Algebra Formulas
Algebra is a significant part of the SAT Math section, comprising questions that require a solid understanding of equations, inequalities, and functions. Here are some crucial algebra formulas and concepts to memorize:
Linear Equations
- Slope-Intercept Form:
The slope-intercept form of a linear equation is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
- Point-Slope Form:
The point-slope form is useful for writing equations when you know a point on the line and the slope:
\[ y - y_1 = m(x - x_1) \]
where \( (x_1, y_1) \) is a point on the line.
Quadratic Equations
- Standard Form:
The standard form of a quadratic equation is:
\[ ax^2 + bx + c = 0 \]
- Quadratic Formula:
To find the roots of a quadratic equation, use:
\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
- Factoring:
Remember that a quadratic can often be factored as:
\[ (x - p)(x - q) = 0 \]
where \( p \) and \( q \) are the roots.
Exponents and Radicals
- Laws of Exponents:
- \( a^m \cdot a^n = a^{m+n} \)
- \( \frac{a^m}{a^n} = a^{m-n} \)
- \( (a^m)^n = a^{m \cdot n} \)
- \( a^{-n} = \frac{1}{a^n} \)
- \( a^{1/n} = \sqrt[n]{a} \)
- Radical Simplification:
- \( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab} \)
- \( \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \)
Geometry Formulas
The SAT Math section also includes numerous geometry questions, which test your understanding of shapes, areas, volumes, and the properties of angles. Here are the essential geometry formulas to remember:
Area and Perimeter
- Rectangle:
- Area: \( A = l \times w \)
- Perimeter: \( P = 2l + 2w \)
- Triangle:
- Area: \( A = \frac{1}{2}bh \)
- Perimeter: \( P = a + b + c \)
- Circle:
- Area: \( A = \pi r^2 \)
- Circumference: \( C = 2\pi r \)
Volume and Surface Area
- Rectangular Prism:
- Volume: \( V = l \times w \times h \)
- Surface Area: \( SA = 2lw + 2lh + 2wh \)
- Cylinder:
- Volume: \( V = \pi r^2 h \)
- Surface Area: \( SA = 2\pi r(h + r) \)
- Sphere:
- Volume: \( V = \frac{4}{3}\pi r^3 \)
- Surface Area: \( SA = 4\pi r^2 \)
Angles and Triangles
- Sum of Angles in a Triangle:
The sum of the interior angles in any triangle is:
\[ 180^\circ \]
- Pythagorean Theorem:
This theorem connects the sides of a right triangle:
\[ a^2 + b^2 = c^2 \]
where \( c \) is the hypotenuse.
- Special Right Triangles:
- 30-60-90 Triangle:
- Side ratios: \( 1 : \sqrt{3} : 2 \)
- 45-45-90 Triangle:
- Side ratios: \( 1 : 1 : \sqrt{2} \)
Statistics and Probability Formulas
Understanding statistics and probability is essential for the SAT Math section. Here are the key formulas:
Mean, Median, and Mode
- Mean:
The average of a set of numbers:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
- Median:
The middle value when a data set is ordered. If there is an even number of values, the median is the average of the two middle values.
- Mode:
The value that appears most frequently in a data set.
Probability
- Basic Probability:
The probability of an event is calculated as:
\[ P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
- Complement Rule:
The probability of the complement of an event \( A \) is:
\[ P(A') = 1 - P(A) \]
Trigonometry Formulas
Trigonometry is another topic covered in the SAT Math section, particularly concerning right triangles. Here are some fundamental trigonometric functions and identities:
Basic Trigonometric Ratios
- Sine, Cosine, and Tangent:
- \( \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \)
- \( \cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}} \)
- \( \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} \)
Trigonometric Identities
- Pythagorean Identity:
\[ \sin^2(\theta) + \cos^2(\theta) = 1 \]
- Angle Sum and Difference Formulas:
- \( \sin(a \pm b) = \sin a \cos b \pm \cos a \sin b \)
- \( \cos(a \pm b) = \cos a \cos b \mp \sin a \sin b \)
Conclusion
In conclusion, memorizing these SAT math formulas is crucial for performing well on the test. Understanding how to apply these formulas will not only help you solve problems more efficiently but also bolster your confidence as you approach the SAT Math section.
As you prepare for the test, consider creating flashcards or practice sheets that highlight these formulas. Regular practice and application of these concepts will make them second nature when you sit down for the exam. Remember, preparation is key, and having these formulas at your fingertips will set you on the path to success. Good luck!
Frequently Asked Questions
What are the key algebra formulas to memorize for the SAT Math section?
Key algebra formulas include the quadratic formula (x = (-b ± √(b² - 4ac)) / 2a), slope-intercept form of a line (y = mx + b), and the formulas for solving systems of equations.
Which geometry formulas are essential for the SAT Math test?
Essential geometry formulas include the area of a triangle (A = 1/2 base height), the Pythagorean theorem (a² + b² = c²), and the circumference and area of a circle (C = 2πr, A = πr²).
What is the formula for finding the distance between two points on the SAT?
The distance formula is d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.
How do I remember the formulas for factoring quadratics for the SAT?
Memorize common factoring patterns such as a² - b² = (a - b)(a + b) and the factored form of a quadratic ax² + bx + c can often be expressed as (px + q)(rx + s).
What are some important statistics formulas to know for the SAT?
Important statistics formulas include the mean (average), median (middle value), mode (most frequent value), range (difference between highest and lowest), and standard deviation.
What should I memorize about percentages for the SAT Math section?
Memorize that percentage = (part/whole) 100, and be familiar with converting between fractions, decimals, and percentages.
Are there specific exponent rules to memorize for the SAT?
Yes, important exponent rules include a^m a^n = a^(m+n), (a^m)^n = a^(mn), and a^m / a^n = a^(m-n).
What volume formulas should I know for the SAT Math section?
Memorize volume formulas for common shapes: rectangular prism (V = l w h), cylinder (V = πr²h), and sphere (V = 4/3πr³).
What is the formula for the slope of a line, and why is it important for the SAT?
The slope formula is m = (y2 - y1) / (x2 - x1). It's important for determining the steepness and direction of a line, which is frequently tested on the SAT.
