Exam prep · intermediate
ACT Math Prep
Algebra through trig skills that power ACT Math. Drill the underlying techniques — not official ACT wording or timed sections.
Skills
85 skills in 4 sections — fundamentals first, then more specific topics. Practice each until Mastery Score 100.
A.Foundations15 skills
- A.1 Number ClassesPractice →Name the most specific set for a number: natural, whole, integer, rational, irrational, or real.
- A.2 Prime & CompositePractice →Classify small positives as prime or composite (1 is neither).
- A.3 Prime FactorizationPractice →Write a positive integer as a product of primes (powers allowed).
- A.4 Greatest Common FactorPractice →Find the GCF of two positive integers.
- A.5 Least Common MultiplePractice →Find the LCM of two positive integers.
- A.6 Square Roots & IrrationalsPractice →Evaluate roots of perfect squares, or say when a square root is irrational.
- A.7 Mean (Average)Practice →Find the mean of a short list of whole numbers.
- A.8 MedianPractice →Find the median of a short list of whole numbers.
- A.9 Adding FractionsPractice →Add fractions with unlike denominators; simplify.
- A.10 Subtracting FractionsPractice →Subtract fractions with unlike denominators; simplify.
- A.11 Simplifying FractionsPractice →Reduce a fraction to lowest terms.
- A.12 Percent of a NumberPractice →Compute a percent of a whole number.
- A.13 Percent Increase & DecreasePractice →Find the percent change between an old and a new value.
- A.14 Solving ProportionsPractice →Solve a/b = x/c for the unknown value.
- A.15 Unit RatesPractice →Find unit rates from ratios.
B.Algebra core27 skills
- B.1 Combining Like TermsPractice →Simplify linear expressions by combining like terms.
- B.2 Distributive PropertyPractice →Expand a(b + c) expressions.
- B.3 One-Step EquationsPractice →Solve ax = b style one-step linear equations.
- B.4 Two-Step EquationsPractice →Solve two-step linear equations in one variable.
- B.5 Absolute Value EquationsPractice →Solve |x − h| = a for both roots.
- B.6 One-Step InequalitiesPractice →Solve simple linear inequalities.
- B.7 Two-Step InequalitiesPractice →Solve ax + b < c or > c and report x ? k.
- B.8 Exponent Product RulePractice →Simplify x^m · x^n by adding exponents.
- B.9 Exponent Power RulePractice →Simplify (x^m)^n by multiplying exponents.
- B.10 Systems by EliminationPractice →Solve 2×2 systems by subtracting equations.
- B.11 Systems by AdditionPractice →Solve 2×2 systems by adding to cancel a variable.
- B.12 Factor Out a GCFPractice →Factor the greatest common factor from a binomial.
- B.13 Difference of SquaresPractice →Factor x² − a² as (x−a)(x+a).
- B.14 Factoring TrinomialsPractice →Factor x² + bx + c into two binomials.
- B.15 Quadratic Roots (Factoring)Practice →Find roots of monic quadratics that factor cleanly.
- B.16 Quadratic FormulaPractice →Solve ax² + bx + c = 0 with the quadratic formula.
- B.17 Add PolynomialsPractice →Combine like terms when adding linear polynomials.
- B.18 Subtracting PolynomialsPractice →Subtract one polynomial from another and collect like terms.
- B.19 Multiply BinomialsPractice →Expand (x+a)(x+b) with FOIL.
- B.20 Negative ExponentsPractice →Evaluate powers with negative exponents as fractions.
- B.21 Scientific NotationPractice →Write large and small numbers in scientific notation.
- B.22 Evaluating ExpressionsPractice →Substitute values into an algebraic expression and simplify.
- B.23 Slope Between PointsPractice →Find the slope through two points.
- B.24 Slope from a GraphPractice →Read rise over run from a graphed line and slope triangle.
- B.25 Slope-Intercept FormPractice →Rewrite Ax + By = C as y = mx + b.
- B.26 Intercepts from a Line GraphPractice →Read x- and y-intercepts directly from a graphed line.
- B.27 Slope–Intercept FeaturesPractice →Read slope m and y-intercept b from y = mx + b.
