Algebra 1 Fall Exam Review

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is less than, greater than, less than or equal to, or greater than or equal to the other.

Front

How do you solve the inequality 2n + 4 < 16?

Back

Subtract 4 from both sides: 2n < 12. Then divide by 2: n < 6.

Front

What is the solution to the system of equations represented by the equations y = 2x + 1 and y = -x + 4?

Back

To find the solution, set the equations equal to each other: 2x + 1 = -x + 4. Solve for x to find the intersection point.

Front

Define domain in the context of a function.

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

Define range in the context of a function.

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if they intersect at a right angle (90 degrees). The slopes of perpendicular lines are negative reciprocals of each other.

Front

How do you find the slope of a line given its equation in slope-intercept form?

Back

In the slope-intercept form y = mx + b, m represents the slope of the line.

Front

What is the slope of the line y = -2x + 1?

Back

The slope of the line is -2.

Front

How do you write the equation of a line perpendicular to y = -2x + 1 that passes through the point (2, 3)?

Back

The slope of the perpendicular line is the negative reciprocal of -2, which is 1/2. Use point-slope form: y - 3 = (1/2)(x - 2). Simplifying gives y = (1/2)x + 2.

Front

What is the solution to the equation - (6m + 8) = 4(17 - m)?

Back

Distributing gives -6m - 8 = 68 - 4m. Rearranging leads to m = -38.