1. Functions and Other Fundamentals

4hr

1.1.1. Interval Notation 4 min

1.1.2. Set Notation3 min

1.1.3. Example4 min

1.1.4. Practice2 min

1.1.5. Practice52 sec

1.1.6. Practice44 sec

1.2.4. Practice 40 sec

1.2.5. Practice 3 min

1.3.1. Operations with Functions3 min

1.3.2. Example2 min

1.3.3. Practice2 min

1.3.4. Practice1 min

1.4.1. Even and Odd Functions3 min

1.4.2. Example2 min

1.5.1. Transformation of Graphs2 min

1.5.2. Example1 min

1.5.3. Practice2 min

1.6.1. Basic of Polynomials4 min

1.6.2. Example2 min

1.6.3. Practice3 min

1.6.4. Polynomial Graphs & Characteristics4 min

1.6.5. Example2 min

1.6.6. Practice2 min

1.7.1. Factoring 5 min

1.7.2. Factoring a Difference & Sum of Cubes3 min

1.7.3. Example2 min

1.7.4. Practice46 sec

1.7.5. Practice2 min

1.7.6. Practice2 min

1.8.1. Dividing Polynomials - Long Division6 min

1.8.2. Example3 min

1.8.3. Dividing Polynomials - Synthetic Division8 min

1.8.4. Example2 min

1.8.5. Practice2 min

1.8.6. Practice3 min

1.9.1. Rational Functions4 min

1.9.2. Solving Rational Equations3 min

1.10.1. Partial Fractions Decomposition4 min

1.10.2. Example: Long Division with Partial Fractions8 min

1.10.3. Example: Rationalizing Substiution5 min

1.10.4. Example: Repeated factors

1.10.5. Practice Question: Partial Fraction

1.10.6. Practice Question: Partial Fraction

1.11.1. Radical Functions59 sec

1.11.2. Solving Radical Equations5 min

1.11.3. Example5 min

1.11.4. Practice8 min

1.12.1. Piecewise Functions4 min

1.12.2. Example5 min

1.12.3. Practice3 min

1.13.1. Absolute Value Function1 min

1.13.2. Example3 min

1.14.1. Inverse Functions3 min

1.14.2. Example3 min

1.14.3. Practice2 min

1.15.1. Exponential Functions3 min

1.15.2. Example1 min

1.15.3. Example2 min

1.16.1. Logarithmic Functions4 min

1.16.2. Example3 min

1.16.3. Example:3 min

1.16.4. Practice2 min

1.17.1. Trigonometric Functions6 min

1.17.2. Example4 min

1.17.3. Trig Identities2 min

1.17.4. Practice3 min

1.17.5. Practice4 min

1.18.1. Inverse Trigonometric Functions4 min

1.18.2. Example3 min

1.18.3. Practice2 min

1.18.4. Practice2 min

1.19.1. Sequences8 min

1.19.2. Series7 min

1.19.3. Practice (Partial sums)2 min

1.19.4. Practice (Geometric series)2 min

1.19.5. Practice (Geometric series)3 min

1.19.6. Practice: Series Application6 min

1.19.7. How to Test if a Series Converges?

1.20.1. Introduction to Conics

2. Limits & Continuity

1.5hr

2.I. AP Calculus Unit 1 Summary

2.1.1. Limit Basics2 min

2.1.2. Example1 min

2.2.1. Limit Laws 2 min

2.2.2. Practice1 min

2.3.1. One-Sided Limits2 min

2.3.2. Example: One-Sided Limit2 min

2.3.3. Practice: One-Sided Limits3 min

2.4.1. Infinite Limits2 min

2.4.2. Example1 min

2.4.3. Example3 min

2.5.1. Limits at Infinity3 min

2.5.2. Example60 sec

2.5.3. Example3 min

2.5.4. Example4 min

2.5.5. Practice 3 min

2.5.6. Practice3 min

2.6.1. Indeterminate Forms50 sec

2.7.1. Computing Limits by Factoring1 min

2.7.2. Example1 min

2.7.3. Practice2 min

2.8.1. Computing Limits by Multiplying by the Conjugate3 min

2.8.2. Example3 min

2.8.3. Practice3 min

2.9.1. Computing Limits by Getting a Common Denominator1 min

2.9.2. Example2 min

2.9.3. Practice4 min

2.10.1. The Fundamental Trig Limit2 min

2.10.2. Example3 min

2.11.1. The Squeeze Theorem2 min

