Math Models Fall Semester Exam 2023 v2

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 the y-coordinate divided by the change in the x-coordinate between two points on the line.

Front

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

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line that passes through the points (-4, -1) and (-2, -5)?

Back

-2

Front

What does the inequality a ≥ 11 represent graphically?

Back

It represents all values of 'a' that are greater than or equal to 11, including 11 itself, typically shown as a solid line on a number line starting from 11 and extending to the right.

Front

What is the difference between a > 11 and a ≥ 11?

Back

a > 11 means 'a' is greater than 11 (not including 11), while a ≥ 11 means 'a' is greater than or equal to 11 (including 11).

Front

How do you evaluate a function f(x) at a specific value?

Back

Substitute the specific value into the function's equation and simplify.

Front

Evaluate f(-4) for the function f(x)=3x²-5.

Back

f(-4) = 43.

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

Calculate (82 ÷ 2) × 3 – 17.

Back

106.

Front

What is an undefined slope?

Back

An undefined slope occurs when a line is vertical, meaning it does not have a defined rise over run.