Formulas To Memorize For Sat

Conquer the SAT: Essential Formulas to Memorize for Math Success

The SAT Math section can feel daunting, but mastering a core set of formulas is a crucial step towards achieving a high score. This article provides a comprehensive list of essential formulas, categorized for easier memorization, along with explanations and examples to solidify your understanding. Memorizing these formulas and practicing their application will significantly boost your confidence and performance on test day. We'll cover everything from basic algebra to more advanced geometry and trigonometry concepts. Let's dive in!

I. Algebra I Formulas: The Foundation

These formulas are the bedrock of SAT math. Mastering them is critical before moving onto more advanced concepts.

1. Linear Equations:

• Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Understanding slope (rise over run) and y-intercept is essential for graphing and analyzing linear relationships.
  • Example: y = 2x + 3 has a slope of 2 and a y-intercept of 3.
• Point-slope form: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. This is useful when you know the slope and a point on the line.
  • Example: A line with slope 3 passing through (1,2) is represented as y - 2 = 3(x - 1).
• Standard form: Ax + By = C, where A, B, and C are integers. This form is less frequently used for calculations but appears in problems.

2. Quadratic Equations:

• Standard form: ax² + bx + c = 0, where a, b, and c are constants.
• Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a. This formula solves for the roots (x-intercepts) of a quadratic equation. Remember the discriminant, b² - 4ac, determines the nature of the roots (real and distinct, real and equal, or complex).
  • Example: Solve 2x² + 5x - 3 = 0 using the quadratic formula.
• Factoring: This method involves expressing the quadratic as a product of two linear expressions. It's often faster than the quadratic formula if the quadratic is easily factorable.
  • Example: x² + 5x + 6 = (x + 2)(x + 3) = 0 implies x = -2 or x = -3.
• Vertex Form: y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Understanding this form helps in quickly identifying the vertex and axis of symmetry.

3. Systems of Equations:

• Substitution: Solve one equation for one variable and substitute it into the other equation.
• Elimination (addition/subtraction): Multiply equations by constants to eliminate a variable when adding or subtracting the equations.

4. Exponents and Radicals:

• Exponent rules: aᵐ * aⁿ = aᵐ⁺ⁿ, aᵐ / aⁿ = aᵐ⁻ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1, a⁻ⁿ = 1/aⁿ. Understanding these rules is crucial for simplifying expressions.
• Radical rules: √(ab) = √a * √b, √(a/b) = √a / √b, √a = a^(1/2). Converting between radicals and exponents is helpful.

II. Geometry Formulas: Shapes and Spaces

Geometry problems on the SAT frequently test your knowledge of formulas for area, volume, and other geometric properties.

1. Triangles:

• Area: (1/2) * base * height
• Pythagorean Theorem: a² + b² = c² (for right-angled triangles only, 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. (These ratios will save you time on many problems)
• Similar Triangles: Corresponding angles are equal and corresponding sides are proportional.

2. Circles:

• Area: πr²
• Circumference: 2πr or πd (where r is the radius and d is the diameter).
• Arc Length: (θ/360) * 2πr (where θ is the central angle in degrees).
• Area of a sector: (θ/360) * πr² (where θ is the central angle in degrees).

3. Rectangles and Squares:

• Rectangle Area: length * width
• Rectangle Perimeter: 2(length + width)
• Square Area: side²
• Square Perimeter: 4 * side

4. Other Polygons:

• Understanding the properties of other polygons such as trapezoids, parallelograms, and rhombuses is helpful. Knowing their area and perimeter formulas will be beneficial.

5. Solids:

• Volume of a rectangular prism (box): length * width * height
• Volume of a cylinder: πr²h (where r is the radius and h is the height)
• Volume of a cone: (1/3)πr²h
• Volume of a sphere: (4/3)πr³

III. Algebra II Formulas: Stepping Up the Complexity

These formulas are often seen in the more challenging questions on the SAT.

1. Logarithms:

• Basic properties: logₐ(xy) = logₐx + logₐy, logₐ(x/y) = logₐx - logₐy, logₐ(xⁿ) = nlogₐx

2. Functions:

• Understanding function notation (f(x)), function composition (f(g(x))), and inverse functions is crucial.

3. Sequences and Series:

• Arithmetic sequence: aₙ = a₁ + (n-1)d (where aₙ is the nth term, a₁ is the first term, n is the number of terms, and d is the common difference).
• Geometric sequence: aₙ = a₁ * r⁽ⁿ⁻¹⁾ (where r is the common ratio).

IV. Trigonometry Formulas (Rare but Important)

While not as frequently tested as algebra and geometry, a basic understanding of trigonometry can be beneficial for some SAT problems.

1. Basic Trigonometric Ratios:

• Sine: sin θ = opposite/hypotenuse
• Cosine: cos θ = adjacent/hypotenuse
• Tangent: tan θ = opposite/adjacent

2. Pythagorean Identity:

• sin²θ + cos²θ = 1

V. Strategies for Memorization and Application

Memorizing formulas is only half the battle. Effective application is key.

• Flashcards: Create flashcards with formulas on one side and explanations/examples on the other.
• Practice Problems: Work through numerous practice problems to apply the formulas in various contexts. The more you practice, the more comfortable you'll become.
• Categorize and Group: Organize formulas by topic (e.g., triangles, quadratic equations) to make memorization more manageable.
• Regular Review: Consistent review is vital. Don't cram everything the night before the test. Regularly revisit the formulas over several weeks or months.
• Understand, Don't Just Memorize: Focus on understanding the underlying concepts behind the formulas. This makes memorization easier and helps you apply them correctly in different situations.
• Identify Your Weak Areas: As you practice, identify the formulas or concepts you struggle with and dedicate extra time to mastering them.

VI. Frequently Asked Questions (FAQs)

Q: Do I need to memorize every single formula in this list?

A: While this list covers most essential formulas, your focus should be on mastering the ones you encounter most frequently in practice tests. Prioritize the Algebra I and Geometry formulas.

Q: What if I forget a formula during the test?

A: The SAT often provides some formulas in the test booklet. However, relying solely on the booklet is risky. Practice will help you internalize these formulas, minimizing the chance of forgetting them under pressure.

Q: Are there any shortcut methods for solving problems?

A: Yes! Practice will allow you to recognize patterns and develop efficient problem-solving strategies. Sometimes, understanding the underlying concepts allows you to solve problems without directly using formulas.

Q: How can I improve my speed on the math section?

A: Practice is key to improving your speed and accuracy. Work through timed practice tests to simulate exam conditions.

Q: Is there a resource to help me practice?

A: Numerous official SAT practice tests and question banks are available online and in preparation books. Consistent practice is crucial for success.

VII. Conclusion: Master the Formulas, Master the SAT

The SAT Math section is conquerable with the right preparation. Mastering these essential formulas, coupled with consistent practice and strategic problem-solving techniques, will significantly enhance your chances of achieving a high score. Remember to focus on understanding the underlying concepts and apply the formulas effectively. Good luck!