graphs
• Remainders of polynomials: Remainder and factor theorem

Geometry

• Angles and parallel lines: Angle facts, Parallel lines and a transversal, Angles in a polygon
• Pythagoras, special triangles: Pythagoras, Special right triangles
• Trig ratios: Right-triangle trigonometry, The unit circle
• Law of sines and cosines: The law of sines, The law of cosines, Area of a triangle with sine
• Circles and arcs: Equation of a circle, Arc length and sector area
• Distance and midpoint: Distance between two points, Midpoint
• Similar triangles: Similar triangles

Statistics and Probability

• Mean, median, mode: Mean, median, mode, range, ACT: Mean from totals
• Counting: Counting choices, Permutations, Combinations
• Probability: Probability, Probability with or, Probability with and, Conditional probability
• Expected value: Expected value
• Spread: Standard deviation

Integrating Essential Skills

• Percent: Percent, Percent, Percents and money
• Rates and units: Ratios, unit rates, compare deals, Converting units
• Proportions: Proportions, Direct and inverse variation
• Area and volume: Perimeter and area, Volume and surface area, Composite shapes, Cones

1. ACT: Mean from totals · the missing score, the mean of two groups (25 problems)
2. ACT: Repeating patterns · the n-th item, the ones digit of a power, a digit of a repeating decimal (24 problems)