SAT Math Complete Reference Cheat Sheet

Key Facts

• Slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$, and a line in slope-intercept form is $y = mx + b$.
• Point-slope form is $y - y_1 = m(x - x_1)$, which is useful when a line gives one point and a slope.
• A quadratic in standard form is $ax^2 + bx + c = 0$, and its solutions are $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
• The discriminant $b^2 - 4ac$ tells the number of real solutions: positive means $2$, zero means $1$, and negative means $0$.
• For a right triangle, the Pythagorean theorem is $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
• Circle area is $A = \pi r^2$, circumference is $C = 2\pi r$, and an arc length is $s = \frac{\theta}{360^{\circ}} \cdot 2\pi r$.
• Percent change is $\frac{\text{new} - \text{old}}{\text{old}} \cdot 100\%$, with increases positive and decreases negative.
• Probability is $P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$ when all outcomes are equally likely.

Vocabulary

Linear function

A function with a constant rate of change that can be written as $f(x) = mx + b$.

Quadratic function

A function that can be written as $f(x) = ax^2 + bx + c$, where $a \ne 0$.

System of equations

A set of two or more equations that must be true at the same time.

Vertex

The highest or lowest point of a parabola, often written as $(h,k)$ in $f(x) = a(x-h)^2 + k$.

Median

The middle value of a data set when the values are arranged from least to greatest.

Standard deviation

A measure of how spread out data values are from the mean.