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Algebra 2 Practice Tests

These Grade 11 Math practice tests develop Algebra 2 skills across functions, transformations, systems, polynomial operations, factoring, rational expressions, exponents, logarithms, complex numbers, and quadratic models.

Skills covered

  • Evaluating functions, domains and ranges, inverses, systems, inequalities, transformations, and vertex form
  • Working with polynomial degree, leading coefficients, products, differences of squares, factoring, zeros, remainders, and end behavior
  • Simplifying and solving rational expressions while tracking restrictions, asymptotes, holes, and variation
  • Applying exponent laws, exponential growth and decay, logarithm definitions, logarithm properties, and equations
  • Using \(i^2=-1\), complex-number operations, discriminants, the quadratic formula, axes of symmetry, vertices, and completing the square

How to use these practice tests

Write each algebraic step clearly and check restrictions before canceling or multiplying. For functions and quadratics, connect the equation to its graph, domain, range, intercepts, vertex, zeros, and end behavior.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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5 Tests
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5. Test

Grade 11 Algebra 2 Practice Tests

Practice Grade 11 Math questions about functions, transformations, systems, polynomial functions, rational expressions, exponents, logarithms, complex numbers, and quadratic functions.

Choose the best answer. Show algebraic steps, respect domain restrictions, use function notation, and check solutions in the original equation when necessary.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

What is i2i^2 by definition?

Please select an answer first.

Correct answer: A

The correct answer is -1.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: The imaginary unit i is defined by i^2 = -1.
  3. Check the result: The correct answer is -1.

The imaginary unit i is defined by i^2 = -1.

2. QuestionMultiple choice

What is −25\sqrt{-25}?

Please select an answer first.

Correct answer: B

The correct answer is 5i.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: Since sqrt(-25) = sqrt(25)sqrt(-1) = 5i.
  3. Check the result: The correct answer is 5i.

Since sqrt(-25) = sqrt(25)sqrt(-1) = 5i.

3. QuestionMultiple choice

What is (3+2i)+(4−i)(3+2i)+(4-i)?

Please select an answer first.

Correct answer: C

The correct answer is 7+i.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: Add real parts and imaginary parts: (3+4) + (2i-i) = 7+i.
  3. Check the result: The correct answer is 7+i.

Add real parts and imaginary parts: (3+4) + (2i-i) = 7+i.

4. QuestionMultiple choice

What is (2+i)(2−i)(2+i)(2-i)?

Please select an answer first.

Correct answer: D

The correct answer is 5.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: The product is a difference of squares: 2^2 - i^2 = 4 - (-1) = 5.
  3. Check the result: The correct answer is 5.

The product is a difference of squares: 2^2 - i^2 = 4 - (-1) = 5.

5. QuestionMultiple choice

What is the discriminant of ax2+bx+c=0ax^2+bx+c=0?

Please select an answer first.

Correct answer: A

The correct answer is b2−4acb^2-4ac.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: The discriminant b^2 - 4ac indicates the type and number of real solutions.
  3. Check the result: The correct answer is b2−4acb^2-4ac.

The discriminant b^2 - 4ac indicates the type and number of real solutions.

6. QuestionMultiple choice

What does a discriminant of zero indicate?

Please select an answer first.

Correct answer: B

The correct answer is One repeated real solution.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: A zero discriminant makes the square-root term in the quadratic formula zero, producing one repeated real root.
  3. Check the result: The correct answer is One repeated real solution.

A zero discriminant makes the square-root term in the quadratic formula zero, producing one repeated real root.

7. QuestionMultiple choice

What is the axis of symmetry of y=x2−6x+5y=x^2-6x+5?

Please select an answer first.

Correct answer: C

The correct answer is x=3x=3.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: For ax^2 + bx + c, the axis is x = -b/(2a) = 6/2 = 3.
  3. Check the result: The correct answer is x=3x=3.

For ax^2 + bx + c, the axis is x = -b/(2a) = 6/2 = 3.

8. QuestionMultiple choice

What is the quadratic formula?

Please select an answer first.

Correct answer: D

The correct answer is x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: The quadratic formula solves ax^2 + bx + c = 0 when a is not zero.
  3. Check the result: The correct answer is x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.

The quadratic formula solves ax^2 + bx + c = 0 when a is not zero.

9. QuestionMultiple choice

What is the vertex of y=(x+1)2−4y=(x+1)^2-4?

Please select an answer first.

Correct answer: A

The correct answer is (−1,−4)(-1,-4).

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: In vertex form y = (x - h)^2 + k, x + 1 = x - (-1), so the vertex is (-1,-4).
  3. Check the result: The correct answer is (−1,−4)(-1,-4).

In vertex form y = (x - h)^2 + k, x + 1 = x - (-1), so the vertex is (-1,-4).

10. QuestionMultiple choice

Why can completing the square help solve a quadratic?

Please select an answer first.

Correct answer: B

The correct answer is It rewrites the expression as a perfect square and reveals vertex or solution information..

  1. Identify the Algebra 2 structure: Determine whether the question involves a function, polynomial, rational expression, exponential or logarithmic relationship, complex number, or quadratic model.
  2. Apply the algebraic relationship: Completing the square transforms a quadratic into a form that can be solved or graphed more directly.
  3. Check the result: The correct answer is It rewrites the expression as a perfect square and reveals vertex or solution information..

Completing the square transforms a quadratic into a form that can be solved or graphed more directly.

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