NumicornNumicornLearn, solve, progress

Precalculus Introduction Practice Tests

These Grade 11 Math practice tests connect core function ideas before advanced calculus study, including notation, domains, ranges, compositions, inverses, transformations, polynomial and rational behavior, exponential and logarithmic relationships, trigonometry, and modeling.

Skills covered

  • Evaluating functions, average rates of change, domains, ranges, and symmetry
  • Computing compositions and inverses and interpreting graph transformations
  • Analyzing polynomial zeros, end behavior, rational domains, holes, and asymptotes
  • Connecting exponential, logarithmic, and trigonometric functions
  • Using piecewise, absolute-value, quadratic, radical, and proportional models

How to use these practice tests

Identify the function family first, write domain restrictions, choose the form that exposes the needed feature, and verify compositions, inverses, transformations, and model outputs.

For more Grade 11 Math practice, return to the Grade 11 Math category.

Select a test

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

5. Test

Grade 11 Precalculus Introduction Practice Tests

Practice Grade 11 Math questions about functions, domains, ranges, composition, inverses, transformations, polynomial and rational functions, exponential and logarithmic models, and trigonometry.

Choose the best answer. Identify the function structure, apply the appropriate algebraic or trigonometric relationship, and check domains and model assumptions.

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

What is the domain of f(x)=9−x2f(x)=\sqrt{9-x^2}?

Please select an answer first.

Correct answer: A

The correct answer is [−3,3][-3,3].

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Require 9-x^2≥0, so x^2≤9 and -3≤x≤3.
  3. Check the result: The correct answer is [−3,3][-3,3].

Require 9-x^2≥0, so x^2≤9 and -3≤x≤3.

2. QuestionMultiple choice

What is the range of f(x)=9−x2f(x)=\sqrt{9-x^2}?

Please select an answer first.

Correct answer: B

The correct answer is [0,3][0,3].

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The square-root output is nonnegative, with maximum 3 when x=0.
  3. Check the result: The correct answer is [0,3][0,3].

The square-root output is nonnegative, with maximum 3 when x=0.

3. QuestionMultiple choice

If y=12xy=\frac{12}{x}, what is y when x=3?

Please select an answer first.

Correct answer: C

The correct answer is 4.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Substitute x=3: y=12/3=4.
  3. Check the result: The correct answer is 4.

Substitute x=3: y=12/3=4.

4. QuestionMultiple choice

What is the average rate of change of f(x)=3x+2f(x)=3x+2 over any interval?

Please select an answer first.

Correct answer: D

The correct answer is 3.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A linear function has constant rate of change equal to its slope, 3.
  3. Check the result: The correct answer is 3.

A linear function has constant rate of change equal to its slope, 3.

5. QuestionMultiple choice

Approximately what is 500(1.06)2500(1.06)^2?

Please select an answer first.

Correct answer: A

The correct answer is 561.8.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Compute 500(1.06)^2=500(1.1236)=561.8.
  3. Check the result: The correct answer is 561.8.

Compute 500(1.06)^2=500(1.1236)=561.8.

6. QuestionMultiple choice

Let f(x)=x+1f(x)=x+1 for x<0 and f(x)=x2f(x)=x^2 for x\ge0. What is f(2)?

Please select an answer first.

Correct answer: B

The correct answer is 4.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Since 2≥0, use the second branch: f(2)=2^2=4.
  3. Check the result: The correct answer is 4.

Since 2≥0, use the second branch: f(2)=2^2=4.

7. QuestionMultiple choice

Solve ∣x−3∣=5|x-3|=5.

Please select an answer first.

Correct answer: C

The correct answer is x=8x=8 or x=−2x=-2.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The absolute-value equation gives x-3=5 or x-3=-5, so x=8 or x=-2.
  3. Check the result: The correct answer is x=8x=8 or x=−2x=-2.

The absolute-value equation gives x-3=5 or x-3=-5, so x=8 or x=-2.

8. QuestionMultiple choice

What is the maximum value of f(x)=−x2+10x−9f(x)=-x^2+10x-9?

Please select an answer first.

Correct answer: D

The correct answer is 16.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The vertex occurs at x=5, and f(5)=-25+50-9=16.
  3. Check the result: The correct answer is 16.

The vertex occurs at x=5, and f(5)=-25+50-9=16.

9. QuestionMultiple choice

Solve ln⁡x=2\ln x=2.

Please select an answer first.

Correct answer: A

The correct answer is x=e2x=e^2.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Convert to exponential form: x=e^2.
  3. Check the result: The correct answer is x=e2x=e^2.

Convert to exponential form: x=e^2.

10. QuestionMultiple choice

Which model is appropriate for a quantity that increases by the same percentage each period?

Please select an answer first.

Correct answer: B

The correct answer is An exponential model.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Repeated percentage change multiplies by a constant factor, which is exponential behavior.
  3. Check the result: The correct answer is An exponential model.

Repeated percentage change multiplies by a constant factor, which is exponential behavior.

Previous testNext test