Topic Review Guides

Our comprehensive Topic Review Guides break down every concept tested on the ACT Math section into clear, manageable lessons. Each guide starts with the fundamentals and builds up to more advanced applications, ensuring you understand not just the "what" but also the "why" behind each mathematical concept. Whether you're reviewing Pre-Algebra basics or tackling complex Trigonometry problems, our guides provide step-by-step explanations, worked examples, and common pitfalls to avoid. We've organized the content to match the ACT's six main content areas, making it easy to focus your study time on the topics where you need the most improvement.

Every topic guide includes multiple practice examples that mirror the style and difficulty of actual ACT questions. You'll see how concepts are tested in different ways, from straightforward calculations to multi-step word problems that require you to apply several concepts together. Each example includes a detailed solution walkthrough, so you can follow along and understand the reasoning behind each step. We also highlight key formulas, shortcuts, and problem-solving strategies specific to that topic, helping you work more efficiently under the time pressure of the actual exam.

Beyond just explaining concepts, our guides help you identify patterns and connections between different topics. Many ACT Math questions require you to combine knowledge from multiple areas—for example, a coordinate geometry problem might also involve algebra, or a trigonometry question might require geometric reasoning. Our guides show you how these topics interconnect, preparing you for the integrated nature of the ACT Math section. With printable PDF versions available for offline study and interactive online versions with embedded practice problems, you can review topics in whatever format works best for your learning style.

1. The "Big Four" Coordinate Formulas
   Why: This is the highest-value guide you can make. Coordinate geometry is 15–20% of the test, and these four formulas are the entry ticket to almost every question in that category.
   Content: Distance Formula, Midpoint Formula, Slope Formula (m), and Slope-Intercept Form (y = mx + b).
   
2. Right Triangles & Trigonometry (SOH CAH TOA)
   Why: Trigonometry is scary to students but is actually very predictable on the ACT. It is almost always right-triangle based.
   Content: SOH CAH TOA definitions, The Pythagorean Theorem (a² + b² = c²), and Special Right Triangles (30-60-90, 45-45-90).
   
3. Linear Algebra & Systems
   Why: "Solving for x" is the bread and butter of the test. Systems of equations appear in both simple formats and complex word problems.
   Content: Solving linear equations, systems of equations (substitution vs. elimination), and interpreting solutions (intersection of two lines).
4. Quadratic Equations
   Why: This covers the "Intermediate Algebra" gap. Students often forget how to handle an equation with an x² term.
   Content: Factoring simple quadratics, The Quadratic Formula (essential memorization), and recognizing parabolas (y = ax² + bx + c).
   
5. Circles (Geometric & Algebraic)
   Why: This topic hits two categories: Plane Geometry and Coordinate Geometry. The equation of a circle is a common "stumper" that is easy to fix.
   Content: Area and Circumference formulas (A = πr², C = 2πr) and the Standard Equation of a Circle: (x - h)² + (y - k)² = r².
6. Exponents & Radicals
   Why: The rules of exponents (multiplying vs. raising to a power) are easy to mix up, and the ACT loves to test fractional exponents.
   Content: Product/Quotient rules, Power to a Power, Negative Exponents, and converting between Radicals and Fractional Exponents (x^1/2 = √x).
7. Ratios, Proportions, & Percents
   Why: This is the core of the Modeling category. These questions are often wordy, and students need a reliable framework to set them up.
   Content: Setting up proportions (a/b = c/d), Percent Change formula, and Direct vs. Inverse Variation.
8. Functions (Notation & Translations)
   Why: Students often panic when they see f(g(x)). This guide demystifies the notation.
   Content: Function evaluation (plugging in numbers), Composite Functions, and Graph Translations (what happens when you do f(x) + 2 vs f(x + 2)).
9. Area, Perimeter, & Volume
   Why: These are "free points" if the student knows the formula.
   Content: Area of triangles, parallelograms, and trapezoids. Volume of cylinders and prisms. (Focus on Trapezoids—students always forget that formula: A = (b₁ + b₂)/2 × h).
10. Statistics & Probability
    Why: These appear at the end of the test and are often easier than the algebra questions, but students are fatigued. A quick review ensures they grab these points.
    Content: Mean, Median, Mode, Range, and Basic Probability (Desired Outcomes / Total Outcomes).