NumicornNumicornLearn, solve, progress

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.

Select a test

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

5. 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

What is the 10th term of the arithmetic sequence with a1=4 and d=3?

Please select an answer first.

Correct answer: A

The correct answer is 31.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: a10=4+(10-1)3=31.
  3. Check restrictions and solutions: The correct answer is 31.

a10=4+(10-1)3=31.

2. QuestionMultiple choice

What is the 5th term of the geometric sequence with a1=2 and r=3?

Please select an answer first.

Correct answer: B

The correct answer is 162.

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: a5=2·3^4=162.
  3. Check restrictions and solutions: The correct answer is 162.

a5=2·3^4=162.

3. QuestionMultiple choice

What is the common difference of 11, 7, 3, -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: Subtract consecutive terms: 7-11=-4.
  3. Check restrictions and solutions: The correct answer is -4.

Subtract consecutive terms: 7-11=-4.

4. QuestionMultiple choice

What is the common ratio of 5, 10, 20, 40, ...?

Please select an answer first.

Correct answer: D

The correct answer is 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: Each term is multiplied by 2.
  3. Check restrictions and solutions: The correct answer is 2.

Each term is multiplied by 2.

5. QuestionMultiple choice

Solve the system 2x+y=8 and x-y=1.

Please select an answer first.

Correct answer: A

The correct answer is (3,2).

  1. Identify the algebraic structure: Determine whether the problem involves an equation, inequality, expression, polynomial, system, sequence, or function.
  2. Apply the algebraic method: Add the equations to get 3x=9, so x=3 and y=2.
  3. Check restrictions and solutions: The correct answer is (3,2).

Add the equations to get 3x=9, so x=3 and y=2.

6. QuestionMultiple choice

What is the determinant of (1234)\begin{pmatrix}1&2\\3&4\end{pmatrix}?

Please select an answer first.

Correct answer: B

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

Compute 1(4)-2(3)=-2.

7. QuestionMultiple choice

What is the solution of 2x=162^x=16?

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: Write 16=2^4, so x=4.
  3. Check restrictions and solutions: The correct answer is 4.

Write 16=2^4, so x=4.

8. QuestionMultiple choice

What is the solution of log⁡3(x)=2\log_3(x)=2?

Please select an answer first.

Correct answer: D

The correct answer is 9.

  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=3^2=9.
  3. Check restrictions and solutions: The correct answer is 9.

Convert to exponential form x=3^2=9.

9. QuestionMultiple choice

What is the vertex of y=(x−1)2−4y=(x-1)^2-4?

Please select an answer first.

Correct answer: A

The correct answer is (1,−4)(1,-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: Vertex form gives h=1 and k=-4.
  3. Check restrictions and solutions: The correct answer is (1,−4)(1,-4).

Vertex form gives h=1 and k=-4.

10. QuestionMultiple choice

What is the axis of symmetry of y=x2+6x+2y=x^2+6x+2?

Please select an answer first.

Correct answer: B

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: Use x=-b/(2a)=-6/2=-3.
  3. Check restrictions and solutions: The correct answer is x=−3x=-3.

Use x=-b/(2a)=-6/2=-3.

Previous testNext test