ACT Math Test

The ACT Math Test assesses students' mathematical skills and problem-solving abilities in preparation for college admission.

Numbers and OperationsAlgebraic Expressions and EquationsGeometry and Measurement
Functions and ModelingStatistics and ProbabilityAdvanced Algebra and Systems of Equations
Using Math in Financial DecisionsMath in Science and EngineeringMath in Everyday Problem-Solving
Pacing Yourself During the TestEliminating Wrong AnswersChecking Your Work Efficiently
Numbers and Operatio...Algebraic Expression...Geometry and Measure...Functions and Modeli...Statistics and Proba...Advanced Algebra and...Using Math in Financ...Math in Science and ...Math in Everyday Pro...Pacing Yourself Duri...Eliminating Wrong An...Checking Your Work E...
Advanced Topics

Advanced Algebra and Systems of Equations

Diving Deeper into Algebra

Some ACT questions involve more complex algebra, such as quadratic equations and systems of equations.

Major Concepts

  • Quadratic Equations: Equations like \(ax^2 + bx + c = 0\).
  • Factoring: Breaking down expressions into simpler parts.
  • Systems of Equations: Solving two or more equations at once.
  • Substitution & Elimination: Methods for solving systems.

Why It Matters

These skills help you balance budgets, solve engineering problems, and even figure out intersection points in maps or schedules.

Strategies

  • Always check your solutions in both equations.
  • For quadratics, try factoring first; if that doesn’t work, use the quadratic formula.

Key Formula

\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Examples

  • Solving \(2x + 3y = 12\) and \(x - y = 2\) together to find \(x\) and \(y\).

  • Factoring \(x^2 - 5x + 6\) into \((x-2)(x-3)\).

In a Nutshell

Advanced algebra helps you solve more challenging problems involving multiple variables.

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Using Math in Financial Decisions