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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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4. 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 x2−9x−3\frac{x^2-9}{x-3}, x≠3.

Please select an answer first.

Correct answer: A

The correct answer is 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: Factor x^2-9=(x-3)(x+3) and cancel.
  3. Check restrictions and solutions: The correct answer is x+3.

Factor x^2-9=(x-3)(x+3) and cancel.

2. QuestionMultiple choice

What is the vertical asymptote of 1x+4\frac{1}{x+4}?

Please select an answer first.

Correct answer: B

The correct answer is x=−4x=-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 denominator is zero at x=-4.
  3. Check restrictions and solutions: The correct answer is x=−4x=-4.

The denominator is zero at x=-4.

3. QuestionMultiple choice

Solve 2x=13\frac{2}{x}=\frac{1}{3}.

Please select an answer first.

Correct answer: C

The correct answer is 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: Cross multiply: 6=x.
  3. Check restrictions and solutions: The correct answer is x=6.

Cross multiply: 6=x.

4. QuestionMultiple choice

What input is excluded from x+1x2−25\frac{x+1}{x^2-25}?

Please select an answer first.

Correct answer: D

The correct answer is x=5 and x=-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: The denominator factors as (x-5)(x+5).
  3. Check restrictions and solutions: The correct answer is x=5 and x=-5.

The denominator factors as (x-5)(x+5).

5. QuestionMultiple choice

What is the domain of f(x)=2x−6f(x)=\sqrt{2x-6}?

Please select an answer first.

Correct answer: A

The correct answer is x≥3x\ge3.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Require 2x-6≥0, which gives x≥3.
  3. Check restrictions and solutions: The correct answer is x≥3x\ge3.

Require 2x-6≥0, which gives x≥3.

6. QuestionMultiple choice

What is the solution of x+1=4\sqrt{x+1}=4?

Please select an answer first.

Correct answer: B

The correct answer is 15.

  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 sides: x+1=16, so x=15.
  3. Check restrictions and solutions: The correct answer is 15.

Square both sides: x+1=16, so x=15.

7. QuestionMultiple choice

What is the horizontal asymptote of 3x2+1x2−2\frac{3x^2+1}{x^2-2}?

Please select an answer first.

Correct answer: C

The correct answer is y=3y=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: Equal degrees give the ratio of leading coefficients.
  3. Check restrictions and solutions: The correct answer is y=3y=3.

Equal degrees give the ratio of leading coefficients.

8. QuestionMultiple choice

Which equation represents inverse variation?

Please select an answer first.

Correct answer: D

The correct answer is y=8xy=\frac{8}{x}.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Inverse variation has the form y=k/x.
  3. Check restrictions and solutions: The correct answer is y=8xy=\frac{8}{x}.

Inverse variation has the form y=k/x.

9. QuestionMultiple choice

What is the product of the roots of x2−6x+8=0x^2-6x+8=0?

Please select an answer first.

Correct answer: A

The correct answer is 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: By Vieta's formulas, the product is c/a=8.
  3. Check restrictions and solutions: The correct answer is 8.

By Vieta's formulas, the product is c/a=8.

10. QuestionMultiple choice

What is the sum of the roots of 2x2−10x+3=02x^2-10x+3=0?

Please select an answer first.

Correct answer: B

The correct answer is 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: The sum is -b/a=10/2=5.
  3. Check restrictions and solutions: The correct answer is 5.

The sum is -b/a=10/2=5.

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