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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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5 Tests
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1. Test

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 ddx(x4)\frac{d}{dx}(x^4)?

Please select an answer first.

Correct answer: A

The correct answer is 4x34x^3.

  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: Apply the power rule d(x^n)/dx=nx^(n-1).
  3. Check the interpretation: The correct answer is 4x34x^3.

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

2. QuestionMultiple choice

What is ddx(5x2−3x+1)\frac{d}{dx}(5x^2-3x+1)?

Please select an answer first.

Correct answer: B

The correct answer is 10x−310x-3.

  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 each term: 10x-3+0.
  3. Check the interpretation: The correct answer is 10x−310x-3.

Differentiate each term: 10x-3+0.

3. QuestionMultiple choice

What is ddx(sin⁡x)\frac{d}{dx}(\sin x)?

Please select an answer first.

Correct answer: C

The correct answer is cos⁡x\cos x.

  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 cos⁡x\cos x.

The derivative of sine is cosine.

4. QuestionMultiple choice

What is ddx(ex)\frac{d}{dx}(e^x)?

Please select an answer first.

Correct answer: D

The correct answer is exe^x.

  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 exponential function e^x is its own derivative.
  3. Check the interpretation: The correct answer is exe^x.

The exponential function e^x is its own derivative.

5. QuestionMultiple choice

What is ddx(ln⁡x)\frac{d}{dx}(\ln x)?

Please select an answer first.

Correct answer: A

The correct answer is 1x\frac{1}{x}.

  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: For x>0, the derivative of ln x is 1/x.
  3. Check the interpretation: The correct answer is 1x\frac{1}{x}.

For x>0, the derivative of ln x is 1/x.

6. QuestionMultiple choice

What is ddx(7)\frac{d}{dx}(7)?

Please select an answer first.

Correct answer: B

The correct answer is 0.

  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: A constant has zero rate of change.
  3. Check the interpretation: The correct answer is 0.

A constant has zero rate of change.

7. QuestionMultiple choice

What is the derivative of f(x)=xf(x)=\sqrt{x}?

Please select an answer first.

Correct answer: C

The correct answer is 12x\frac{1}{2\sqrt{x}}.

  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: Rewrite √x as x^(1/2) and apply the power rule.
  3. Check the interpretation: The correct answer is 12x\frac{1}{2\sqrt{x}}.

Rewrite √x as x^(1/2) and apply the power rule.

8. QuestionMultiple choice

What is f′(2)f'(2) for f(x)=x3−4xf(x)=x^3-4x?

Please select an answer first.

Correct answer: D

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: f'(x)=3x^2-4, so f'(2)=12-4=8.
  3. Check the interpretation: The correct answer is 8.

f'(x)=3x^2-4, so f'(2)=12-4=8.

9. QuestionMultiple choice

What is the derivative of f(x)=(x2+1)3f(x)=(x^2+1)^3?

Please select an answer first.

Correct answer: A

The correct answer is 6x(x2+1)26x(x^2+1)^2.

  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: Use the chain rule: 3(x^2+1)^2·2x.
  3. Check the interpretation: The correct answer is 6x(x2+1)26x(x^2+1)^2.

Use the chain rule: 3(x^2+1)^2·2x.

10. QuestionMultiple choice

What is the derivative of f(x)=cos⁡(2x)f(x)=\cos(2x)?

Please select an answer first.

Correct answer: B

The correct answer is −2sin⁡(2x)-2\sin(2x).

  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 chain rule multiplies the derivative of cosine by the inner derivative 2.
  3. Check the interpretation: The correct answer is −2sin⁡(2x)-2\sin(2x).

The chain rule multiplies the derivative of cosine by the inner derivative 2.

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