Cheat Sheet Sat Formula Sheet

Conquer the SAT: Your Ultimate Formula Cheat Sheet and Beyond

The SAT can feel like a daunting mountain to climb, especially when faced with complex math problems. But fear not! With the right tools and strategies, you can conquer the SAT math section. Which means this full breakdown provides you with a complete SAT formula cheat sheet, explaining each formula, its applications, and offering helpful tips and tricks to master the material. And we'll go beyond simply listing formulas, diving deep into understanding why they work and how to apply them effectively in various SAT question types. This isn't just a cheat sheet; it's your roadmap to success.

I. The Essential SAT Math Formulas: Your Cheat Sheet

This section provides a concise yet comprehensive list of formulas frequently tested on the SAT. Remember, rote memorization isn't enough; understand the underlying concepts.

A. Arithmetic and Number Properties:

• Order of Operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This is crucial for ensuring accurate calculations.
• Prime Numbers: A number greater than 1 that has only two factors: 1 and itself (e.g., 2, 3, 5, 7, 11...). Understanding prime factorization is key for simplifying expressions and solving problems involving greatest common factors (GCF) and least common multiples (LCM).
• Factors and Multiples: Factors are numbers that divide evenly into a given number. Multiples are numbers that are products of a given number. Knowing how to find factors and multiples is essential for number theory questions.
• Average (Mean): Sum of numbers / Number of numbers. The SAT frequently tests average problems in various contexts.
• Median: The middle value when a set of numbers is arranged in order. If there's an even number of values, the median is the average of the two middle values.
• Mode: The number that appears most frequently in a set of numbers.
• Range: The difference between the highest and lowest values in a set of numbers.
• Percent Change: [(New Value - Old Value) / Old Value] x 100%. Understanding percent increase and decrease is vital for many word problems.

B. Algebra:

• Linear Equations: y = mx + b, where m is the slope and b is the y-intercept. Be comfortable finding the slope using two points: m = (y₂ - y₁) / (x₂ - x₁).
• Slope-Intercept Form: y = mx + b. This is the most common form for representing linear equations.
• Point-Slope Form: y - y₁ = m(x - x₁). Useful for finding the equation of a line given a point and the slope.
• Standard Form: Ax + By = C. Another way to represent a linear equation.
• Solving Systems of Equations: Use substitution or elimination methods to find the values of x and y that satisfy both equations.
• Quadratic Equations: ax² + bx + c = 0. Know how to solve using factoring, the quadratic formula (x = [-b ± √(b² - 4ac)] / 2a), or completing the square. Understanding the discriminant (b² - 4ac) tells you the nature of the roots (real, imaginary, etc.).
• Factoring Quadratic Expressions: Learn to factor expressions like x² + 5x + 6 into (x + 2)(x + 3).
• Exponents and Radicals: Understand the rules of exponents (e.g., xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾, xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾, (xᵃ)ᵇ = x⁽ᵃᵇ⁾) and radicals (e.g., √(ab) = √a * √b, √(a/b) = √a / √b).

C. Geometry:

• Area of a Rectangle: Length x Width
• Area of a Square: Side²
• Area of a Triangle: (1/2) x Base x Height
• Area of a Circle: πr²
• Circumference of a Circle: 2πr
• Volume of a Rectangular Prism: Length x Width x Height
• Volume of a Cube: Side³
• Volume of a Cylinder: πr²h
• Pythagorean Theorem: a² + b² = c² (for right-angled triangles, where a and b are legs and c is the hypotenuse)
• Special Right Triangles: Know the ratios of sides in 30-60-90 and 45-45-90 triangles.
• Similar Triangles: Corresponding angles are congruent, and corresponding sides are proportional.
• Angle Relationships: Understand supplementary angles (add up to 180°), complementary angles (add up to 90°), vertical angles (are equal).

D. Data Analysis:

• Interpreting Graphs and Charts: The SAT often presents data in various graphical forms (bar graphs, line graphs, pie charts, scatterplots). Be able to extract information and draw conclusions.

II. Beyond the Formulas: Mastering SAT Math Strategies

Simply memorizing formulas isn't sufficient for SAT success. Here are key strategies to complement your formula knowledge:

For more on this topic, read our article on x 2 x 4 1 or check out who conducted the little albert experiment.