2.11.2. Example2 min

2.11.3. Practice2 min

2.12.1. Continuity2 min

2.12.2. Example2 min

2.12.3. Practice4 min

2.13.1. The Epsilon Delta Definition of a Limit

2.13.2. Example3 min

2.13.3. Practice

2.14.1. The Intermediate Value Theorem2 min

2.14.2. Example2 min

2.14.3. Practice2 min

2.15.1. Extreme Value Theorem1 min

2.Q. Exam-Like Questions17 Qns

3. Differentiation

2.6hr

3.1.1. Derivatives as a Rate of Change2 min

3.1.2. Average Rate of Change46 sec

3.1.3. Example2 min

3.1.4. Practice1 min

3.2.1. The Limit Definition of a Derivative2 min

3.2.2. Example3 min

3.2.3. Practice5 min

3.3.1. Differentiation Laws51 sec

3.4.1. The Power Rule1 min

3.4.2. Example2 min

3.4.3. Practice51 sec

3.5.1. Tangent Lines1 min

3.5.2. Example3 min

3.5.3. Practice2 min

3.6.1. Normal Lines1 min

3.6.2. Example3 min

3.6.3. Practice

3.6.4. Practice1 min

3.7.1. The Product Rule49 sec

3.7.2. Example2 min

3.7.3. Example2 min

3.7.4. Practice2 min

3.8.1. The Quotient Rule1 min

3.8.2. Example2 min

3.8.3. Practice4 min

3.9.1. The Chain Rule1 min

3.9.2. Example2 min

3.9.3. Practice3 min

3.10.1. Higher Order Derivatives2 min

3.10.2. Example3 min

3.10.3. Practice2 min

3.10.4. Practice

3.10.5. Practice2 min

3.11.1. Derivatives of Trigonometric Functions1 min

3.11.2. Example39 sec

3.11.3. Example3 min

3.11.4. Example1 min

3.11.5. Practice3 min

3.11.6. Practice2 min

3.12.1. Derivatives of Exponential Functions1 min

3.12.2. Example52 sec

3.12.3. Example3 min

3.12.4. Practice1 min

3.13.1. Implicit Differentiation2 min

3.13.2. Example3 min

3.13.3. Practice3 min

3.13.4. Example3 min

3.14.1. Derivatives of Inverse Functions52 sec

3.14.2. Example2 min

3.14.3. Practice3 min

3.15.1. Derivatives of Logarithmic Functions1 min

3.15.2. Example56 sec

3.15.3. Example2 min

3.15.4. Practice2 min

3.15.5. Practice: Log and Ln2 min

3.16.1. Inverse Trig Derivatives1 min

3.16.2. Example1 min

3.16.3. Practice3 min

4. Applications of Differentiation

4hr

4.1.1. Related Rates1 min

4.2.1. Differentials2 min

4.2.2. Example3 min

4.2.3. Practice2 min

4.3.1. Linearization (Linear Approximation)59 sec

4.3.2. Example3 min

4.3.3. Practice3 min

4.3.4. Practice3 min

4.4.1. Rolle's Theorem1 min

4.4.2. Example2 min

4.4.3. Practice1 min

4.5.1. Fermat's Theorem47 sec

4.6.1. The Mean Value Theorem1 min

4.6.2. Example2 min

4.6.3. Practice2 min

4.7.1. Intervals of Increase and Decrease1 min

4.7.2. Example2 min

4.7.3. Practice3 min

4.8.1. Critical Points and Extrema2 min

4.8.2. Example

4.8.3. Practice3 min

4.9.1. 1st and 2nd Derivative Tests3 min

4.9.2. Example7 min

4.9.3. Example

4.9.4. Practice3 min

4.10.1. Maximum and Minimum on Closed Intervals2 min

4.10.2. Example4 min

4.10.3. Practice3 min

4.10.4. Practice3 min

4.11.1. Concavity and Inflection Points56 sec

4.11.2. Example6 min

4.11.3. Practice6 min

4.12.1. Curve Sketching2 min

4.12.2. Example7 min

4.12.3. Practice9 min

4.12.4. Practice

4.13.1. L’Hopital’s Rule2 min

4.13.2. Example2 min

4.13.3. Practice5 min

4.14.1. Solving General Indeterminate Forms2 min

4.14.2. Example2 min

4.14.3. Practice5 min

4.14.4. Practice2 min

4.15.1. Optimization1 min

4.15.2. Example4 min

4.15.3. Example4 min

4.15.4. Practice6 min

4.15.5. Practice4 min

4.16.1. Related Rates

4.16.2. Related Rates5 min

