Formula Sheet For Sat Math

Conquer the SAT Math Section: Your Ultimate Formula Sheet and Guide

The SAT Math section can feel daunting, but with the right preparation and a solid understanding of key formulas, you can significantly improve your score. This comprehensive guide provides a detailed formula sheet covering all essential concepts, along with explanations and examples to help you master the material. We'll cover everything from basic arithmetic to advanced algebra and geometry, ensuring you're equipped to tackle any problem the SAT throws your way. This resource will be your ultimate companion for achieving your target SAT Math score.

I. Arithmetic and Number Properties

This section covers fundamental concepts crucial for many SAT Math problems.

A. Number Properties:

• Even/Odd Numbers: Even numbers are divisible by 2 (e.g., 2, 4, 6), while odd numbers are not (e.g., 1, 3, 5). Knowing the rules of even and odd number operations is essential (e.g., even + even = even, odd + odd = even, even x odd = even).

• Positive/Negative Numbers: Understanding the rules for multiplying and dividing positive and negative numbers is crucial. Remember: positive x positive = positive, negative x negative = positive, positive x negative = negative.

• Prime Numbers: Prime numbers are whole numbers greater than 1 that are only divisible by 1 and themselves (e.g., 2, 3, 5, 7, 11). 1 is not a prime number.

• Factors and Multiples: Factors are numbers that divide evenly into a given number. Multiples are numbers that are products of a given number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, while multiples of 12 are 12, 24, 36, etc.

• Greatest Common Factor (GCF) and Least Common Multiple (LCM): The GCF is the largest number that divides evenly into two or more numbers. The LCM is the smallest number that is a multiple of two or more numbers. You can find the GCF and LCM using prime factorization.

B. Percentages:

• Percentage Increase/Decrease: Percentage increase = [(New Value - Old Value) / Old Value] x 100%. Percentage decrease is calculated similarly.

• Percent Change: This refers to the relative change in a value over time, often used in problems involving growth or decay.

C. Ratios and Proportions:

• Ratio: A ratio compares two quantities. It can be expressed as a fraction (a/b), using a colon (a:b), or using the word "to" (a to b).

• Proportion: A proportion is an equation stating that two ratios are equal (a/b = c/d). You can solve proportions using cross-multiplication (ad = bc).

D. Exponents and Radicals:

• Exponent Rules:

  • x^a * x^b = x^a+b
  • x^a / x^b = x^a-b
  • (x^a)^b = x^ab
  • x⁰ = 1 (x ≠ 0)
  • x^-a = 1/x^a (x ≠ 0)

• Radical Rules:

  • √(ab) = √a * √b
  • √(a/b) = √a / √b
  • √x² = |x| (absolute value of x)

II. Algebra

This section covers algebraic concepts crucial for solving equations and inequalities.

A. Linear Equations and Inequalities:

• Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept.

• Point-Slope Form: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.

• Standard Form: Ax + By = C

• Solving Linear Equations: Use inverse operations to isolate the variable.

• Solving Linear Inequalities: Similar to solving equations, but remember to reverse the inequality sign if you multiply or divide by a negative number.

B. Systems of Linear Equations:

• Solving by Substitution: Solve one equation for one variable and substitute into the other equation.

• Solving by Elimination: Multiply equations by constants to eliminate a variable, then solve for the remaining variable.

C. Quadratic Equations:

• Standard Form: ax² + bx + c = 0

• Factoring: Rewrite the quadratic as a product of two linear expressions.

• Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

• Discriminant: b² - 4ac. Determines the number and type of solutions (positive: two real solutions; zero: one real solution; negative: two complex solutions).

D. Functions:

• Function Notation: f(x) represents the output of a function for a given input x.

• Evaluating Functions: Substitute the given value of x into the function's expression.

• Composition of Functions: f(g(x)) means applying function g to x, then applying function f to the result.

