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Advanced Algebra Review Practice Tests

These Grade 12 Math practice tests review the algebraic tools needed for advanced mathematics, including equations, inequalities, systems, exponents, radicals, logarithms, polynomials, rational expressions, complex numbers, sequences, and quadratic functions.

Skills covered

  • Solving linear, quadratic, absolute-value, radical, logarithmic, exponential, and rational equations
  • Solving inequalities and systems and interpreting determinants and solution restrictions
  • Applying exponent and logarithm laws, simplifying radicals, and rationalizing denominators
  • Factoring polynomials, using the Remainder and Factor Theorems, and analyzing roots
  • Working with complex numbers, arithmetic and geometric sequences, and quadratic graphs

How to use these practice tests

Choose the algebraic form that exposes the needed structure, track restrictions when multiplying or squaring, and substitute solutions back into the original equation or expression.

For more Grade 12 Math practice, return to the Grade 12 Math category.

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

3. Test

Grade 12 Advanced Algebra Review Practice Tests

Practice Grade 12 Math questions about equations, inequalities, systems, exponents, radicals, logarithms, polynomials, factoring, rational expressions, complex numbers, sequences, and quadratic functions.

Choose the best answer. Apply the appropriate algebraic rule, preserve domain restrictions, check extraneous solutions, and verify the result in the original expression.

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

Factor x2+7x+12x^2+7x+12.

Please select an answer first.

Correct answer: A

The correct answer is (x+3)(x+4)(x+3)(x+4).

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: The factors 3 and 4 multiply to 12 and add to 7.
  3. Check restrictions and solutions: The correct answer is (x+3)(x+4)(x+3)(x+4).

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

2. QuestionMultiple choice

Factor x2−16x^2-16.

Please select an answer first.

Correct answer: B

The correct answer is (x−4)(x+4)(x-4)(x+4).

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Use the difference of squares.
  3. Check restrictions and solutions: The correct answer is (x−4)(x+4)(x-4)(x+4).

Use the difference of squares.

3. QuestionMultiple choice

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

Please select an answer first.

Correct answer: C

The correct answer is 4.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: By the Remainder Theorem, p(1)=1+2+1=4.
  3. Check restrictions and solutions: The correct answer is 4.

By the Remainder Theorem, p(1)=1+2+1=4.

4. QuestionMultiple choice

If x+5 is a factor of p(x), what is p(-5)?

Please select an answer first.

Correct answer: D

The correct answer is 0.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: The Factor Theorem gives p(-5)=0.
  3. Check restrictions and solutions: The correct answer is 0.

The Factor Theorem gives p(-5)=0.

5. QuestionMultiple choice

What is the leading coefficient of −4x5+2x2−1-4x^5+2x^2-1?

Please select an answer first.

Correct answer: A

The correct answer is -4.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: The leading term is -4x^5.
  3. Check restrictions and solutions: The correct answer is -4.

The leading term is -4x^5.

6. QuestionMultiple choice

What is the degree of 7x4−2x+97x^4-2x+9?

Please select an answer first.

Correct answer: B

The correct answer is 4.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: The highest exponent is 4.
  3. Check restrictions and solutions: The correct answer is 4.

The highest exponent is 4.

7. QuestionMultiple choice

Which polynomial has zeros 2 and -3?

Please select an answer first.

Correct answer: C

The correct answer is x2+x−6x^2+x-6.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: The product (x-2)(x+3) expands to x^2+x-6.
  3. Check restrictions and solutions: The correct answer is x2+x−6x^2+x-6.

The product (x-2)(x+3) expands to x^2+x-6.

8. QuestionMultiple choice

What is the complex conjugate of 6+2i6+2i?

Please select an answer first.

Correct answer: D

The correct answer is 6−2i6-2i.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Change the sign of the imaginary part.
  3. Check restrictions and solutions: The correct answer is 6−2i6-2i.

Change the sign of the imaginary part.

9. QuestionMultiple choice

What is i4i^4?

Please select an answer first.

Correct answer: A

The correct answer is 1.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Since i^2=-1, i^4=(i^2)^2=1.
  3. Check restrictions and solutions: The correct answer is 1.

Since i^2=-1, i^4=(i^2)^2=1.

10. QuestionMultiple choice

What is the modulus of 5−12i5-12i?

Please select an answer first.

Correct answer: B

The correct answer is 13.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: The modulus is √(5^2+(-12)^2)=13.
  3. Check restrictions and solutions: The correct answer is 13.

The modulus is √(5^2+(-12)^2)=13.

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