Calculus

Need some Calculus help? What is Calculus? Calculus is concerned with change and motion; it deals with the quantities that approach certain values.

Sir Isaac Newton invented his version of calculus in order to explain the motion of planets around the sun. Today, calculus is used in calculating the orbits of satellites and spacecrafts, in predicting population sizes, in estimating how fast prices rise, in forecasting weather, in calculating life insurance premiums, and in many other areas.

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The topics covered are: Differential Calculus, Integral Calculus, Sequences and Series, Parametric Curves and Polar Coordinates, Multivariable Calculus, and Differential Equations.

AP Calculus AB and BC Free Response Past Papers and Solutions

AP Calculus AB and BC Multiple Choice Past Papers & Solutions

Solutions to Sample Questions

The following are solutions to sample questions of the CollegeBoard AP/AB and AP/BC Calculus examination.

AP Calculus AB & BC sample questions & solutions

AP Calculus Practice Multiple Choice 2020

AP Calculus AB 2020 Exam Sample Questions

AP Calculus BC Sample Free Response Solutions 2020
AP / AB Calculus Free Response Solutions
AP / AB Calculus Test - Sample Questions 1 to 8
AP / AB Calculus Test - Sample Questions 9 to 16
AP / AB Calculus Test - Sample Questions 17 to 24
AP / AB Calculus Test - Sample Questions 25 to 28
AP / BC Calculus Test - Sample Questions 1 to 8
AP / BC Calculus Test - Sample Questions 9 to 16

Differential Calculus

The study of differential calculus is concerned with how one quantity changes in relation to another quantity. The central concept of differential calculus is the derivative.

Highlights of Calculus

Highlights of Calculus (Part 1)
Big Picture of Calculus
Big Picture: Derivatives
Max and Min & Second Derivative
The Exponential Function
Big Picture: Integrals
Derivative of sin x & cos x
Product Rule & Quotient Rule
Chains f(g(x)) & the Chain Rule

Highlights of Calculus (Part 2)
Limits & Continuous Functions
Inverse Functions f^-1 (y) & x = ln y
Derivatives of ln y & sin^-1 (y)
Growth Rates & Log Graphs
Linear Approximation/Newton’s Method
Power Series/Euler’s Great Formula
Differential Equations of Motion
Differential Equations of Growth
Limits

Introduction to Calculus
The Limits of a Function Definition & Techniques to find Limits
Mean Value Theorem What is Mean Value Theorem?
L’Hopitals Rule Indeterminate Quotients, Product, Differences & Power
Newton’s Method Used to approximate a root.
Derivative Rules

Derivatives Definition & Slope of Tangent
Power Rule Constant Multiple Rule, Sum Rule, Difference Rule
Product Rule Find the derivative of the product of two functions
Quotient Rule Find the derivative of the quotient of two functions
Chain Rule Find the derivative of composite functions
More Chain Rule Examples

Derivative Rules Product Rule, Quotient Rule, Chain Rule, Power Rule, Exponential & Logarithmic Functions, Trigonometric Functions, Inverse Trigonometric Functions, Hyperbolic Functions & Inverse Hyperbolic Functions
Examples using the Derivative Rules
More Examples using the Derivative Rules
Trigonometric Derivatives

Trigonometric Derivatives Derivatives of sin, cos, tan, scs, sec, cot
More Derivatives Involving Trigonometric Functions
Inverse Trigonometric Derivatives Derivatives of the inverse of sin, cos, tan, scs, sec, cot
Trigonometric Substitution
Deriving the Derivative Formulas for Tan, Cot, Sec, Cosecant, Arctan
Exponential & Logarithmic Differentiation

Derivatives of Exponential Functions Derivatives of e ^x, a^x, a^g(x)
Derivative of the Natural Log Derivatives of ln(x), ln[g(x)]
Examples of Logarithmic Differentiation
Implicit Differentiation

Implicit Differentiation Find the derivatives of non-functions
Examples using Implicit Differentiation
Derivatives of Hyperbolic Functions

Hyperbolic Functions Hyperbolic Identities, Derivatives of Hyperbolic Functions & Derivatives of Inverse Hyperbolic Functions
Derivative Tests, Maxima & Minima

Second Derivative & Higher Derivatives Find the derivatives of derivatives & their applications
Maxima and Minima Maximum amd Minimum Values, Fermat’s Theorem, Critical Number, Extreme Value Theorem, Closed Interval Method
Maximum & Minimum
Finding Critical Numbers
Derivative Test First Derivative Test, Second Derivative Test, Minima, Maxima, Increasing/Decreasing Test
Concavity Problems

Concavity Problems I Analyze functions through increasing, decreasing, concavity, inflection points, critical points, & extremum
Concavity Problems II Analyze functions through increasing, decreasing, concavity, inflection points, critical points, & extremum
Optimization & Rate Problems

Optimization Problems using Derivatives
More Optimization Problems using Derivatives
Related Rates using Derivatives
More Related Rates using Derivatives
Curve Sketching & Asymptotes

Curve Sketching using Calculus
Asymptotes Vertical Asymptote, Horizontal Asymptote, Oblique Asymptote

Multivariable Calculus

Big Picture of Calculus

Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as: driving a car, climbing a mountain, growing to full adult height.

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Big Picture: Derivatives

Calculus finds the relationship between the distance traveled and the speed - easy for constant speed, not so easy for changing speed. Professor Strang is finding the “rate of change” & the “slope of a curve” & the “derivative of a function.”

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Big Picture: Integrals

The second half of calculus looks for the distance traveled even when the speed is changing. Finding this “integral” is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance. I know the speed at each moment of my trip, so how far did I go?

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Calculus Calculator with step by step solutions

Functions, Operations on Functions,
Polynomial & Rational Functions,
Exponential & Logarithmic Functions,
Sequences & Series
Evaluating Limits, Derivatives,
Applications of Differentiation, Integrals,
Applications of Integration,
Techniques of Integration,
Parametric Equations & Polar Coordinates

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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Calculus

AP Calculus AB and BC Free Response Past Papers and Solutions

AP Calculus AB and BC Multiple Choice Past Papers & Solutions

Solutions to Sample Questions

Differential Calculus

Integral Calculus

Sequences, Series & Tests

Parametric Curves & Polar Coordinates

Multivariable Calculus