Math Summative Reviews: Units 1-8

A specific order of operations for solving mathematical expressions. It stands for Brackets, Orders (exponents), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).

A number that can be written as a fraction, where both the numerator and denominator are integers. Examples include 1/2, 3/4, and 5/8.

A ratio that compares a part to a whole, often expressed as a percentage. For example, 25% represents 25 out of every 100.

A statement that two ratios are equal. It can be expressed as a/b = c/d.

A variable whose value depends on another variable. In a relationship, the dependent variable is what changes based on the independent variable.

A variable whose value does not depend on any other variable. In a relationship, the independent variable is the one that is changed or manipulated.

A relationship between two variables where, as one variable increases, the other variable also increases. The graph of this relationship will have an upward slope.

A relationship between two variables where, as one variable increases, the other variable decreases. The graph of this relationship will have a downward slope.

Multiplying two terms with the same base: Add the exponents.

Dividing two terms with the same base: Subtract the exponents.

A number multiplied by a variable, like 5 in 5x

A variable multiplied by itself a number of times, like x in x²

Terms with the same variable and exponents, like 3x² and 5x²

An expression with one or more terms, each with a variable raised to a non-negative integer exponent.

Simplifying expressions by combining like terms, multiplying exponents, and applying the order of operations.

Solving an equation to find the value of the unknown variable.

The product of identical factors (e.g., 4 x 4 x 4 = 4³ )

When multiplying powers with the same base, add the exponents. (e.g., 4⁴ x 4³ = 4⁷)

When dividing powers with the same base, subtract the exponents. (e.g., 6²⁶/6²¹ = 6⁵ )

When raising a power to another power, multiply the exponents. (e.g., (5³)⁻⁶ = 5⁻¹⁸ )

When solving equations involving powers, try to isolate the variable by using the rules of exponents.

Any number raised to the power of zero equals 1 (e.g., 5⁰ = 1)

Any number raised to the power of one equals itself (e.g., 5¹ = 5)

Any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent (e.g., 5⁻² = 1/ 5²)

Multiplying powers with the same base is done by adding the exponents.

Dividing powers with the same base is done by subtracting the exponents.

Raising a power to another power is done by multiplying the exponents.

The distributive property allows us to multiply a sum by a number by distributing the multiplication to each term of the sum.

The change in y-values over the change in x-values between two points on a line.

A sequence of numbers generated by adding a constant difference to each term.

A relationship that can be represented by a straight line on a graph. Its 1st differences are constant.

A relationship that cannot be represented by a straight line on a graph. Its 1st differences are not constant.

An equation that represents a line, expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

An equation that represents a line, expressed in the form Ax + By = C, where A, B, and C are constants.

Lines that have the same slope but different y-intercepts.

Lines that intersect at a right angle. Their slopes are negative reciprocals of each other.

The point where a line crosses the vertical (y) axis. It is represented by the constant term 'b' in the slope-intercept form.

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. This form is useful for visualizing the equation and finding the x and y intercepts.

A relationship where the value of the dependent variable changes proportionally to the independent variable. It can be represented by an equation in the form y = kx, where 'k' is the constant of variation.

A relationship where the value of the dependent variable depends on both the independent variable and a constant term. It can be represented by an equation in the form y = mx + b

Finding the values of the unknown variables in a system of equations. This involves manipulating the equations to eliminate one variable and solve for the other.