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Calculus Practice Tests

These Grade 12 Math practice tests connect limits with derivatives, rates of change, optimization, motion, antiderivatives, definite integrals, accumulation, area, and the Fundamental Theorem of Calculus.

Skills covered

  • Using power, product, chain, trigonometric, exponential, and logarithmic derivative rules
  • Interpreting derivatives as slopes, velocity, acceleration, marginal change, and monotonicity
  • Finding antiderivatives and evaluating definite integrals with the constant of integration
  • Applying the Fundamental Theorem of Calculus to accumulation functions and net signed area
  • Solving optimization, motion, concavity, average-value, and tangent-line problems

How to use these practice tests

Decide whether the question asks for local change or accumulated change. Then apply a derivative or integral rule and interpret the result with its sign, units, interval, and context.

For more Grade 12 Math practice, return to the Grade 12 Math category.

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Grade 12 Calculus Practice Tests

Practice Grade 12 Math questions about derivatives, derivative rules, rates of change, extrema, antiderivatives, definite integrals, the Fundamental Theorem of Calculus, area, motion, and applications.

Choose the best answer. Identify the derivative or integral structure, apply the matching rule, and interpret the result as a slope, rate, accumulation, area, or motion quantity.

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

What is an antiderivative of 6x26x^2?

Please select an answer first.

Correct answer: A

The correct answer is 2x3+C2x^3+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: Differentiate 2x^3+C to get 6x^2.
  3. Check the interpretation: The correct answer is 2x3+C2x^3+C.

Differentiate 2x^3+C to get 6x^2.

2. QuestionMultiple choice

What is ∫4x3 dx\int 4x^3\,dx?

Please select an answer first.

Correct answer: B

The correct answer is x4+Cx^4+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: Increase the power and divide: 4·x^4/4=x^4.
  3. Check the interpretation: The correct answer is x4+Cx^4+C.

Increase the power and divide: 4·x^4/4=x^4.

3. QuestionMultiple choice

What is ∫cos⁡x dx\int \cos x\,dx?

Please select an answer first.

Correct answer: C

The correct answer is sin⁡x+C\sin x+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: The derivative of sine is cosine.
  3. Check the interpretation: The correct answer is sin⁡x+C\sin x+C.

The derivative of sine is cosine.

4. QuestionMultiple choice

What is ∫ex dx\int e^x\,dx?

Please select an answer first.

Correct answer: D

The correct answer is ex+Ce^x+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: e^x is its own antiderivative.
  3. Check the interpretation: The correct answer is ex+Ce^x+C.

e^x is its own antiderivative.

5. QuestionMultiple choice

Why is +C included in an indefinite integral?

Please select an answer first.

Correct answer: A

The correct answer is All antiderivatives differ by a constant.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: Differentiating any constant gives zero, so the constant cannot be determined from the derivative alone.
  3. Check the interpretation: The correct answer is All antiderivatives differ by a constant.

Differentiating any constant gives zero, so the constant cannot be determined from the derivative alone.

6. QuestionMultiple choice

What is ∫023x2 dx\int_0^2 3x^2\,dx?

Please select an answer first.

Correct answer: B

The correct answer is 8.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: An antiderivative is x^3, and x^3 from 0 to 2 equals 8.
  3. Check the interpretation: The correct answer is 8.

An antiderivative is x^3, and x^3 from 0 to 2 equals 8.

7. QuestionMultiple choice

What is ∫132x dx\int_1^3 2x\,dx?

Please select an answer first.

Correct answer: C

The correct answer is 8.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: An antiderivative is x^2, so 3^2-1^2=8.
  3. Check the interpretation: The correct answer is 8.

An antiderivative is x^2, so 3^2-1^2=8.

8. QuestionMultiple choice

What is ∫1x dx\int \frac{1}{x}\,dx for x>0?

Please select an answer first.

Correct answer: D

The correct answer is ln⁡x+C\ln x+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: The antiderivative of 1/x is ln x on the positive domain.
  3. Check the interpretation: The correct answer is ln⁡x+C\ln x+C.

The antiderivative of 1/x is ln x on the positive domain.

9. QuestionMultiple choice

What is ∫(2x+5) dx\int (2x+5)\,dx?

Please select an answer first.

Correct answer: A

The correct answer is x2+5x+Cx^2+5x+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: Integrate each term: x^2+5x+C.
  3. Check the interpretation: The correct answer is x2+5x+Cx^2+5x+C.

Integrate each term: x^2+5x+C.

10. QuestionMultiple choice

What is the general form of an antiderivative of a derivative f'(x)?

Please select an answer first.

Correct answer: B

The correct answer is f(x)+Cf(x)+C.

  1. Identify the calculus structure: Determine whether the problem asks for a derivative, rate, extremum, antiderivative, area, accumulation, or motion quantity.
  2. Apply the calculus rule: The original function f is an antiderivative of f'.
  3. Check the interpretation: The correct answer is f(x)+Cf(x)+C.

The original function f is an antiderivative of f'.

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