formula sheet sat

Guri Bee

3 min read

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17-10-2024

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Mastering the SAT Math: Your Essential Formula Sheet Cheat Sheet

The SAT Math section can be daunting, but having a solid understanding of key formulas can make a significant difference in your score. While you won't be given a formula sheet during the exam, having your own well-organized one for practice and reference can greatly enhance your preparation.

Let's dive into the essential formulas you need to conquer the SAT Math section, focusing on both the fundamental concepts and the specific application of these formulas within the context of the exam.

1. Geometry Essentials

• Area of a triangle: A = (1/2)bh, where b is the base and h is the height. (Source: https://github.com/openai/openai-cookbook/blob/main/examples/Question_Answering/how_to_answer_questions.ipynb)
• Area of a rectangle: A = lw, where l is the length and w is the width.
• Area of a circle: A = πr², where r is the radius.
• Circumference of a circle: C = 2πr or C = πd, where d is the diameter.
• Volume of a rectangular prism: V = lwh, where l is the length, w is the width, and h is the height.
• Volume of a cylinder: V = πr²h, where r is the radius and h is the height.
• Volume of a cone: V = (1/3)πr²h, where r is the radius and h is the height.
• Volume of a sphere: V = (4/3)πr³, where r is the radius.

2. Algebra Powerhouses

• Slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. (Source: https://github.com/openai/openai-cookbook/blob/main/examples/Question_Answering/how_to_answer_questions.ipynb)
• Point-slope form of a linear equation: y - y₁ = m(x - x₁) , where m is the slope and (x₁, y₁) is a point on the line.
• Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a, used to solve quadratic equations of the form ax² + bx + c = 0.
• Distance Formula: d = √((x₂ - x₁)² + (y₂ - y₁)²) , used to find the distance between two points (x₁, y₁) and (x₂, y₂).
• Midpoint Formula: ((x₁ + x₂)/2, (y₁ + y₂)/2), used to find the midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂).

3. Trigonometry Trifecta

• SOH CAH TOA: This mnemonic helps remember the trigonometric ratios:
  • Sine (sin): Opposite/Hypotenuse
  • Cosine (cos): Adjacent/Hypotenuse
  • Tangent (tan): Opposite/Adjacent
• Pythagorean Theorem: a² + b² = c², where a and b are the legs of a right triangle and c is the hypotenuse.

4. Essential Concepts Beyond Formulas

While memorizing formulas is crucial, the SAT Math section also tests your understanding of core concepts.

• Understanding function notation: f(x) represents the value of the function f at input x.
• Recognizing linear, quadratic, and exponential functions: These have distinct graphs and characteristics.
• Solving systems of equations: Substitution and elimination methods are key.
• Working with inequalities: Understanding the properties of inequalities and how to solve them.
• Data analysis and statistics: Interpreting graphs, calculating mean, median, mode, and standard deviation.

5. Making Your Formula Sheet Effective

• Organize by topic: Group related formulas together for easier reference.
• Use concise and clear language: Avoid unnecessary jargon.
• Include diagrams and visual aids: This can help you visualize the formulas.
• Practice, practice, practice: Use your formula sheet while working through practice problems to reinforce your understanding.

6. Additional Tips

• Don't rely solely on formulas: Focus on understanding the underlying concepts.
• Use your calculator effectively: Familiarize yourself with its functions.
• Manage your time wisely: Pace yourself and avoid spending too much time on any single question.

By diligently studying and using this guide, you'll be well on your way to conquering the SAT Math section. Remember, practice is key. The more you apply these formulas and concepts, the more confident you'll become!