The Ultimate CLEP Calculus Course: A Comprehensive Review

Calculus, a cornerstone of mathematics, deals with rates of change (differentiation) and accumulation of quantities (integration). For CLEP, the Calculus exam features 44 questions to be completed in 90 minutes, covering limits, derivatives, integrals, and applications. It’s challenging due to its abstract concepts and problem-solving demands. Scoring is on a scale of 20-80, with a passing score typically around 50. Mastering calculus is crucial for STEM fields and enhances analytical skills. CLEP Calculus is respected, allowing students to earn college credit and save on tuition. It’s ranked among the more difficult CLEP tests, but rewarding for dedicated learners.

AP Calculus AB and BC are more comprehensive and rigorous than CLEP Calculus, with broader content and longer exam formats.

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CLEP Calculus Complete Course

Functions

• Function Notation
• Adding and Subtracting Functions
• Multiplying and Dividing Functions
• Composition of Functions
• Writing Functions
• Graphing Functions
• Parent Functions
• Function Inverses
• Inverse Variation
• Domain and Range of function
• Piecewise Function
• Positive, Negative, Increasing and Decreasing Functions on Intervals

Advanced Functions

• Exponential Function
• Linear, Quadratic and Exponential Models
• Linear vs Exponential Growth
• Logarithms
• Properties of logarithms
• Natural Logarithms
• Sine, Cosine, and Tangent
• Reciprocal Functions: Cosecant, Secant, and Cotangent
• Domain and Range of Trigonometric Functions
• Trigonometric Function Values for Key Angles
• The Unit Circle
• Additional trigonometric reminders
• Periodic properties of trigonometric functions
• Floor and Ceiling Functions

Limit and Continuity

• Functions with Undefined Limits
• Limit at Infinity
• Continuity at a Point
• Continuity over an Interval
• Removing Discontinuity
• Limit Laws
• The Squeeze Theorem
• Indeterminate and Undefined
• Infinity Cases
• Trigonometric Limits
• Rationalizing Trigonometric Functions
• Redefining Function’s Value
• Rationalizing Infinite Limits

Derivative Basics

• Derivative Introduction
• Average and Instantaneous Rates of Change
• The Derivative of a Function
• Derivative of Trigonometric Functions
• Power Rule
• Product Rule
• Quotient Rule
• Chain Rule
• Derivative of Radicals
• Derivative of Logarithms and Exponential Functions
• Differentiability
• Differentiating Inverse Functions
• Derivative of Reciprocal Trigonometric Functions

Applications of Derivatives

• Optimization Problems
• L’Hôpital
• Implicit Relations
• Implicit Differentiation
• Related Rates
• Higher Order Derivatives
• Extreme Value Theorem
• Second Derivatives: Minimum vs. Maximum
• Curve Sketching Using Derivatives
• Mean Value Theorem
• Newton’s Method

Integrals

• What is Integral?
• Applications of Integrals
• Exponential Growth and Decay
• The Anti-Derivative
• Sigma Notation (Summation Notation)
• Riemann Sums
• Rules of Integration
• Power Rule
• Fundamental Theorem of Calculus
• Trigonometric Integrals
• Substitution Rule
• Integral of Radicals
• Exponential and Logarithmic Integrals

Applications of Integrals

• Average Value of a Function
• Accumulation Problems
• Finding Area Between Curves
• Modeling Particle Motion
• Simple Growth and Decay