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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
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2. 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

Simplify x3⋅x5x^3\cdot x^5.

Please select an answer first.

Correct answer: A

The correct answer is x8x^8.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Add exponents when multiplying like bases.
  3. Check restrictions and solutions: The correct answer is x8x^8.

Add exponents when multiplying like bases.

2. QuestionMultiple choice

Simplify x7x2\frac{x^7}{x^2}, x≠0.

Please select an answer first.

Correct answer: B

The correct answer is x5x^5.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Subtract exponents when dividing like bases.
  3. Check restrictions and solutions: The correct answer is x5x^5.

Subtract exponents when dividing like bases.

3. QuestionMultiple choice

Simplify (2x3)2(2x^3)^2.

Please select an answer first.

Correct answer: C

The correct answer is 4x64x^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: Square both the coefficient and the power: 2^2x^6.
  3. Check restrictions and solutions: The correct answer is 4x64x^6.

Square both the coefficient and the power: 2^2x^6.

4. QuestionMultiple choice

Rewrite x−3x^{-3} with a positive exponent.

Please select an answer first.

Correct answer: D

The correct answer is 1x3\frac{1}{x^3}.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: A negative exponent indicates a reciprocal.
  3. Check restrictions and solutions: The correct answer is 1x3\frac{1}{x^3}.

A negative exponent indicates a reciprocal.

5. QuestionMultiple choice

Simplify 50\sqrt{50}.

Please select an answer first.

Correct answer: A

The correct answer is 525\sqrt{2}.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: 50=25·2, so √50=5√2.
  3. Check restrictions and solutions: The correct answer is 525\sqrt{2}.

50=25·2, so √50=5√2.

6. QuestionMultiple choice

Rationalize 35\frac{3}{\sqrt{5}}.

Please select an answer first.

Correct answer: B

The correct answer is 355\frac{3\sqrt{5}}{5}.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Multiply numerator and denominator by √5.
  3. Check restrictions and solutions: The correct answer is 355\frac{3\sqrt{5}}{5}.

Multiply numerator and denominator by √5.

7. QuestionMultiple choice

Solve log⁡2x=5\log_2 x=5.

Please select an answer first.

Correct answer: C

The correct answer is 32.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Convert to exponential form: x=2^5=32.
  3. Check restrictions and solutions: The correct answer is 32.

Convert to exponential form: x=2^5=32.

8. QuestionMultiple choice

Solve ex=1e^x=1.

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: e^0=1.
  3. Check restrictions and solutions: The correct answer is 0.

e^0=1.

9. QuestionMultiple choice

Simplify log⁡b(xy)\log_b(xy).

Please select an answer first.

Correct answer: A

The correct answer is log⁡bx+log⁡by\log_b x+\log_b y.

  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 rule for logarithms turns multiplication into addition.
  3. Check restrictions and solutions: The correct answer is log⁡bx+log⁡by\log_b x+\log_b y.

The product rule for logarithms turns multiplication into addition.

10. QuestionMultiple choice

What is the domain of ln⁡(x−2)\ln(x-2)?

Please select an answer first.

Correct answer: B

The correct answer is x>2x>2.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: A logarithm requires a positive argument.
  3. Check restrictions and solutions: The correct answer is x>2x>2.

A logarithm requires a positive argument.

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