Basic Math Review Lecture Notes

Comprehensive vocabulary flashcards covering basic math concepts from number types and properties to geometry and introductory algebra.

Natural Numbers

The set of numbers containing $\{1, 2, 3, 4, 5, …\}$.

Whole Numbers

The set of numbers containing $\{0, 1, 2, 3, 4, …\}$.

Integers

The set of numbers containing $\{…, -3, -2, -1, 0, 1, 2, …\}$.

Rational Numbers

All numbers that can be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers and $b \neq 0$.

Irrational Numbers

Real numbers that cannot be written as the quotient of two integers but can be represented on the number line.

Real Numbers

Include all numbers that can be represented on the number line, comprising all rational and irrational numbers.

Prime Numbers

A number greater than $1$ that has only itself and $1$ as factors, such as $2$, $3$, and $7$.

Composite Numbers

A number that is not prime, for example, $8$ because $8 = 2 \times 2 \times 2 = 2^3$.

Identity Property of Zero (Addition)

The property stating that $a + 0 = a$.

Inverse Property (Addition)

The property stating that $a + (-a) = 0$.

Commutative Property (Addition)

The property stating that the order of addition does not matter: $a + b = b + a$.

Associative Property (Addition)

The property stating that the grouping of numbers in addition does not matter: $a + (b + c) = (a + b) + c$.

Property of Zero (Multiplication)

The property stating that $a \times 0 = 0$.

Identity Property of One (Multiplication)

The property stating that $a \times 1 = a$.

Inverse Property (Multiplication)

The property stating that $a \times \frac{1}{a} = 1$, when $a \neq 0$.

Commutative Property (Multiplication)

The property stating that the order of multiplication does not matter: $a \times b = b \times a$.

Associative Property (Multiplication)

The property stating that the grouping of numbers in multiplication does not matter: $a \times (b \times c) = (a \times b) \times c$.

Absolute Value

The distance of a number from zero on the number line, which is always $\geq 0$. For example, $|-5| = 5$ and $|5| = 5$.

Least Common Multiple (LCM)

The smallest number that is a multiple of all the given numbers in a set.

Greatest Common Factor (GCF)

The largest number that can be evenly divided into each of the given numbers in a set.

Numerator

The top number of a fraction representing the number of parts.

Denominator

The bottom number of a fraction representing the whole.

Order of Operations

The specific sequence to solve expressions: 1st Parentheses, 2nd Exponents, 3rd Multiplication and Division (left to right), 4th Addition and Subtraction (left to right).

Rate

A comparison of two quantities with different units, such as $55\,mph$.

Ratio

A comparison of two quantities with the same units, such as $23:1$.

Proportion

A mathematical statement in which two ratios or rates are equal, such as \frac{$30}{5\,hr} = \frac{$60}{10\,hr}.

Percent

The number of parts out of $100$.

Simple Interest Formula

The formula $I = p \times r \times t$, where $I$ is interest, $p$ is principal, $r$ is percentage rate, and $t$ is time.

Scientific Notation

A way to express very large or small numbers in the form $a \times 10^n$, where $1 \leq |a| < 10$ and $n$ is an integer.

Mean

The average of a list of data, found by dividing the sum of all data values by the number of values.

Median

The number that separates an ordered list of data into two equal parts; if the count is even, it is the average of the two middle numbers.

Mode

The number in a data set that occurs most frequently.

Distance Formula

The formula $d = r \times t$, where $d$ is distance, $r$ is rate, and $t$ is time.

Perimeter

The distance around a geometric figure; for a rectangle, $P = 2L + 2W$, and for a square, $P = 4s$.

Area

The two-dimensional space inside a figure; for a rectangle $A = L \times W$, and for a triangle $A = \frac{1}{2}b \times h$.

Right Triangle

A triangle containing a $90^{\circ}$ angle.

Hypotenuse

The side of a right triangle that is opposite the $90^{\circ}$ angle.

Pythagorean Theorem

The theorem for right triangles stating that if $a$ and $b$ are the legs and $c$ is the hypotenuse, then $a^2 + b^2 = c^2$.

Circumference

The distance around a circle, calculated as $C = \pi \times d$ or $C = 2 \times \pi \times r$, where $\pi \approx 3.14$.

Variable

A letter that represents a number that is unknown or can change.

Constant

A term in an algebraic expression that does not change.

Algebraic Expression

A combination of constants, variables, numerals, and at least one mathematical operation.

Equation

A mathematical sentence indicating that two expressions are equal.

Solution

A number that makes a mathematical equation true.