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Algebra 2 Practice Test

April Patigas

Updated on September 11, 2026

This free Algebra 2 practice test checks whether students can work confidently with polynomials, complex numbers, functions, rational exponents, exponential models, logarithms, quadratics, and introductory trigonometry. Ten multiple-choice questions provide a fast snapshot of the topics to review next.

Algebra 2 Practice Test: 10 Questions With Answers

ALGEBRA 2 DIAGNOSTIC TEST

Directions: Choose the best answer for each question. Show work when needed.

1 / 10

Which expression is equivalent to (3x² − 2x + 5) − (x² + 4x − 7)?

 

2x² − 6x + 12

2x² + 2x − 2

4x² − 6x + 12

2x² − 6x − 2

2 / 10

Which is the solution to z² + 4z + 13 = 0 with a positive imaginary part?

−2 + 3i

−4 + i

2 + 3i

2 − 3i

3 / 10

Which is the complete factorization of 2x³ − 8x² − 10x?

2x(x − 5)(x + 1)

2(x − 5)(x + 1)

x(2x − 5)(x + 1)

2x(x − 10)(x + 1)

4 / 10

Which statement correctly describes the end behavior of y = −x³ + 3x² + 4x − 12?

As x → ∞, y → ∞

As x → ∞, y → −∞

Both ends rise

Both ends fall

5 / 10

Which expression is equivalent to x^(7/4), assuming x > 0?

 

⁴√(x⁷)

√(x⁷)

(x^(1/7))⁴

x^(4/7)

6 / 10

For P(t) = 100(2)^(t/3), what is P(6)?

200

300

400

600

7 / 10

What is the value of log₃(81)?

3

4

9

27

8 / 10

Which transformation is NOT applied to f(x) = x² to obtain g(x) = −(x − 3)² + 5?

 

Reflection over the x-axis

Shift right 3 units

Shift up 5 units

Vertical stretch by a factor of 3

9 / 10

What is the solution set of x² − 5x − 14 = 0?

 

{−2, 7}

{2, −7}

{−1, 14}

{1, −14}

10 / 10

If θ = π/6, what is sin θ?

1/2

√2/2

√3/2

1

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Algebra 2 Practice Test for Core High School Topics

Brighterly’s Algebra 2 practice test focuses on the ideas that move students from basic equation solving toward advanced function analysis.

The questions ask students to simplify and factor polynomials, solve with complex numbers, interpret function behavior and transformations, connect radicals with rational exponents, and evaluate exponential and logarithmic expressions.

A final trigonometry question checks readiness for the next stage of high school math.

More About the Algebra 2 Practice Test

Each question isolates a high-value Algebra 2 skill. The set is short enough for a quick diagnostic, but broad enough to reveal whether a student is mainly struggling with symbolic manipulation, equation solving, or interpreting functions.

1. Polynomials. Subtract polynomial expressions, factor out a greatest common factor, complete a cubic factorization, and connect the leading term to end behavior.
2. Complex numbers and quadratics. Identify a nonreal solution, solve a quadratic by factoring, and read a quadratic transformation from vertex form.
3. Exponents and radicals. Rewrite a rational exponent as a radical expression while keeping the same value.
4. Exponential and logarithmic functions. Evaluate an exponential model at a given input and interpret a logarithm as an exponent.
5. Trigonometric readiness. Recall an exact sine value for a standard angle, a skill that becomes increasingly important in Precalculus.

Next Steps After the Algebra 2 Practice Test

Use the result to organize review in a logical order:

1. Label every missed question by skill. “Polynomial subtraction” or “end behavior” is a more useful note than simply marking the answer wrong.
2. Practice related questions in a set. Work on one topic at a time with the Algebra 2 worksheets, then mix topics again once the method is reliable.
3. Take a broader grade-level test. The 11th grade math test adds systems, inequalities, and other junior-year skills to the diagnostic picture.
4. Get help with recurring gaps. An Algebra 2 tutor can connect rules to function behavior and show why each method works.

Benefits of the Algebra 2 Practice Test