Algebra 2 Radical and Rational Equations Test with Point Values (PDF)

Algebra 2 math test: Radical and Rational Equations – Maths PDF

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This radical rational equations test for Algebra 2 covers radical and rational equations (Common Core A-REI.A.2), with a free PDF to print.

This 45-minute test on radical and rational equations 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: Radical and Rational Equations
Standards: A-REI.A.2
Time: 45 minutes
Total: 20 points

Radical rational equations test: questions

Question 1 – Basic radical equation [1 pt]

Solve \(\sqrt{3x + 1} = 7\).

Question 2 – Extraneous solution [3 pts]

Graphs of both sides.

Solve \(\sqrt{x + 12} = x\). Identify any extraneous solution.

Question 3 – Rational equation [2 pts]

Solve \(\frac{5}{x + 1} = \frac{2}{x}\).

Question 4 – No solution [3 pts]

Solve \(\frac{x}{x + 3} = \frac{-3}{x + 3} + 2\) and explain your result.

Question 5 – Binomial equals radical [2 pts]

Solve \(x – 3 = \sqrt{x – 1}\).

Question 6 – Two machines [3 pts]

Two machines print a batch.

Machine B takes 6 hours longer than machine A to print a batch of flyers, and together they print it in 4 hours. Write an equation and find the time machine A needs alone.

Question 7 – Free fall [2 pts]

The time for an object to fall \(h\) feet is \(t = \frac{\sqrt{h}}{4}\) seconds. How far does an object fall in 5 seconds?

Question 8 – Cube root [2 pts]

Solve \(\sqrt[3]{x + 2} = 3\).

Question 9 – Check by substitution [2 pts]

Compare both sides.

Use the table to decide which of \(x = 0\), \(x = 5\), \(x = -3\) solves \(\sqrt{x + 4} = x – 2\).

Key facts behind this radical rational equations test

Key facts

Isolate the radical before squaring.
Squaring can create extraneous solutions; always check.
Rational equations: multiply by the LCD to clear fractions.
Reject answers that make a denominator 0.
A principal square root is never negative.

How to use this radical rational equations 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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