NumicornNumicornLearn, solve, progress

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.

Select a test

5 Tests
1. Test2. Test3. Test4. Test5. Test

2. 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 degree of 4x5−2x2+74x^5-2x^2+7?

Please select an answer first.

Correct answer: A

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 degree is the greatest exponent of x with a nonzero coefficient, which is 5.
  3. Check the result: The correct answer is 5.

The degree is the greatest exponent of x with a nonzero coefficient, which is 5.

2. QuestionMultiple choice

What is the leading coefficient of −3x4+x−8-3x^4+x-8?

Please select an answer first.

Correct answer: B

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 leading term is -3x^4, so its coefficient is -3.
  3. Check the result: The correct answer is -3.

The leading term is -3x^4, so its coefficient is -3.

3. QuestionMultiple choice

What is (x+3)(x+2)(x+3)(x+2)?

Please select an answer first.

Correct answer: C

The correct answer is x2+5x+6x^2+5x+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: Use the distributive property: x^2 + 2x + 3x + 6 = x^2 + 5x + 6.
  3. Check the result: The correct answer is x2+5x+6x^2+5x+6.

Use the distributive property: x^2 + 2x + 3x + 6 = x^2 + 5x + 6.

4. QuestionMultiple choice

Which is the factored form of x2−25x^2-25?

Please select an answer first.

Correct answer: D

The correct answer is (x−5)(x+5)(x-5)(x+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: This is a difference of squares: a^2 - b^2 = (a-b)(a+b).
  3. Check the result: The correct answer is (x−5)(x+5)(x-5)(x+5).

This is a difference of squares: a^2 - b^2 = (a-b)(a+b).

5. QuestionMultiple choice

What is the greatest common factor of 6x3+9x26x^3+9x^2?

Please select an answer first.

Correct answer: A

The correct answer is 3x23x^2.

  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: Both terms share 3x^2, leaving 3x + 2 after factoring.
  3. Check the result: The correct answer is 3x23x^2.

Both terms share 3x^2, leaving 3x + 2 after factoring.

6. QuestionMultiple choice

Which is the factored form of x2+7x+12x^2+7x+12?

Please select an answer first.

Correct answer: B

The correct answer is (x+3)(x+4)(x+3)(x+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: The numbers 3 and 4 multiply to 12 and add to 7.
  3. Check the result: The correct answer is (x+3)(x+4)(x+3)(x+4).

The numbers 3 and 4 multiply to 12 and add to 7.

7. QuestionMultiple choice

What is the remainder when p(x)=x2+3x+2p(x)=x^2+3x+2 is divided by x−1x-1?

Please select an answer first.

Correct answer: C

The correct answer is 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: By the Remainder Theorem, evaluate p(1): 1 + 3 + 2 = 6.
  3. Check the result: The correct answer is 6.

By the Remainder Theorem, evaluate p(1): 1 + 3 + 2 = 6.

8. QuestionMultiple choice

If x=2x=2 is a zero of a polynomial, which factor must it have?

Please select an answer first.

Correct answer: D

The correct answer is x−2x-2.

  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 r corresponds to the factor x - r, so x = 2 gives x - 2.
  3. Check the result: The correct answer is x−2x-2.

A zero r corresponds to the factor x - r, so x = 2 gives x - 2.

9. QuestionMultiple choice

What is the end behavior of an even-degree polynomial with a positive leading coefficient?

Please select an answer first.

Correct answer: A

The correct answer is Both ends rise..

  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: An even degree gives matching end directions, and a positive leading coefficient makes both ends rise.
  3. Check the result: The correct answer is Both ends rise..

An even degree gives matching end directions, and a positive leading coefficient makes both ends rise.

10. QuestionMultiple choice

Why can a polynomial of degree 4 have at most 4 real zeros?

Please select an answer first.

Correct answer: B

The correct answer is A nonzero polynomial has no more real zeros than its degree..

  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 Fundamental Theorem of Algebra limits the total number of complex zeros, counted with multiplicity, to the degree.
  3. Check the result: The correct answer is A nonzero polynomial has no more real zeros than its degree..

The Fundamental Theorem of Algebra limits the total number of complex zeros, counted with multiplicity, to the degree.

Previous testNext test