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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

1. 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

Solve 2x+7=192x+7=19.

Please select an answer first.

Correct answer: A

The correct answer is 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: Subtract 7 and divide by 2: x=12/2=6.
  3. Check restrictions and solutions: The correct answer is 6.

Subtract 7 and divide by 2: x=12/2=6.

2. QuestionMultiple choice

Solve 3(x−2)=2x+53(x-2)=2x+5.

Please select an answer first.

Correct answer: B

The correct answer is 11.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Expand to 3x-6=2x+5, then x=11.
  3. Check restrictions and solutions: The correct answer is 11.

Expand to 3x-6=2x+5, then x=11.

3. QuestionMultiple choice

Solve x2−9=0x^2-9=0.

Please select an answer first.

Correct answer: C

The correct answer is x=3 or 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 as (x-3)(x+3)=0.
  3. Check restrictions and solutions: The correct answer is x=3 or x=-3.

Factor as (x-3)(x+3)=0.

4. QuestionMultiple choice

Solve ∣x−4∣=2|x-4|=2.

Please select an answer first.

Correct answer: D

The correct answer is x=2 or 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: Set x-4=2 or x-4=-2.
  3. Check restrictions and solutions: The correct answer is x=2 or x=6.

Set x-4=2 or x-4=-2.

5. QuestionMultiple choice

Solve 5−2x>115-2x>11.

Please select an answer first.

Correct answer: A

The correct answer is x<−3x<-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: Subtract 5, divide by -2, and reverse the inequality.
  3. Check restrictions and solutions: The correct answer is x<−3x<-3.

Subtract 5, divide by -2, and reverse the inequality.

6. QuestionMultiple choice

What is the solution to x2<4x^2<4?

Please select an answer first.

Correct answer: B

The correct answer is −2<x<2-2<x<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: The numbers whose distance from zero is less than 2 lie between -2 and 2.
  3. Check restrictions and solutions: The correct answer is −2<x<2-2<x<2.

The numbers whose distance from zero is less than 2 lie between -2 and 2.

7. QuestionMultiple choice

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

Please select an answer first.

Correct answer: C

The correct answer is (4,3).

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Add the equations to get 2x=8, so x=4 and y=3.
  3. Check restrictions and solutions: The correct answer is (4,3).

Add the equations to get 2x=8, so x=4 and y=3.

8. QuestionMultiple choice

What is the determinant of (2314)\begin{pmatrix}2&3\\1&4\end{pmatrix}?

Please select an answer first.

Correct answer: D

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 determinant is 2(4)-3(1)=5.
  3. Check restrictions and solutions: The correct answer is 5.

The determinant is 2(4)-3(1)=5.

9. QuestionMultiple choice

What is the solution of x3=5\frac{x}{3}=5?

Please select an answer first.

Correct answer: A

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: Multiply both sides by 3.
  3. Check restrictions and solutions: The correct answer is 15.

Multiply both sides by 3.

10. QuestionMultiple choice

What is the extraneous solution risk when solving a radical equation?

Please select an answer first.

Correct answer: B

The correct answer is Squaring can introduce a value that does not satisfy the original equation.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Always check radical-equation solutions in the original equation.
  3. Check restrictions and solutions: The correct answer is Squaring can introduce a value that does not satisfy the original equation.

Always check radical-equation solutions in the original equation.

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