Free Printable Worksheets for learning Calculus at the High School level

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Quiz on Calculus

Multiple Choice

  1. What is the derivative of the function f(x) = x2? a. x2 b. 2x c. 4x d. x3

  2. What is the integral of the function f(x) = x2? a. x3 b. x2 c. 2x d. 3x

  3. What is the derivative of the function f(x) = sin(x)? a. cos(x) b. sin(x) c. tan(x) d. csc(x)

True/False

  1. The derivative of a function is the rate of change of the function.

  2. The integral of a function is the area under the curve of the function.

  3. The derivative of the function f(x) = x2 is x3.

Fill-in-the-Blank

  1. The derivative of the function f(x) = cos(x) is ___________.

  2. The integral of the function f(x) = x2 is ___________.

  3. The derivative of the function f(x) = ex is ___________.

Short Answer

  1. What is the fundamental theorem of calculus?

  2. What is the chain rule?

  3. What is the power rule?

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Practice Sheet for Calculus

Introduction

Calculus is a branch of mathematics that deals with the study of change. It is used to study the behavior of functions and their derivatives. Calculus can be used to solve problems in many areas of science, engineering, and economics.

Differential Calculus

Differential calculus is the study of how a function changes as its inputs change. It is used to find the rate of change of a function at any given point. The derivative of a function is a measure of the rate of change.

Examples

  1. Find the derivative of the function $f(x) = x2$.

Answer: The derivative of $f(x) = x2$ is $f'(x) = 2x$.

  1. Find the derivative of the function $f(x) = \frac{1}{x}$.

Answer: The derivative of $f(x) = \frac{1}{x}$ is $f'(x) = -\frac{1}{x2}$.

Practice Problems

  1. Find the derivative of the function $f(x) = x3$.

Answer: The derivative of $f(x) = x3$ is $f'(x) = 3x2$.

  1. Find the derivative of the function $f(x) = \sin(x)$.

Answer: The derivative of $f(x) = \sin(x)$ is $f'(x) = \cos(x)$.

  1. Find the derivative of the function $f(x) = \cos(x)$.

Answer: The derivative of $f(x) = \cos(x)$ is $f'(x) = -\sin(x)$.

  1. Find the derivative of the function $f(x) = \ln(x)$.

Answer: The derivative of $f(x) = \ln(x)$ is $f'(x) = \frac{1}{x}$.

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