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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.

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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

Solve 3x+1=813^{x+1}=81.

Please select an answer first.

Correct answer: A

The correct answer is x=3x=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: Since 81=3^4, x+1=4 and x=3.
  3. Check the result: The correct answer is x=3x=3.

Since 81=3^4, x+1=4 and x=3.

2. QuestionMultiple choice

What is the domain of f(x)=ln⁡(2x−6)f(x)=\ln(2x-6)?

Please select an answer first.

Correct answer: B

The correct answer is x>3x>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: A logarithm requires 2x-6>0, so x>3.
  3. Check the result: The correct answer is x>3x>3.

A logarithm requires 2x-6>0, so x>3.

3. QuestionMultiple choice

Simplify log⁡b(x4)\log_b(x^4) for x>0.

Please select an answer first.

Correct answer: C

The correct answer is 4log⁡bx4\log_b x.

  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 power rule for logarithms moves the exponent to the front.
  3. Check the result: The correct answer is 4log⁡bx4\log_b x.

The power rule for logarithms moves the exponent to the front.

4. QuestionMultiple choice

What is the period of y=4cos⁡(2x−π)y=4\cos(2x-\pi)?

Please select an answer first.

Correct answer: D

The correct answer is π\pi.

  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 sine or cosine, the period is 2π/|B|, so 2π/2=π.
  3. Check the result: The correct answer is π\pi.

For sine or cosine, the period is 2π/|B|, so 2π/2=π.

5. QuestionMultiple choice

What is sin⁡(π6)\sin(\frac{\pi}{6})?

Please select an answer first.

Correct answer: A

The correct answer is 12\frac{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 unit-circle value at π/6 gives sine equal to 1/2.
  3. Check the result: The correct answer is 12\frac{1}{2}.

The unit-circle value at π/6 gives sine equal to 1/2.

6. QuestionMultiple choice

Which identity is always true?

Please select an answer first.

Correct answer: B

The correct answer is sin⁡2x+cos⁡2x=1\sin^2 x+\cos^2 x=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 Pythagorean identity follows from the unit circle.
  3. Check the result: The correct answer is sin⁡2x+cos⁡2x=1\sin^2 x+\cos^2 x=1.

The Pythagorean identity follows from the unit circle.

7. QuestionMultiple choice

Convert 5π3\frac{5\pi}{3} radians to degrees.

Please select an answer first.

Correct answer: C

The correct answer is 300 degrees.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Multiply by 180/π: (5π/3)(180/π)=300 degrees.
  3. Check the result: The correct answer is 300 degrees.

Multiply by 180/π: (5π/3)(180/π)=300 degrees.

8. QuestionMultiple choice

What is the amplitude of y=−6sin⁡x+2y=-6\sin x+2?

Please select an answer first.

Correct answer: D

The correct answer is 6.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Amplitude is the absolute value of the sine coefficient, |−6|=6.
  3. Check the result: The correct answer is 6.

Amplitude is the absolute value of the sine coefficient, |−6|=6.

9. QuestionMultiple choice

If tan⁡θ=34\tan\theta=\frac{3}{4} and theta is acute, what is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: A

The correct answer is 35\frac{3}{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: A 3-4-5 right triangle gives opposite 3 and hypotenuse 5.
  3. Check the result: The correct answer is 35\frac{3}{5}.

A 3-4-5 right triangle gives opposite 3 and hypotenuse 5.

10. QuestionMultiple choice

What is the inverse of the exponential function y=2xy=2^x?

Please select an answer first.

Correct answer: B

The correct answer is y=log⁡2xy=\log_2 x.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Logarithms and exponentials with the same base are inverse functions.
  3. Check the result: The correct answer is y=log⁡2xy=\log_2 x.

Logarithms and exponentials with the same base are inverse functions.

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