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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

What is the common difference of the arithmetic sequence 7, 12, 17, ...?

Please select an answer first.

Correct answer: A

The correct answer is 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: Subtract consecutive terms: 12-7=5.
  3. Check the result: The correct answer is 5.

Subtract consecutive terms: 12-7=5.

2. QuestionMultiple choice

What is the nth term of the arithmetic sequence with first term 4 and common difference 3?

Please select an answer first.

Correct answer: B

The correct answer is an=3n+1a_n=3n+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: Use a_n=a_1+(n-1)d=4+3(n-1)=3n+1.
  3. Check the result: The correct answer is an=3n+1a_n=3n+1.

Use a_n=a_1+(n-1)d=4+3(n-1)=3n+1.

3. QuestionMultiple choice

What is the common ratio of the geometric sequence 2, 6, 18, ...?

Please select an answer first.

Correct answer: C

The correct answer is 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: Each term is multiplied by 3.
  3. Check the result: The correct answer is 3.

Each term is multiplied by 3.

4. QuestionMultiple choice

What is the sum of the first 4 terms of 3, 6, 12, 24, ...?

Please select an answer first.

Correct answer: D

The correct answer is 45.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Add 3+6+12+24=45.
  3. Check the result: The correct answer is 45.

Add 3+6+12+24=45.

5. QuestionMultiple choice

What is the modulus of z=3−4iz=3-4i?

Please select an answer first.

Correct answer: A

The correct answer is 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 modulus is |z|=√(3^2+(-4)^2)=5.
  3. Check the result: The correct answer is 5.

The modulus is |z|=√(3^2+(-4)^2)=5.

6. QuestionMultiple choice

What is i2i^2?

Please select an answer first.

Correct answer: B

The correct answer is -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 imaginary unit is defined by i^2=-1.
  3. Check the result: The correct answer is -1.

The imaginary unit is defined by i^2=-1.

7. QuestionMultiple choice

What is the product (2+i)(3−i)(2+i)(3-i)?

Please select an answer first.

Correct answer: C

The correct answer is 7+i7+i.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Expand: 6-2i+3i-i^2=7+i.
  3. Check the result: The correct answer is 7+i7+i.

Expand: 6-2i+3i-i^2=7+i.

8. QuestionMultiple choice

Which polar form represents a complex number with modulus 2 and argument π3\frac{\pi}{3}?

Please select an answer first.

Correct answer: D

The correct answer is 2(cos⁡π3+isin⁡π3)2(\cos\frac{\pi}{3}+i\sin\frac{\pi}{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: Polar form is r(cos θ+i sin θ), so substitute r=2 and θ=π/3.
  3. Check the result: The correct answer is 2(cos⁡π3+isin⁡π3)2(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}).

Polar form is r(cos θ+i sin θ), so substitute r=2 and θ=π/3.

9. QuestionMultiple choice

What does the binomial coefficient (nk)\binom{n}{k} count?

Please select an answer first.

Correct answer: A

The correct answer is Ways to choose k objects from n objects without regard to order.

  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 combination coefficient counts selections where order does not matter.
  3. Check the result: The correct answer is Ways to choose k objects from n objects without regard to order.

The combination coefficient counts selections where order does not matter.

10. QuestionMultiple choice

What is the coefficient of x^2 in (1+x)4(1+x)^4?

Please select an answer first.

Correct answer: B

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: The x^2 coefficient is (42)=6\binom{4}{2}=6.
  3. Check the result: The correct answer is 6.

The x^2 coefficient is (42)=6\binom{4}{2}=6.

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