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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

Evaluate lim⁡x→2(x2+3x−1)\lim_{x\to2}(x^2+3x-1).

Please select an answer first.

Correct answer: A

The correct answer is 9.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Polynomials are continuous, so substitute x=2: 4+6-1=9.
  3. Check the result: The correct answer is 9.

Polynomials are continuous, so substitute x=2: 4+6-1=9.

2. QuestionMultiple choice

Evaluate lim⁡x→3x2−9x−3\lim_{x\to3}\frac{x^2-9}{x-3}.

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: Factor x^2-9=(x-3)(x+3), then the limit is 3+3=6.
  3. Check the result: The correct answer is 6.

Factor x^2-9=(x-3)(x+3), then the limit is 3+3=6.

3. QuestionMultiple choice

What is the derivative of f(x)=x5f(x)=x^5?

Please select an answer first.

Correct answer: C

The correct answer is 5x45x^4.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Apply the power rule d(x^n)/dx=nx^(n-1).
  3. Check the result: The correct answer is 5x45x^4.

Apply the power rule d(x^n)/dx=nx^(n-1).

4. QuestionMultiple choice

What is the derivative of f(x)=7x−4f(x)=7x-4?

Please select an answer first.

Correct answer: D

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: The derivative of a linear function is its slope.
  3. Check the result: The correct answer is 7.

The derivative of a linear function is its slope.

5. QuestionMultiple choice

What is the derivative of f(x)=sin⁡xf(x)=\sin x?

Please select an answer first.

Correct answer: A

The correct answer is cos⁡x\cos 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 basic derivative rule is d(sin x)/dx=cos x.
  3. Check the result: The correct answer is cos⁡x\cos x.

The basic derivative rule is d(sin x)/dx=cos x.

6. QuestionMultiple choice

At a differentiable local maximum, what is usually true?

Please select an answer first.

Correct answer: B

The correct answer is f′(x)=0f'(x)=0.

  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 differentiable interior local extremum has a horizontal tangent, so its first derivative is zero.
  3. Check the result: The correct answer is f′(x)=0f'(x)=0.

A differentiable interior local extremum has a horizontal tangent, so its first derivative is zero.

7. QuestionMultiple choice

What does the definite integral ∫abf(x) dx\int_a^b f(x)\,dx represent geometrically?

Please select an answer first.

Correct answer: C

The correct answer is Net signed area between the graph and the x-axis from a to b.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Areas below the x-axis count negatively, so the integral gives net signed area.
  3. Check the result: The correct answer is Net signed area between the graph and the x-axis from a to b.

Areas below the x-axis count negatively, so the integral gives net signed area.

8. QuestionMultiple choice

What is the value of ∫023 dx\int_0^2 3\,dx?

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: The integral of a constant is rectangle area: 3(2-0)=6.
  3. Check the result: The correct answer is 6.

The integral of a constant is rectangle area: 3(2-0)=6.

9. QuestionMultiple choice

If s(t)=t2+4ts(t)=t^2+4t, what is the velocity at t=3?

Please select an answer first.

Correct answer: A

The correct answer is 10.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Velocity is s'(t)=2t+4, so s'(3)=10.
  3. Check the result: The correct answer is 10.

Velocity is s'(t)=2t+4, so s'(3)=10.

10. QuestionMultiple choice

What is the main purpose of a limit in calculus?

Please select an answer first.

Correct answer: B

The correct answer is To describe the value a function approaches near an input.

  1. Identify the precalculus structure: Determine whether the problem concerns functions, algebraic behavior, trigonometry, sequences, complex numbers, or a limit.
  2. Apply the relationship: Limits describe nearby behavior and provide the foundation for continuity and derivatives.
  3. Check the result: The correct answer is To describe the value a function approaches near an input.

Limits describe nearby behavior and provide the foundation for continuity and derivatives.

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