C.Geometry & trigonometry29 skills
- C.1 Triangle Angle SumPractice →Find a missing angle in a triangle.
- C.2 Triangle Angles in a DiagramPractice →Use a labeled triangle diagram to find a missing interior angle.
- C.3 Angles with Parallel LinesPractice →Use corresponding angles formed by a transversal of parallel lines.
- C.4 Complementary & Supplementary AnglesPractice →Find the missing angle in a complementary or supplementary pair.
- C.5 Pythagorean TheoremPractice →Find a missing side of a right triangle.
- C.6 Right-Triangle DiagramPractice →Find a missing side from a labeled right-triangle diagram.
- C.7 Rectangle AreaPractice →Compute area of a rectangle.
- C.8 Triangle AreaPractice →Find the area of a triangle from base and height.
- C.9 Parallelogram & Trapezoid AreaPractice →Find areas of parallelograms and trapezoids.
- C.10 Circle AreaPractice →Compute area given radius (coefficient of π).
- C.11 CircumferencePractice →Find a circle's circumference in terms of π.
- C.12 Volume of a CylinderPractice →Find a cylinder's volume in terms of π.
- C.13 Distance Between PointsPractice →Find the distance between two points in the plane.
- C.14 MidpointPractice →Find the midpoint of a segment in the plane.
- C.15 Angles from a DiagramPractice →Read a marked angle between two rays in a figure.
- C.16 Which Circle Matches?Practice →Match (x − h)² + (y − k)² = r² to the correct graphed circle.
- C.17 Right-Triangle TrigPractice →SOH-CAH-TOA with integer sides.
- C.18 Inverse Trig ValuesPractice →Evaluate arcsin, arccos, and arctan at special values, in degrees.
- C.19 Unit Circle ValuesPractice →Recall exact sine and cosine at common angles.
- C.20 Coordinates on the Unit CirclePractice →Read exact sine and cosine coordinates from a unit-circle diagram.
- C.21 Exact Trig ValuesPractice →Recall exact sin, cos, and tan of special angles in degrees.
- C.22 Degrees & RadiansPractice →Convert between degree and radian measure.
- C.23 Coterminal AnglesPractice →Find the coterminal angle between 0° and 360°.
- C.24 Reference AnglesPractice →Find the reference angle for an angle in degrees.
- C.25 Pythagorean IdentityPractice →Use sin²θ + cos²θ = 1 to find a missing value.
- C.26 Tangent-Secant IdentityPractice →Use 1 + tan²θ = sec²θ to move between the two.
- C.27 Cofunction ValuesPractice →Use sin(90° − θ) = cos θ and related cofunctions.
- C.28 Sine Graph FeaturesPractice →Find amplitude or period from y = a sin(bx) and its graph.
- C.29 Amplitude & PeriodPractice →Read amplitude and period from A sin(Bx) or A cos(Bx).
D.Functions & precalculus14 skills
- D.1 Function EvaluationPractice →Evaluate polynomial functions at a point.
- D.2 Function CompositionPractice →Evaluate (f ∘ g)(x) at a number.
- D.3 Exponent LawsPractice →Simplify products and powers of powers.
- D.4 Evaluating LogarithmsPractice →Evaluate logarithms of perfect powers exactly.
- D.5 Log Product RulePractice →Expand log(ab) using log laws (base 10 style).
- D.6 Solving Exponential & Log EquationsPractice →Solve bˣ = c and log_b(x) = k when everything is a perfect power.
- D.7 Basic Trig EquationsPractice →Solve sin θ = k on [0, 2π) for standard values.
- D.8 Inverse of Linear FunctionsPractice →Find the inverse of f(x) = ax + b.
- D.9 Arithmetic SequencesPractice →Find the nth term of an arithmetic sequence.
- D.10 Geometric SequencesPractice →Find the nth term of a geometric sequence.
- D.11 Parabola Key FeaturesPractice →Find vertex or y-intercept from vertex form.
- D.12 Zeros from a Parabola GraphPractice →Read a parabola’s positive x-intercept from its graph.
- D.13 Adding Complex NumbersPractice →Add and subtract numbers in a + bi form.
- D.14 Simplifying RadicalsPractice →Pull perfect-square factors out of a square root.