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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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1. 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 the domain of f(x)=1x−3f(x)=\frac{1}{x-3}?

Please select an answer first.

Correct answer: A

The correct answer is All real numbers except 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: The denominator cannot equal zero, so x - 3 = 0 is excluded from the domain.
  3. Check the result: The correct answer is All real numbers except x=3x=3.

The denominator cannot equal zero, so x - 3 = 0 is excluded from the domain.

2. QuestionMultiple choice

If f(x)=2x+5f(x)=2x+5, what is f(3)f(3)?

Please select an answer first.

Correct answer: B

The correct answer is 11.

  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: Substitute 3: f(3) = 2(3) + 5 = 11.
  3. Check the result: The correct answer is 11.

Substitute 3: f(3) = 2(3) + 5 = 11.

3. QuestionMultiple choice

Which relation is a function?

Please select an answer first.

Correct answer: C

The correct answer is \{(1,2),(2,4),(3,6)\}.

  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 function assigns exactly one output to each input; the first coordinates in this relation are all different.
  3. Check the result: The correct answer is \{(1,2),(2,4),(3,6)\}.

A function assigns exactly one output to each input; the first coordinates in this relation are all different.

4. QuestionMultiple choice

What is the inverse operation of adding 7?

Please select an answer first.

Correct answer: D

The correct answer is Subtracting 7.

  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: Subtraction by the same amount reverses addition: x + 7 - 7 = x.
  3. Check the result: The correct answer is Subtracting 7.

Subtraction by the same amount reverses addition: x + 7 - 7 = x.

5. QuestionMultiple choice

What transformation changes f(x)f(x) to f(x)+4f(x)+4?

Please select an answer first.

Correct answer: A

The correct answer is A vertical shift up 4 units.

  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: Adding 4 outside the function changes every output and shifts the graph upward.
  3. Check the result: The correct answer is A vertical shift up 4 units.

Adding 4 outside the function changes every output and shifts the graph upward.

6. QuestionMultiple choice

What is the vertex of y=(x−2)2+3y=(x-2)^2+3?

Please select an answer first.

Correct answer: B

The correct answer is (2,3)(2,3).

  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: Vertex form y = (x - h)^2 + k has vertex (h,k), so h = 2 and k = 3.
  3. Check the result: The correct answer is (2,3)(2,3).

Vertex form y = (x - h)^2 + k has vertex (h,k), so h = 2 and k = 3.

7. QuestionMultiple choice

What is the slope of the line through (1,4)(1,4) and (3,10)(3,10)?

Please select an answer first.

Correct answer: C

The correct answer is 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: The slope is (10 - 4)/(3 - 1) = 6/2 = 3.
  3. Check the result: The correct answer is 3.

The slope is (10 - 4)/(3 - 1) = 6/2 = 3.

8. QuestionMultiple choice

Solve the system y=2x+1y=2x+1 and y=−x+7y=-x+7.

Please select an answer first.

Correct answer: D

The correct answer is (2,5)(2,5).

  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: Set the expressions equal: 2x + 1 = -x + 7, so x = 2 and y = 5.
  3. Check the result: The correct answer is (2,5)(2,5).

Set the expressions equal: 2x + 1 = -x + 7, so x = 2 and y = 5.

9. QuestionMultiple choice

Which inequality represents all values at least 4?

Please select an answer first.

Correct answer: A

The correct answer is x≥4x\geq 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: At least includes 4 and all greater values, so the correct symbol is greater than or equal to.
  3. Check the result: The correct answer is x≥4x\geq 4.

At least includes 4 and all greater values, so the correct symbol is greater than or equal to.

10. QuestionMultiple choice

What does the range of a function describe?

Please select an answer first.

Correct answer: B

The correct answer is The set of possible output values.

  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 range contains the y-values or outputs produced by the function.
  3. Check the result: The correct answer is The set of possible output values.

The range contains the y-values or outputs produced by the function.

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