Overview
The SAT Math section is a crucial part of the SAT exam, and it can be daunting to know where to start. That’s why we’ve compiled this comprehensive SAT Math reference sheet to provide you with all the information you need to know to ace your exam.
This reference sheet covers everything from basic algebra to advanced calculus, and it includes all the formulas, equations, and theorems you need to know. It’s the perfect tool to use as you prepare for your exam, and it can also be a helpful reference during the test itself.
Basic Algebra
- Variables: Letters that represent unknown values
- Constants: Numbers or values that do not change
- Equations: Statements that set two expressions equal to each other
- Inequalities: Statements that compare two expressions
- Polynomials: Expressions that consist of variables and constants combined using addition, subtraction, and multiplication
- Quadratic equations: Equations that have a term with a squared variable
- Exponential equations: Equations that have a term with a variable as an exponent
- Logarithmic equations: Equations that have a term with a logarithm
Geometry
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Shapes:
- Triangles: Equilateral, isosceles, scalene, right, and obtuse
- Quadrilaterals: Squares, rectangles, trapezoids, parallelograms, and rhombuses
- Circles: Definition, circumference, and area
- Spheres: Definition, volume, and surface area
- Angles: Acute, right, obtuse, and reflex
- Congruence: When two shapes have the same size and shape
- Similarity: When two shapes have the same shape but different sizes
- Area and volume: Formulas for calculating the area and volume of different shapes
Trigonometry
- Sine, cosine, and tangent: Functions that relate the sides of a right triangle
- Trigonometric identities: Equations that relate the trigonometric functions
- Law of sines and cosines: Theorems that relate the sides and angles of triangles
- Unit circle: A circle with radius 1 that is used to define the trigonometric functions
Calculus
- Derivatives: Functions that give the rate of change of a function
- Integrals: Functions that give the area under a curve
- Limits: Values that a function approaches as the input approaches a certain value
Statistics
- Mean, median, and mode: Measures of central tendency
- Standard deviation and variance: Measures of dispersion
- Probability: The likelihood that an event will occur
- Normal distribution: A bell-shaped curve that is used to model many real-world phenomena
Tables
Table 1: Important Formulas
| Formula | Description |
|---|---|
| (A = lw) | Area of a rectangle |
| (V = lwh) | Volume of a rectangular prism |
| (\sin\theta = \frac{opposite}{hypotenuse}) | Sine of an angle |
| (\cos\theta = \frac{adjacent}{hypotenuse}) | Cosine of an angle |
| (\tan\theta = \frac{opposite}{adjacent}) | Tangent of an angle |
Table 2: Important Theorems
| Theorem | Description |
|---|---|
| Pythagorean theorem | (a^2 + b^2 = c^2) |
| Law of sines | (\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}) |
| Law of cosines | (c^2 = a^2 + b^2 – 2ab\cos C) |
Table 3: Important Identities
| Identity | Description |
|---|---|
| (\sin^2\theta + \cos^2\theta = 1) | Pythagorean identity |
| (\tan\theta = \frac{\sin\theta}{\cos\theta}) | Tangent identity |
| (\sin(A + B) = \sin A \cos B + \cos A \sin B) | Sum identity for sine |
Table 4: Common Values
| Value | Description |
|---|---|
| (\pi) | Approximately 3.14 |
| (e) | Approximately 2.718 |
| (i) | Imaginary unit, approximately 0.707 |
Tips and Tricks
- Start by practicing the basics. Make sure you have a solid understanding of the basic concepts before moving on to more advanced topics.
- Use flashcards to memorize formulas and equations. This is a great way to review material and make sure you remember it on test day.
- Do practice problems regularly. The best way to prepare for the SAT Math section is to practice as much as possible.
- Take timed practice tests. This will help you get used to the format of the test and learn how to manage your time effectively.
- Don’t be afraid to ask for help. If you’re struggling with a concept, ask your teacher or a tutor for help.
Conclusion
The SAT Math reference sheet is a valuable resource that can help you ace your SAT exam. By using this reference sheet, you can review the material you need to know, practice your skills, and build your confidence.
Don’t forget to bookmark this page so you can come back to it whenever you need to refresh your memory or practice your skills.