Algebra 1 Final Review

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 6n^2 - 7n^4 + 8 is a polynomial.

Front

How do you add polynomials?

Back

To add polynomials, combine like terms by adding their coefficients. For example, (6n^2 - 7n^4 + 8) + (6 + 8n + 4n^4) = -3n^4 + 6n^2 + 8n + 14.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you model a savings account with a function?

Back

To model a savings account, use a linear function where the initial amount is the y-intercept and the monthly savings is the slope. For example, Bob's savings can be modeled as y = 40x + 150.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run). For example, the slope between points (10, 1) and (5, 2) is -1/5.

Front

How do you find the slope between two points?

Back

To find the slope between two points (x1, y1) and (x2, y2), use the formula: slope = (y2 - y1) / (x2 - x1).

Front

Back

This inequality represents a range of values for x that satisfy the condition. Solving it gives x <= -5.

Front

How do you solve an inequality?

Back

To solve an inequality, isolate the variable on one side using inverse operations, similar to solving an equation, while reversing the inequality sign if multiplying or dividing by a negative number.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. Solutions are the values that satisfy all equations simultaneously.

Front

How do you represent a word problem as a system of equations?

Back

Identify the variables, translate the relationships into equations, and ensure the equations represent the conditions given in the problem.