Algebra 2 Rational Expressions Test with Point Values (PDF)

Algebra 2 math test: Rational Expressions – Maths PDF

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This rational expressions test for Algebra 2 covers rational expressions (Common Core A-APR.D.7, A-SSE.A.2), with a free PDF to print.

This 45-minute test on rational expressions has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Rational Expressions
Standards: A-APR.D.7, A-SSE.A.2
Time: 45 minutes
Total: 20 points

Rational expressions test: questions

Question 1 – Excluded values [2 pts]

State the excluded values of \(\frac{x – 5}{x^{2} – 3x – 10}\), then simplify the expression.

Question 2 – Simplify [2 pts]

Simplify \(\frac{x^{2} + 2x – 15}{x^{2} – 9}\).

Question 3 – Multiply [2 pts]

Multiply and simplify: \(\frac{2x}{x + 4} \cdot \frac{x^{2} – 16}{6x}\).

Question 4 – Divide [2 pts]

Divide: \(\frac{x^{2} – 4}{x + 3} \div \frac{x + 2}{x^{2} + 6x + 9}\).

Question 5 – Add [3 pts]

Add: \(\frac{2}{x – 3} + \frac{4}{x + 1}\). Give the answer as a single simplified fraction.

Question 6 – Complex fraction [2 pts]

Simplify \(\frac{\frac{1}{x} + \frac{1}{3}}{\frac{1}{x} – \frac{1}{3}}\).

Question 7 – Two pumps [2 pts]

Aisha paints 1/6 of the fence per hour and Diego 1/4 per hour: together 5/12.

Pump A empties a tank in 6 hours and pump B empties it in 4 hours. How long do the two pumps take together? (The bars show the hourly rates.)

Question 8 – Structure and holes [3 pts]

y = (x² – 4)/(x – 2) is the line y = x + 2 with a hole at x = 2.

Simplify \(g(x) = \frac{x^{4} – 16}{x^{2} – 4}\) by recognizing the structure, and state the excluded values.

Question 9 – Find the error [2 pts]

Comparison at two values.

A student wrote \(\frac{x + 6}{6} = x + 1\). Use the table to show the claim is false and write the correct simplification.

Key facts behind this rational expressions test

Key facts

Rational expression = polynomial ÷ polynomial.
Factor first, then cancel common factors only.
Excluded values make the original denominator 0.
Divide by multiplying by the reciprocal.
Add or subtract over the least common denominator.

How to use this rational expressions test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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