SAT Math Problem Solving and Data Analysis Reference Cheat Sheet

Key Facts

• A ratio compares quantities using division, so the ratio of $a$ to $b$ is $\frac{a}{b}$ or $a:b$.
• A unit rate has a denominator of $1$, such as $\frac{240\text{ miles}}{4\text{ hours}}=60\text{ miles per hour}$.
• Percent means per hundred, so $p\%$ is equal to $\frac{p}{100}$.
• Percent change is $\frac{\text{new value}-\text{old value}}{\text{old value}}\times 100\%$.
• The mean of $n$ values is $\bar{x}=\frac{x_1+x_2+\cdots+x_n}{n}$.
• Probability is $P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{number of total outcomes}}$ when outcomes are equally likely.
• For independent events, $P(A\text{ and }B)=P(A)\cdot P(B)$.
• A line of best fit can be written as $y=mx+b$, where $m$ is the predicted change in $y$ for each $1$-unit increase in $x$.

Vocabulary

Ratio

A comparison of two quantities by division, often written as $a:b$ or $\frac{a}{b}$.

Unit Rate

A rate that compares a quantity to exactly $1$ unit of another quantity.

Percent Change

The relative change from an old value to a new value, calculated by $\frac{\text{new}-\text{old}}{\text{old}}\times 100\%$.

Mean

The arithmetic average of a data set, found by dividing the sum of the values by the number of values.

Median

The middle value of an ordered data set, or the average of the two middle values when there is an even number of values.

Correlation

A measure of the direction and strength of the relationship between two quantitative variables.