NumicornNumicornLearn, solve, progress

Precalculus Practice Tests

These Grade 12 Math practice tests cover the algebraic and trigonometric foundations used in advanced mathematics, including functions, polynomial and rational behavior, exponential and logarithmic models, trigonometry, sequences, complex numbers, limits, derivatives, and integrals.

Skills covered

  • Analyzing function domains, ranges, inverses, transformations, compositions, and rates of change
  • Using polynomial factors, rational asymptotes, complex numbers, and binomial coefficients
  • Applying exponential, logarithmic, and trigonometric identities, periods, amplitudes, and conversions
  • Working with arithmetic and geometric sequences, series, and polar complex-number form
  • Evaluating introductory limits, derivatives, integrals, and motion models

How to use these practice tests

Identify the function family or algebraic structure first. Then select the relevant identity, theorem, formula, or graph feature and verify domain restrictions, signs, and units.

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

Select a test

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

1. Test

Grade 12 Precalculus Practice Tests

Practice Grade 12 Math questions about functions, polynomial and rational behavior, exponential and logarithmic models, trigonometry, sequences, complex numbers, limits, derivatives, integrals, and advanced algebra.

Choose the best answer. Identify the mathematical structure, apply the appropriate formula or theorem, and check domains, units, signs, and limiting behavior.

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

If f(x)=x2−4x+1f(x)=x^2-4x+1, what is the x-coordinate of its vertex?

Please select an answer first.

Correct answer: A

The correct answer is 2.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: For ax^2+bx+c, the vertex x-coordinate is -b/(2a)=4/2=2.
  3. Check the result: The correct answer is 2.

For ax^2+bx+c, the vertex x-coordinate is -b/(2a)=4/2=2.

2. QuestionMultiple choice

What is the inverse of f(x)=3x−7f(x)=3x-7?

Please select an answer first.

Correct answer: B

The correct answer is f−1(x)=x+73f^{-1}(x)=\frac{x+7}{3}.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Set y=3x-7, swap x and y, and solve x=3y-7 for y=(x+7)/3.
  3. Check the result: The correct answer is f−1(x)=x+73f^{-1}(x)=\frac{x+7}{3}.

Set y=3x-7, swap x and y, and solve x=3y-7 for y=(x+7)/3.

3. QuestionMultiple choice

What is the range of f(x)=x+2−5f(x)=\sqrt{x+2}-5?

Please select an answer first.

Correct answer: C

The correct answer is y≥−5y\ge -5.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The square-root term is at least 0, so subtracting 5 gives a minimum output of -5.
  3. Check the result: The correct answer is y≥−5y\ge -5.

The square-root term is at least 0, so subtracting 5 gives a minimum output of -5.

4. QuestionMultiple choice

If f(x)=2x+1f(x)=2x+1 and g(x)=x2g(x)=x^2, what is (g∘f)(x)(g\circ f)(x)?

Please select an answer first.

Correct answer: D

The correct answer is (2x+1)2(2x+1)^2.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The composition g(f(x)) substitutes 2x+1 into g, giving (2x+1)^2.
  3. Check the result: The correct answer is (2x+1)2(2x+1)^2.

The composition g(f(x)) substitutes 2x+1 into g, giving (2x+1)^2.

5. QuestionMultiple choice

Which equation represents a horizontal shift of y=x2y=x^2 right 3 units?

Please select an answer first.

Correct answer: A

The correct answer is y=(x−3)2y=(x-3)^2.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Replacing x with x-3 shifts the graph right by 3 units.
  3. Check the result: The correct answer is y=(x−3)2y=(x-3)^2.

Replacing x with x-3 shifts the graph right by 3 units.

6. QuestionMultiple choice

What is the average rate of change of f(x)=x2+1f(x)=x^2+1 from x=2 to x=5?

Please select an answer first.

Correct answer: B

The correct answer is 7.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Compute (f(5)-f(2))/(5-2)=(26-5)/3=7.
  3. Check the result: The correct answer is 7.

Compute (f(5)-f(2))/(5-2)=(26-5)/3=7.

7. QuestionMultiple choice

Which function is even?

Please select an answer first.

Correct answer: C

The correct answer is f(x)=x4−3x2+2f(x)=x^4-3x^2+2.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Only even powers occur, so f(-x)=f(x) and the function is even.
  3. Check the result: The correct answer is f(x)=x4−3x2+2f(x)=x^4-3x^2+2.

Only even powers occur, so f(-x)=f(x) and the function is even.

8. QuestionMultiple choice

What is the domain of f(x)=x−1x−4f(x)=\frac{\sqrt{x-1}}{x-4}?

Please select an answer first.

Correct answer: D

The correct answer is [1,4)∪(4,∞)[1,4)\cup(4,\infty).

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The radicand requires x≥1, and the denominator excludes x=4.
  3. Check the result: The correct answer is [1,4)∪(4,∞)[1,4)\cup(4,\infty).

The radicand requires x≥1, and the denominator excludes x=4.

9. QuestionMultiple choice

If f(x)=x−1x+2f(x)=\frac{x-1}{x+2}, what is the horizontal asymptote?

Please select an answer first.

Correct answer: A

The correct answer is y=1y=1.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: The numerator and denominator have equal degree, so the asymptote is the ratio of leading coefficients, y=1.
  3. Check the result: The correct answer is y=1y=1.

The numerator and denominator have equal degree, so the asymptote is the ratio of leading coefficients, y=1.

10. QuestionMultiple choice

What does the horizontal line test determine?

Please select an answer first.

Correct answer: B

The correct answer is Whether a function is one-to-one.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: A horizontal line intersecting a graph at most once indicates the function is one-to-one.
  3. Check the result: The correct answer is Whether a function is one-to-one.

A horizontal line intersecting a graph at most once indicates the function is one-to-one.

Previous testNext test