A letter or symbol used to stand for an unknown number in a math problem.

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A number that stays the same and doesn't change.

A group of numbers and symbols that show a mathematical operation or value.

A math sentence with an equal sign showing that two expressions are equal to each other.

A number that is multiplied by a variable in a math problem.

A number, a variable, or a combination of both that are separated by addition or subtraction signs.

A math sentence that shows the relationship between two values using symbols such as > (greater than), < (less than), or = (equal to).

The distance of a number from zero on the number line.

A math rule that relates one input value to one output value.

A small number written above and to the right of a number or a variable that tells how many times that number or variable is multiplied by itself.

Perform operations inside parentheses first. Ex. Simplify the expression 4 x (5 - 2) + 1. Answer is 4 x 3 + 1 = 13.

Evaluate exponents (powers and square roots). Ex. Simplify the expression 3² + 4 x √16. Answer is 3² + 4 x 4 = 19.

Multiply and divide from left to right. Ex. Simplify the expression 9 ÷ 3 x 2 - 1. Answer is 3 x 2 - 1 = 5.

Add and subtract from left to right. Ex. Simplify the expression 8 - 4 + 6 ÷ 2. Answer is 8 - 4 + 3 = 7.

What do you do if there are multiple operations inside parentheses?

Perform the operations from left to right. Ex. Simplify the expression 6 - (3 + 1) x 2. Answer is 6 - 4 x 2 = -2.

Work from the inside out. Ex. Simplify the expression 5 x (2 - (3 + 1)). Answer is 5 x (2 - 4) = -10.

Treat them as part of the number they're attached to. Ex. Simplify the expression -4 x 3 + 7. Answer is -12 + 7 = -5.

Move on to the next step in order of operations. Ex. Simplify the expression 6 + 3² ÷ 3 x 2. Answer is 6 + 9 ÷ 3 x 2 = 6 + 6 = 12.

Simplify them first. Ex. Simplify the expression 3 + 1/4 x 8. Answer is 3 + 2 = 5.

What happens if there are multiple operations with the same level of precedence?

Work from left to right. Ex. Simplify the expression 4 x 3 ÷ 6 - 1. Answer is 12 ÷ 6 - 1 = 2 - 1 = 1.

Adding zero doesn't change the value. Ex. 5 + 0 = 5.

Multiplying by one doesn't change the value. Ex. 7 x 1 = 7.

Order doesn't change the sum. Ex. 3 + 7 = 7 + 3.

Order doesn't change the product. Ex. 4 x 6 = 6 x 4.

Grouping doesn't change the sum. Ex. (2 + 4) + 6 = 2 + (4 + 6).

Grouping doesn't change the product. Ex. (3 x 5) x 2 = 3 x (5 x 2).

Multiplying a sum distributes the multiplication to each addend. Ex. 3 x (4 + 2) = 3 x 4 + 3 x 2.

Every number has an opposite that adds to zero. Ex. 5 + (-5) = 0.

Every number (except 0) has a reciprocal that multiplies to one. Ex. 2 x 1/2 = 1.

Any number times zero equals zero. Ex. 9 x 0 = 0.

x = pi/6 or x = 11pi/6.

An equation that forms a straight line. Ex. y = 2x + 3.

Plot points and draw a line. Ex. Graph y = -3x + 4.

y = mx + b. Ex. Equation with slope 2 and y-intercept -3.

Change in y over change in x. Ex. Slope of line passing through (2, 5) and (4, 9).

The y-coordinate where the line crosses the y-axis. Ex. y-intercept of y = -2x + 7.

The x-coordinate where the line crosses the x-axis. Ex. x-intercept of y = 3x - 6.

y - y1 = m(x - x1). Ex. Equation passing through (1, 4) with slope -2.

Ax + By = C. Ex. Equation 2x - 3y = 6 in standard form.

Lines with same slope and never intersect.

Lines that intersect at a right angle and have negative reciprocal slopes.

Rewriting an expression as simpler expressions. Ex. Factoring x^2 - 4 as (x - 2)(x + 2).

The largest factor that divides evenly into all terms.

a^2 - b^2 = (a + b)(a - b). Ex. Factoring 25 - x^2 as (5 + x)(5 - x).

a^3 + b^3 = (a + b)(a^2 - ab + b^2) or a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Grouping terms with common factors and factoring out the GCF of each group.

Finding two numbers that multiply to ac and add to b, then factoring as (mx + n)(px + q).

A number that shows how many times a base is multiplied by itself. Ex. 2³ = 2 × 2 × 2 = 8

A symbol that represents the root of a number. Ex. √16 = 4, because 4 × 4 = 16

To multiply two powers with the same base, add the exponents. Ex. 3² × 3³ = 3^(2+3) = 3⁵

To divide two powers with the same base, subtract the exponents. Ex. 2⁶ ÷ 2³ = 2^(6-3) = 2³

To raise a power to another power, multiply the exponents. Ex. (2³)² = 2^(3×2) = 2⁶ = 64

A relation where each input (x) corresponds to exactly one output (y). Ex. y = 2x + 1 is a function.

[-8, 4]. Explained, For x = -2 to x = 2, y ranges from -8 to 4.

[3, +∞). Explained, x - 3 must be non-negative for the square root to be real, so x ≥ 3.

Yes. Explained, Each x-value corresponds to exactly one y-value.