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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.

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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

Which base produces exponential growth in y=abxy=ab^x when a>0?

Please select an answer first.

Correct answer: A

The correct answer is A base b greater than 1.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: For b>1, repeated multiplication increases the value as x increases.
  3. Check the result: The correct answer is A base b greater than 1.

For b>1, repeated multiplication increases the value as x increases.

2. QuestionMultiple choice

What is the inverse function of y=exy=e^x?

Please select an answer first.

Correct answer: B

The correct answer is y=ln⁡xy=\ln x.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The natural logarithm is the inverse of the exponential function with base e.
  3. Check the result: The correct answer is y=ln⁡xy=\ln x.

The natural logarithm is the inverse of the exponential function with base e.

3. QuestionMultiple choice

Solve 2x=322^x=32.

Please select an answer first.

Correct answer: C

The correct answer is x=5x=5.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Since 32=2^5, equal bases give x=5.
  3. Check the result: The correct answer is x=5x=5.

Since 32=2^5, equal bases give x=5.

4. QuestionMultiple choice

What is the domain of f(x)=log⁡(x)f(x)=\log(x)?

Please select an answer first.

Correct answer: D

The correct answer is x>0x>0.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A logarithm requires a positive argument.
  3. Check the result: The correct answer is x>0x>0.

A logarithm requires a positive argument.

5. QuestionMultiple choice

What is cos⁡0\cos 0?

Please select an answer first.

Correct answer: A

The correct answer is 1.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The unit-circle point at angle 0 is (1,0), so cosine is 1.
  3. Check the result: The correct answer is 1.

The unit-circle point at angle 0 is (1,0), so cosine is 1.

6. QuestionMultiple choice

What is the period of y=sin⁡(3x)y=\sin(3x)?

Please select an answer first.

Correct answer: B

The correct answer is 2π3\frac{2\pi}{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 period is 2pi/|3|=2pi/3.
  3. Check the result: The correct answer is 2π3\frac{2\pi}{3}.

The period is 2pi/|3|=2pi/3.

7. QuestionMultiple choice

Convert 90∘90^\circ to radians.

Please select an answer first.

Correct answer: C

The correct answer is π2\frac{\pi}{2}.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: A quarter turn is 90 degrees or pi/2 radians.
  3. Check the result: The correct answer is π2\frac{\pi}{2}.

A quarter turn is 90 degrees or pi/2 radians.

8. QuestionMultiple choice

What is the vertical asymptote of y=log⁡(x−1)y=\log(x-1)?

Please select an answer first.

Correct answer: D

The correct answer is x=1x=1.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: The logarithm argument is zero at x=1, producing the vertical asymptote.
  3. Check the result: The correct answer is x=1x=1.

The logarithm argument is zero at x=1, producing the vertical asymptote.

9. QuestionMultiple choice

What is ln⁡(e2)\ln(e^2)?

Please select an answer first.

Correct answer: A

The correct answer is 2.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Natural logarithm and e^x are inverse functions.
  3. Check the result: The correct answer is 2.

Natural logarithm and e^x are inverse functions.

10. QuestionMultiple choice

What does a base between 0 and 1 represent in an exponential model?

Please select an answer first.

Correct answer: B

The correct answer is Exponential decay.

  1. Identify the precalculus structure: Determine the function type, domain, transformation, composition, inverse, asymptote, model, or trigonometric relationship involved.
  2. Apply the relationship: Repeated multiplication by a positive factor less than 1 causes decay.
  3. Check the result: The correct answer is Exponential decay.

Repeated multiplication by a positive factor less than 1 causes decay.

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