A1 Basic Fall Final 2024 Study Guide

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, typically represented as 'm' in the slope-intercept form of a linear equation (y = mx + b). It is calculated as the rise over run, or the change in y divided by the change in x.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does it mean for two expressions to be equivalent?

Back

Two expressions are equivalent if they have the same value for all values of the variables involved.

Front

How do you simplify the expression 6(2f - 8) + 4f?

Back

First, distribute: 12f - 48 + 4f = 16f - 48.

Front

What is the solution to the equation 3x + 3 = -6?

Back

To solve for x, subtract 3 from both sides: 3x = -9, then divide by 3: x = -3.

Front

What is the order of operations in mathematics?

Back

The order of operations is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often abbreviated as PEMDAS.

Front

How do you evaluate the expression (12 ÷ 2)² + 9 ÷ 3?

Back

First, calculate inside the parentheses: (6)² + 3 = 36 + 3 = 39.

Front

What is a variable in algebra?

Back

A variable is a symbol (often a letter) that represents an unknown value in mathematical expressions or equations.

Front

What does 'the difference of 5 times a number and 3' mean in algebraic terms?

Back

It is expressed as 5n - 3, where n is the variable representing the unknown number.

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.