MATHEMATICAL TERMS

Additive Inverse - for any given number x, x + 0 = 0 + x = x.

Example:
1+(-1)=0, must e zero as result.

1+0 = 1, this also equals 0 + 1.

0+1 = 1

Algebraic Expression - a composition of a positive or a negative number and letters. Those letter(s) may have exponent or not. Also,it can be formed by fractional way.

Example:

$-2x$ , -2 is the negative number before letter x.

$3x^{2}y$ , 3 is the positive number before $x^{2}y$ .

$\frac{2x}{y}$ ,this is also an example of an expression.

$3x^{2}-2x$ , these sets of expressions can also be an expression. As long there is no equal symbol between them it will remain an expressions.

$3x^{2}=2x$ , this is an example of equation, "not" an expression. See the equal symbol between expressions.

Area - the total measurement of the surface of a polygon.

Example:

Multiply the length and width of a rectangle.

Arithmetic Sequence - the constant pattern that increases or decreases at the same rate or value. It has the same constant difference.
Example:
2,4,6,8,___; what is the number in the series? So the answer is 10.
-5,-10,-15,___; what is the number in the series? So the answer is -20.

1. Average: The average (or mean) of a set of numbers is the sum of those numbers divided by the total number of numbers.

Example: the average of 2, 4, and 6 is (2 + 4 + 6) / 3 = 4.

2. Arc: An arc is a portion of the circumference of a circle, typically measured in degrees.

Example: a quarter circle has an arc of 90 degrees.

3. Axis: An axis is a reference line used to measure or plot points in a coordinate system.

Example: the x-axis and y-axis are the two axes used in a Cartesian coordinate system.

4. Asymptote: An asymptote is a line that a curve approaches but never touches, as the curve extends infinitely.

Example: the curve y = 1/x has two asymptotes: the x-axis and the y-axis.

5. Average rate of change: The average rate of change of a function over an interval is the change in the output of the function divided by the change in the input of the function, for that interval.

Example: the average rate of change of the function f(x) = x^2 over the interval [1, 3] is (f(3) - f(1)) / (3 - 1) = (9 - 1) / 2 = 4.

1. Absolute value: The absolute value of a number is its distance from zero on the number line.

Example: the absolute value of -5 is 5, and the absolute value of 3 is 3.

2. Addition: Addition is a basic arithmetic operation that involves combining two or more numbers to get a total or sum. For example, 2 + 3 = 5 and 10 + 5 + 8 = 23.

3. Area: The area of a shape is the amount of space it occupies in two-dimensional space.

Example: the area of a square with a side length of 4 units is 16 square units (4 x 4).

4. Algebra: Algebra is a branch of mathematics that involves using symbols and letters to represent variables and unknown quantities, and manipulating them to solve equations.

Example: solving the equation x + 3 = 7 involves using algebra to find that x = 4.

5. Angle: An angle is the measure of the space between two intersecting lines, usually measured in degrees.

Example: a right angle is 90 degrees, while a straight angle is 180 degrees.

DMG