Algebra 1 Ultimate Review

Moving a constant term to the other side of the equation by applying the opposite operation.

Combining terms with the same variable on one side of the equation.

Distributing a number multiplied by an expression inside parentheses.

The process of turning words into a mathematical equation to find a solution.

Understanding the problem's context, identifying key information, and determining what is being asked.

Identifying the unknown quantity and assigning it a variable (usually x).

Translating the words into mathematical symbols, including operations and relationships.

Solving the equation to find the value of the variable.

The rate of change of a line, representing the rise (vertical change) over the run (horizontal change) between any two points on the line.

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

An equation of a line that is solved for y, representing the relationship between the slope (m), y-intercept (b), and any point (x,y) on the line.

Identifying the slope and y-intercept of a line by comparing the equation in slope-intercept form (y = mx + b) to the provided equation.

Writing the equation of a line given the slope and a point on the line by substituting the values into the slope-intercept form (y = mx + b) and solving for the y-intercept.

The act of manipulating equations by adding or subtracting the same value to both sides to achieve a specific form or isolate a variable.

The process of finding the equation of a line when given more than one point on the line, by calculating the slope from the points and then applying the slope and a point to find the equation.

The steepness or incline of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

The point where a line crosses the y-axis. It represents the value of y when x = 0.

A mathematical equation that represents a straight line. It's usually written in the form y = mx + b, where m is the slope and b is the y-intercept.

The process of finding the slope of a line when you know two points on the line. You calculate the difference in y-coordinates divided by the difference in x-coordinates.

Using the slope and a point on the line to determine the y-intercept (b) in the equation y = mx + b.

The equation of a line expressed in the form y = mx + b, where m is the slope and b is the y-intercept. It's useful because it directly shows the slope and y-intercept.

The process of plotting a linear equation on a graph. Start by plotting the y-intercept, then use the slope to find other points on the line.

A line passing through two points. It can be represented by a linear equation.

A mathematical method for solving systems of equations by graphing the equations and finding their intersection point.

A mathematical method for solving systems of equations by substituting the value of one variable from one equation into the other equation.

A mathematical expression that represents the repeated multiplication of a base by itself a certain number of times.

A set of rules that define how to manipulate exponents in mathematical expressions.

The number that is multiplied by itself in an exponential expression.

The number that indicates how many times the base is multiplied by itself in an exponential expression.

A way to represent a variable or unknown quantity in mathematical expressions.

When multiplying powers with the same base, add the exponents. For example, x⁵ * x² = x⁷.

When raising a power to another power, multiply the exponents. For example, (y⁴)² = y⁸.

When dividing powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. For example, 2³ ÷ 2² = 2¹ = 2.

Any number raised to the power of zero equals 1. For example, 5⁸⁷⁰ = 1.

A negative exponent means the inverse of the base raised to the positive version of the exponent. For example, x⁻³ = 1/x³. Note: only the base is affected.

When multiplying polynomials, distribute each term of the first polynomial to every term in the second polynomial. This can be done using the FOIL (First, Outer, Inner, Last) method.

The FOIL method is a mnemonic for multiplying binomials. It stands for First, Outer, Inner, Last, representing the order of multiplying terms.

In a radical equation, the radical should be isolated on one side of the equation before solving. This means simplifying the equation so that only the radical term remains on one side of the '=' sign.

To solve a radical equation, raise both sides of the equation to the power of the radical index. This eliminates the radical sign and helps you solve for the unknown variable.

After solving a radical equation, it's crucial to check your solution by plugging it back into the original equation. This step verifies that the solution is valid and doesn't create an undefined result.

A solution that satisfies the simplified equation but makes the original radical undefined. For example, a negative value under a square root.

The process of solving radical equations involves manipulating the equation to isolate the radical, then raising both sides to the appropriate power to eliminate the radical. Finally, check the solution to validate its authenticity.

To solve a radical equation with multiple radicals, isolate each radical individually, raise both sides to the corresponding power, and then repeat the process until all radicals are eliminated.

In radical equations, the domain refers to the set of permissible values for the variable that make the radical defined. For example, in a square root, the radicand (expression inside the root) must be non-negative.

When dealing with radical equations, it's essential to remember the order of operations (PEMDAS) to simplify the expressions correctly. Simplify operations inside parentheses, exponents, multiplication & division, then addition & subtraction.