Formulas To Remember For Sat

Conquer the SAT: Essential Formulas You Need to Remember

The SAT can feel like a daunting mountain to climb, but with the right preparation and strategies, conquering it becomes significantly easier. Mathematics is a major component of the SAT, and while a comprehensive understanding of mathematical concepts is crucial, memorizing key formulas can provide a significant advantage. This article provides a detailed breakdown of the essential formulas you need to remember for the SAT Math section, categorized for easy reference and understanding. Mastering these will significantly boost your score and confidence. We'll delve into each formula, providing examples and explaining their applications in different SAT question types.

I. Algebra and Functions

This section covers the core algebraic concepts frequently tested on the SAT. Understanding and memorizing these formulas is fundamental to success.

1. Linear Equations:

• Slope-Intercept Form: y = mx + b, where m is the slope and b is the y-intercept. This is arguably the most important formula in algebra. Knowing how to manipulate this equation to find slope, y-intercept, or to write the equation of a line given different information is essential.

• Point-Slope Form: y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. This form is particularly useful when you know the slope and a point on the line.

• Standard Form: Ax + By = C, where A, B, and C are constants. While less frequently used for calculations, understanding this form is crucial for interpreting equations and recognizing relationships between lines.

• Finding the slope between two points: m = (y₂ - y₁) / (x₂ - x₁). This formula is crucial for determining the slope given two points on a line.

2. Quadratic Equations:

• Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a, where the quadratic equation is in the form ax² + bx + c = 0. This formula allows you to solve for the x-intercepts (roots) of any quadratic equation. Remember to identify a, b, and c correctly.

• Factoring Quadratic Equations: This isn't strictly a formula, but the ability to factor quadratic equations like x² + 5x + 6 = (x + 2)(x + 3) is vital for solving them quickly and efficiently. Practice recognizing common factoring patterns.

• Vertex Form: y = a(x - h)² + k, where (h, k) represents the vertex of the parabola. Understanding this form allows for quick identification of the parabola's vertex and axis of symmetry.

3. Systems of Equations:

Solving systems of equations, often involving both linear and quadratic equations, is a common SAT problem type. While there isn't one single formula, remember the methods:

• Substitution: Solve one equation for one variable and substitute it into the other equation.
• Elimination: Multiply equations by constants to eliminate one variable and solve for the other.

4. Functions:

• Function Notation: f(x) represents the output of a function f when the input is x. Understanding function notation is key to interpreting and evaluating functions.

• Composite Functions: (f ∘ g)(x) = f(g(x)) represents the composition of functions f and g. This means you substitute the function g(x) into the function f(x).

• Inverse Functions: If f(x) and g(x) are inverse functions, then f(g(x)) = g(f(x)) = x. Understanding how to find the inverse of a function is important.

II. Geometry

Geometry questions on the SAT often require applying formulas efficiently. Here's a list of essential geometrical formulas:

1. Lines and Angles:

• Vertical Angles: Vertical angles are always equal.
• Supplementary Angles: Two angles that add up to 180°.
• Complementary Angles: Two angles that add up to 90°.
• Parallel Lines and Transversals: Understanding alternate interior angles, alternate exterior angles, corresponding angles, and consecutive interior angles is crucial for solving problems involving parallel lines.

2. Triangles:

• Area of a Triangle: Area = (1/2) * base * height. Remember that the height must be perpendicular to the base.

• Pythagorean Theorem: a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse. This is one of the most frequently used formulas on the SAT.

• Special Right Triangles: Knowing the ratios of sides in 30-60-90 and 45-45-90 triangles can significantly speed up problem-solving. (For a 30-60-90 triangle, the sides are in the ratio x : x√3 : 2x; for a 45-45-90 triangle, the sides are in the ratio x : x : x√2).

• Similar Triangles: Similar triangles have proportional sides and equal corresponding angles.

3. Circles:

• Area of a Circle: Area = πr², where r is the radius.

• Circumference of a Circle: Circumference = 2πr or Circumference = πd, where d is the diameter.

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

• Area of a Sector: Area of Sector = (θ/360) * πr², where θ is the central angle in degrees.

4. Other Geometric Shapes:

• Area of a Rectangle: Area = length * width
• Perimeter of a Rectangle: Perimeter = 2(length + width)
• Area of a Square: Area = side²
• Perimeter of a Square: Perimeter = 4 * side
• Area of a Parallelogram: Area = base * height
• Area of a Trapezoid: Area = (1/2)(b₁ + b₂)h, where b₁ and b₂ are the lengths of the parallel bases and h is the height.
• Volume of a Rectangular Prism: Volume = length * width * height
• Volume of a Cube: Volume = side³
• Volume of a Cylinder: Volume = πr²h, where r is the radius and h is the height.

III. Data Analysis and Probability

This section covers statistical concepts and probability calculations often found on the SAT.

1. Mean, Median, and Mode:

• Mean: The average of a data set (sum of values divided by the number of values).
• Median: The middle value in a data set when arranged in order.
• Mode: The value that appears most frequently in a data set.

2. Standard Deviation: While you won't need to calculate standard deviation directly, understanding its concept – a measure of the spread of data around the mean – is crucial for interpreting data presented in graphs and charts.

3. Probability:

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

IV. Practice and Application

Memorizing these formulas is only half the battle. The key to success lies in applying them effectively. Practice solving various SAT math problems using these formulas. Focus on understanding the underlying concepts rather than simply memorizing the formulas themselves. Work through practice tests and identify your weaknesses. The more you practice, the more comfortable you will become with these formulas and the more effectively you'll be able to use them on test day.

V. Frequently Asked Questions (FAQ)

Q: Do I need to memorize every single formula?

A: While this list is comprehensive, some formulas are used more frequently than others. Prioritize the ones used most often in practice tests.

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

A: Try to derive the formula from the problem's context or look for alternative approaches. Sometimes, you can use logic and reasoning to solve a problem even without memorizing the specific formula.

Q: Are there any resources to help me practice using these formulas?

A: Numerous online resources, textbooks, and practice tests are available to help you hone your skills. Focus on consistent practice and targeted review of areas where you struggle.

VI. Conclusion

Mastering these essential formulas is a crucial step towards achieving a high score on the SAT Math section. Consistent practice, understanding the underlying concepts, and utilizing various problem-solving strategies will significantly improve your performance. Remember, success on the SAT requires dedication, perseverance, and a strategic approach. By focusing on these formulas and practicing consistently, you'll be well-equipped to tackle the mathematical challenges presented on the test and achieve your desired score. Good luck!