• Understand the Concepts: Don't just memorize formulas; understand why they work. This deeper understanding will allow you to apply them effectively in diverse problem scenarios.
• Practice Regularly: Consistent practice is crucial. Work through numerous problems, focusing on areas where you struggle.
• Identify Your Weaknesses: Pinpoint the specific areas where you need improvement and dedicate extra time to mastering those concepts.
• Use Process of Elimination: If you're stuck, eliminate obviously incorrect answer choices to improve your chances of guessing correctly.
• Plug in Numbers: For algebra problems, try plugging in simple numbers to test the validity of different answer choices.
• Draw Diagrams: For geometry problems, draw clear diagrams to visualize the problem and identify relevant relationships.
• Manage Your Time: Practice pacing yourself during the test to ensure you have enough time to answer all the questions.
• Review Your Mistakes: Analyze your wrong answers to understand where you went wrong and avoid repeating those mistakes.

III. Deep Dive into Selected Formulas: Practical Applications

Let's explore some key formulas in more detail, demonstrating their practical application in different SAT question types.

A. The Quadratic Formula:

The quadratic formula, x = [-b ± √(b² - 4ac)] / 2a, is essential for solving quadratic equations of the form ax² + bx + c = 0. On the flip side, it's crucial to understand its implications beyond simply finding solutions. The discriminant (b² - 4ac) provides valuable information:

• b² - 4ac > 0: Two distinct real solutions.
• b² - 4ac = 0: One real solution (a repeated root).
• b² - 4ac < 0: Two complex (imaginary) solutions. The SAT rarely tests complex solutions, but understanding the discriminant's role is important.

Example: Solve the equation 2x² - 5x + 2 = 0 using the quadratic formula.

Here, a = 2, b = -5, and c = 2. Substituting these values into the formula, we get:

x = [5 ± √((-5)² - 4 * 2 * 2)] / (2 * 2) = [5 ± √9] / 4 = [5 ± 3] / 4

This gives us two solutions: x = 2 and x = 1/2.

B. Similar Triangles:

Similar triangles have corresponding angles that are congruent and corresponding sides that are proportional. This property is frequently used in SAT geometry problems.

Example: Two triangles are similar. The sides of the smaller triangle are 3, 4, and 5. The longest side of the larger triangle is 15. What is the perimeter of the larger triangle?

Since the triangles are similar, the ratio of corresponding sides is constant. The ratio of the longest sides is 15/5 = 3. That's why, the sides of the larger triangle are 3 * 3 = 9, 3 * 4 = 12, and 3 * 5 = 15. The perimeter is 9 + 12 + 15 = 36.

C. Percent Change:

Understanding percent change is vital for many SAT word problems.

Example: The price of a shirt increased from $20 to $25. What is the percent increase?

Percent increase = [(New Value - Old Value) / Old Value] x 100% = [(25 - 20) / 20] x 100% = (5/20) x 100% = 25%

IV. Frequently Asked Questions (FAQ)

• Do I need to memorize every formula? While a strong understanding of the core formulas is vital, memorizing every single formula isn't necessary. Focus on the most frequently tested ones and understand how to derive others if needed.
• What if I forget a formula during the test? Try to derive the formula from first principles or use alternative methods to solve the problem. Sometimes, you can use logic and reasoning to eliminate incorrect answer choices.
• How can I improve my speed and accuracy? Consistent practice is key. Work through many practice problems, focusing on speed and accuracy. Identify your weaknesses and address them.
• Are there any resources beyond this cheat sheet? Numerous SAT prep books and online resources can provide additional practice problems and explanations.

V. Conclusion: Your Journey to SAT Math Mastery

This complete walkthrough provides you with a powerful foundation for conquering the SAT math section. Remember, success on the SAT is not just about memorizing formulas; it's about understanding the underlying concepts, developing effective problem-solving strategies, and practicing consistently. Think about it: use this cheat sheet as a starting point, and combine it with diligent practice and strategic preparation to achieve your target score. Believe in yourself, and you'll conquer the SAT!