Rational Expressions and Functions: math test, Grade 11 – download the PDF

1 Simplifying / 3 pts

Simplify and state the restrictions.

1. \(\dfrac{x^2+2x-15}{x^2-9}\)
2. \(\dfrac{6x^3y}{15xy^2}\)

2 Multiplying and dividing / 4 pts

Compute and simplify.

1. \(\dfrac{x^2-25}{x+2}\cdot\dfrac{x^2+2x}{x-5}\)
2. \(\dfrac{x^2-x-12}{x^2-1}\div\dfrac{x-4}{x+1}\)

3 Adding and subtracting / 4 pts

Write each result as a single fraction.

1. \(\dfrac{4}{x-3}+\dfrac{2}{x+3}\)
2. \(\dfrac{x}{x-5}-\dfrac{3}{x+1}\)

4 Analyzing a function / 4 pts

Let \(f(x)=\dfrac{2x+6}{x-4}\).

1. Find the vertical and horizontal asymptotes.
2. Find the \(x\)-intercept and the \(y\)-intercept.
3. Compute \(f(6)\) and \(f(2)\).

5 Solving an equation / 3 pts

Solve \(\dfrac{3}{x-2}+1=\dfrac{12}{x^2-4}\). Check your answers.

6 Travel time / 2 pts

The time \(t\) of a trip varies inversely with the speed \(r\). At 45 miles per hour the trip takes 4 hours. How long does it take at 60 miles per hour?