The ACT Math section can feel like a daunting challenge, but with the right preparation, it’s entirely conquerable. Covering a broad range of topics from algebra to trigonometry, this section tests your mathematical reasoning, problem-solving skills, and ability to apply key formulas under time pressure. To help you excel, we’ve compiled the ultimate ACT Math cheat sheet, complete with essential formulas, strategies, and tips to boost your confidence and score. Whether you’re aiming for a perfect 36 or just looking to improve, this guide is your go-to resource.
Why You Need a Cheat Sheet
The ACT Math section consists of 60 questions to be answered in 60 minutes, covering pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. While the test provides some formulas, most must be memorized.
Furthermore, a mental “cheat sheet” of key formulas and strategic tips can save precious time and reduce stress. Let’s dive into the must-know formulas and actionable advice to maximize your performance.
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Pre-Algebra and Elementary Algebra (20-25% of Questions)
This section tests foundational math skills, including percentages, ratios, proportions, and basic equations.
- Percentage Formula:
- Percent = (Part / Whole) × 100
- Example: If 20 out of 80 students are boys, the percentage is (20/80) × 100 = 25%.
- Average (Arithmetic Mean):
- Average = Sum of terms / Number of terms
- Tip: For consecutive numbers, the average is the middle number (for odd counts) or the average of the two middle numbers (for even counts).
- Proportion:
- a/b = c/d → ad = bc (cross-multiplication)
- Useful for scaling problems, like map distances or recipe adjustments.
- Linear Equations:
- Slope-intercept form: y = mx + b (m = slope, b = y-intercept)
- Slope: m = (y₂ – y₁) / (x₂ – x₁)
- Tip: Memorize how to find the slope from two points—it’s a common question!
Pro Tip: Practice mental math for percentages and averages to save time. If a question involves decimals, convert to fractions for easier calculations (e.g., 0.25 = 1/4).
Intermediate Algebra (15-20% of Questions)
This section dives deeper into algebraic manipulation, quadratic equations, and functions.
- Quadratic Formula:
- For ax² + bx + c = 0, x = [-b ± √(b² – 4ac)] / 2a
- Use this to solve quadratic equations when factoring isn’t straightforward.
- Factoring Quadratics:
- Example: x² + 5x + 6 = (x + 2)(x + 3)
- Look for factors of the constant (c) that add up to the middle coefficient (b).
- Exponent Rules:
- xᵐ × xⁿ = xᵐ⁺ⁿ
- xᵐ / xⁿ = xᵐ⁻ⁿ
- (xᵐ)ⁿ = xᵐⁿ
- Tip: Negative exponents flip to the denominator (e.g., x⁻² = 1/x²).
- Function Notation:
- f(x) represents a function’s output for input x.
- Example: If f(x) = 2x + 3, then f(4) = 2(4) + 3 = 11.
Pro Tip: For quadratics, check if factoring is quicker than the quadratic formula. Also, practice function composition (e.g., f(g(x))) to handle complex function questions.
Coordinate Geometry (15-20% of Questions)
This section focuses on graphs, lines, and conic sections.
- Distance Formula:
- Distance = √[(x₂ – x₁)² + (y₂ – y₁)²]
- Use to find the length between two points on a coordinate plane.
- Midpoint Formula:
- Midpoint = [(x₁ + x₂)/2, (y₁ + y₂)/2]
- Tip: This is often tested alongside the distance formula.
- Equation of a Circle:
- (x – h)² + (y – k)² = r², where (h, k) is the center and r is the radius.
Pro Tip: Sketch graphs for coordinate geometry problems to visualize relationships. For parallel/perpendicular lines, remember parallel lines have equal slopes, and perpendicular slopes are negative reciprocals (e.g., if slope = 2, perpendicular slope = -1/2).
Plane Geometry (20-25% of Questions)
Geometry questions test properties of shapes, area, perimeter, and volume.
- Area Formulas:
- Triangle: A = (1/2) × base × height
- Rectangle: A = length × width
- Circle: A = πr²
- Trapezoid: A = (1/2) × (base₁ + base₂) × height
- Perimeter/Circumference:
- Rectangle: P = 2(length + width)
- Circle: C = 2πr or πd
- Volume Formulas:
- Rectangular prism: V = length × width × height
- Cylinder: V = πr²h
- Sphere: V = (4/3)πr³
- Pythagorean Theorem:
- a² + b² = c² (for right triangles, c is the hypotenuse)
- Common Pythagorean triples: (3, 4, 5), (5, 12, 13).
