AMC 8 Strategy & Reference Cheat Sheet

Key Facts

• The average of $n$ numbers is $\frac{\text{sum of the numbers}}{n}$, so the sum is $n \cdot \text{average}$.
• A percent means parts per $100$, so $p\%$ of $x$ is $\frac{p}{100}x$.
• For a circle, the circumference is $C = 2\pi r = \pi d$ and the area is $A = \pi r^2$.
• For a triangle, the area is $A = \frac{1}{2}bh$, where $b$ is the base and $h$ is the perpendicular height.
• The Pythagorean theorem for a right triangle is $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
• The probability of an event is $P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total equally likely outcomes}}$.
• The number of ways to make sequential choices is found by multiplying the number of options at each step, such as $a \cdot b \cdot c$.
• If $a \equiv b \pmod{m}$, then $a$ and $b$ have the same remainder when divided by $m$.

Vocabulary

Estimation

Estimation is using nearby values or size comparisons to predict a reasonable answer before calculating exactly.

Ratio

A ratio compares two quantities by division, such as $\frac{a}{b}$ or $a:b$.

Remainder

A remainder is the amount left after dividing one integer by another, as in $17 = 5 \cdot 3 + 2$.

Factor

A factor of a number is an integer that divides it evenly with no remainder.

Complement

The complement of an event is everything outside that event, and its probability is $1 - P(\text{event})$.

Invariant

An invariant is a quantity or property that stays the same while other parts of a problem change.