E. Exponents and Logarithms:

• Logarithmic Properties:
  • log_b(xy) = log_bx + log_by
  • log_b(x/y) = log_bx - log_by
  • log_b(x^a) = a log_bx
  • log_bb = 1
  • log_b1 = 0

III. Geometry

This section covers essential geometric concepts and formulas.

A. Lines and Angles:

• Vertical Angles: Opposite angles formed by intersecting lines are equal.

• Supplementary Angles: Two angles whose measures add up to 180°.

• Complementary Angles: Two angles whose measures add up to 90°.

• Parallel Lines and Transversals: When a transversal intersects parallel lines, corresponding angles, alternate interior angles, and alternate exterior angles are equal.

B. Triangles:

• Area: (1/2) * base * height

• Pythagorean Theorem: a² + b² = c² (for right triangles)

• Special Right Triangles: 30-60-90 and 45-45-90 triangles have specific side ratios.

• Similar Triangles: Triangles with the same shape but different sizes; corresponding angles are equal, and corresponding sides are proportional.

C. Circles:

• Area: πr²

• Circumference: 2πr

• Arc Length: (θ/360°) * 2πr, where θ is the central angle in degrees.

• Area of a Sector: (θ/360°) * πr²

D. Solids:

• Volume of a Rectangular Prism: length * width * height

• Volume of a Cylinder: πr²h

• Volume of a Cone: (1/3)πr²h

• Volume of a Sphere: (4/3)πr³

• Surface Area of a Rectangular Prism: 2(lw + lh + wh)

IV. Data Analysis, Statistics, and Probability

This section covers concepts related to interpreting data and calculating probabilities.

A. Mean, Median, and Mode:

• Mean (Average): The sum of the numbers divided by the number of numbers.

• Median: The middle value when the numbers are arranged in order.

• Mode: The value that appears most frequently.

B. Standard Deviation: A measure of the spread or dispersion of a data set. (The SAT usually doesn't require you to calculate the standard deviation directly; understanding its meaning is more important).

C. Probability:

• Basic Probability: Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

• Independent Events: The outcome of one event does not affect the outcome of another event. P(A and B) = P(A) * P(B)

• Dependent Events: The outcome of one event affects the outcome of another event. P(A and B) = P(A) * P(B|A), where P(B|A) is the probability of B given A has occurred.

V. Advanced Topics (Occasionally Appearing on the SAT)

While not always present, understanding these topics can provide an edge.

A. Trigonometry (Basic): Understanding the definitions of sine, cosine, and tangent (SOH CAH TOA) is helpful for some problems involving right triangles.

B. Sequences and Series: Familiarize yourself with arithmetic and geometric sequences and their formulas for the nth term and the sum of the first n terms.

C. Matrices (Rare): Basic matrix operations (addition, scalar multiplication) might appear in a few problems.

VI. Strategies and Practice

Having a formula sheet is only half the battle. Effective preparation also involves:

• Consistent Practice: Work through numerous practice problems from official SAT materials.

• Identify Weak Areas: Track your mistakes to pinpoint areas needing improvement.

• Review Concepts: Don't just memorize formulas; understand their derivations and applications.

• Time Management: Practice working under timed conditions to improve your speed and efficiency.

VII. Frequently Asked Questions (FAQ)

Q: Do I need to memorize every formula on this sheet?

A: It's beneficial to be familiar with all the formulas, but memorizing them all isn't necessarily required. Focus on understanding the concepts and how to apply the formulas. You'll likely remember many through repeated use.

Q: Are there any formulas NOT included in this sheet that might appear on the SAT?

A: The vast majority of SAT math problems are covered by the formulas here. However, very rarely, a problem might require a bit of creative problem-solving that uses simple algebra rather than a specific formula.

Q: Can I bring this formula sheet to the SAT?

A: No, you cannot bring any formula sheets or other external aids to the SAT. This sheet is for study and practice purposes only.

VIII. Conclusion

This comprehensive formula sheet and guide will equip you with the knowledge and strategies needed to conquer the SAT Math section. Remember, consistent practice and a thorough understanding of the underlying concepts are key to achieving your desired score. Good luck!