Pro Tip: For geometry problems, draw diagrams and label all given information. Look for special triangles (e.g., 30-60-90 or 45-45-90) to simplify calculations.
Trigonometry (5-10% of Questions)
Though a smaller portion, trigonometry can be tricky without preparation.
- SOH-CAH-TOA:
- Sin θ = Opposite/Hypotenuse
- Cos θ = Adjacent/Hypotenuse
- Tan θ = Opposite/Adjacent
- Trigonometric Identities:
- Sin²θ + Cos²θ = 1
- Tan θ = Sin θ / Cos θ
- Unit Circle Basics:
- Know key angles (0°, 30°, 45°, 60°, 90°) and their sine/cosine values.
- Example: Sin 30° = 1/2, Cos 45° = √2/2.
Pro Tip: Memorize the unit circle for quick recall. For word problems, convert angles to radians if needed (e.g., 180° = π radians).
General Test Tips
- Time Management: Aim for 1 minute per question. Skip tough questions and return to them if time allows.
- Answer Choices: Use the answer choices to your advantage—plug them in for algebra problems or estimate for geometry.
- Practice with Real Tests: Use official ACT practice tests to familiarize yourself with question formats.
- Calculator Use: Bring an approved calculator (e.g., TI-84) and know its functions, but don’t rely on it for basic arithmetic.
- Eliminate Wrong Answers: Narrow down choices by eliminating obviously incorrect options, especially in word problems.
Final Thoughts
Mastering the ACT Math section requires a balance of memorizing key formulas and practicing strategic problem-solving. Create flashcards for the formulas listed above and review them daily. Focus on your weak areas—whether it’s trigonometry or coordinate geometry—and practice those question types. Most importantly, stay calm during the test. With this cheat sheet in your mental toolkit, you’ll be well-equipped to tackle the ACT Math section with confidence.
For more practice, check out resources like the official ACT website or Khan Academy’s free ACT prep materials. Good luck—you’ve got this!
FAQs: ACT Cheat Sheets, Formulas & Tips
1. What is the ACT Math Cheat Sheet?
The ACT Math Cheat Sheet is a condensed guide featuring key formulas, concepts, and strategies to help students quickly review important topics before the ACT Math section.
2. Where can I find an ACT Math Cheat Sheet PDF?
You can find downloadable ACT Math Cheat Sheet PDFs on test prep websites like Kaplan, Magoosh, or through ACT-focused study groups on platforms like Reddit or Discord.
3. Is there an official ACT Math Formula Sheet PDF?
No, the ACT does not provide an official formula sheet. Students are expected to memorize necessary formulas. However, unofficial formula sheets from test prep companies like Kaplan are available online.
4. What is included in an ACT English Cheat Sheet?
An ACT English Cheat Sheet typically includes grammar rules, punctuation guidelines, sentence structure tips, and strategy hacks for answering rhetorical skills questions.
5. Is there an ACT Science Cheat Sheet available?
Yes, an ACT Science Cheat Sheet often includes tips for interpreting graphs, understanding scientific experiments, and managing time effectively—since this section focuses more on analysis than science facts.
6. What is the ACT Formula Sheet from Kaplan?
Kaplan’s ACT Formula Sheet is a popular resource that outlines key math formulas for algebra, geometry, and trigonometry. It’s often included in their prep books or online resources.
7. Does the ACT provide a reference sheet during the test?
No. The ACT does not provide any formula or reference sheet during the exam. You must memorize all relevant formulas.
8. Is there a general ACT Cheat Sheet PDF covering all sections?
Yes, comprehensive ACT cheat sheets include tips and strategies for all sections: English, Math, Reading, and Science. They’re available as free or paid resources online.
9. What are the best ACT Math Tips for high scores?
- Memorize key formulas
- Practice pacing (60 questions in 60 minutes)
- Focus on problem-solving strategies
- Use process of elimination
- Plug in answer choices when needed
10. Are there ACT Math Cheat Sheets specific to 2024 or 2025?
Yes, many updated cheat sheets are labeled by year (e.g., ACT Math Cheat Sheet 2024 or 2025) to reflect recent test trends and updated formats, but core math content remains largely the same.
11. Is there a Geometry-specific ACT Math Cheat Sheet?
Yes. Some cheat sheets focus specifically on ACT Geometry, covering area, perimeter, volume, angles, circles, and coordinate geometry formulas.
12. What are the essential formulas on the ACT Math Formulas Cheat Sheet?
Essentials include:
- Slope formula
- Distance formula
- Area and perimeter of shapes
- Volume formulas
- SOHCAHTOA for trigonometry
- Quadratic formula
- Arithmetic & geometric sequences
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