4.16.3. Related Rates5 min

4.16.4. Linear Approximation4 min

4.16.5. Linear Approximation

4.16.6. Taylor Series from Definition7 min

4.16.7. Taylor Polynomials

4.16.8. Maclaurin Polynomial

4.16.9. Newton's Method2 min

4.16.10. Newton's Method

4.16.11. L'Hopital's Rule

4.16.12. L'Hopital's Rule

4.16.13. L'Hopital's Rule

4.16.14. Limits

4.16.15. L'Hopital's Rule

4.16.16. L'Hopital's Rule

4.16.17. Limits

4.16.18. Limits

4.16.19. Extreme Value Theorem

4.16.20. Rolle's Theorem1 min

4.16.21. Rolle's Theorem6 min

4.16.26. Intervals of Increase and Decrease

4.16.27. Intervals of Increase and Decrease3 min

4.16.28. Critical Points6 min

4.16.29. Critical Points1 min

4.16.30. Extrema5 min

4.16.31. Extrema6 min

4.16.32. Second Derivative Test10 min

4.16.33. Curve Sketching

4.16.34. Curve Sketching12 min

4.16.35. Curve Sketching

4.16.36. Optimization

4.16.37. Optimization

4.16.38. Optimization

5. Integration

2.8hr

5.1.1. Antiderivatives (Indefinite Integral)3 min

5.2.1. Antiderivatives (Indefinite Integral) of Trig Functions4 min

5.2.2. Example1 min

5.2.3. Practice1 min

5.2.4. Practice1 min

5.3.1. Antiderivatives (Indefinite Integrals) of Inverse Trig Functions2 min

5.3.2. Example1 min

5.3.3. Practice1 min

5.4.1. Antiderivatives (Indefinite Integral) of Exponential Functions1 min

5.4.2. Example42 sec

5.4.3. Practice1 min

5.4.4. Practice2 min

5.5.1. Antiderivatives (Indefinite Integral) of

\frac{1}{x}

2 min

5.5.2. Example2 min

5.5.3. Practice1 min

5.6.1. Initial Conditions2 min

5.6.2. Example2 min

5.6.3. Practice5 min

5.7.1. Finite Sums & Summation Notation3 min

5.7.2. Example5 min

5.7.3. Practice4 min

5.7.4. Practice4 min

5.8.1. Approximating Areas & Riemann Sums 3 min

5.8.2. Example4 min

5.8.3. Practice3 min

5.9.1. The Definite Integrals & Area Under a Curve2 min

5.9.2. Example7 min

5.9.3. Practice2 min

5.9.4. Practice12 min

5.10.1. Properties of the Definite Integral2 min

5.10.2. Practice2 min

5.10.3. Practice2 min

5.11.1. Computing Definite Integrals Geometrically44 sec

5.11.2. Example1 min

5.11.3. Practice1 min

5.12.1. Antiderivatives & Indefinite Integrals6 min

5.12.2. Practice1 min

5.12.3. Practice1 min

5.12.4. Practice (initial condition)2 min

5.13.1. Fundamental Theorem of Calculus - Part I2 min

5.13.2. Example1 min

5.13.3. Example48 sec

5.13.4. Practice1 min

5.13.5. Practice2 min

5.14.1. Fundamental Theorem of Calculus - Part 21 min

5.14.2. Example2 min

5.14.3. Example

5.14.4. Practice 4 min

5.14.5. Practice3 min

5.14.6. Practice1 min

5.15.1. Integration by Substitution2 min

5.15.2. Example4 min

5.15.3. Example3 min

5.15.4. Example (w/ Back-Substitution)4 min

5.15.5. Practice

5.15.6. Practice

5.15.7. Practice

5.15.8. Practice (w/ Back-Substitution)

6. Applications of Integrals

1.6hr

6.1.1. Average value of a function3 min

6.1.2. Example2 min

6.1.3. Practice2 min

6.1.4. Displacement, Velocity, and Acceleration4 min

6.1.5. Rates of Change and Integrals3 min

6.2.1. Area between Curves3 min

6.2.2. Practice4 min

6.2.3. Practice3 min

6.2.4. Practice (multiple regions)4 min

6.3.1. Volumes - Cross Sections Method3 min

6.3.2. Practice4 min

6.3.3. Practice3 min

6.4.1. Volumes of Revolution (Disk/Washer)3 min

6.4.2. Practice (around the x-axis)2 min

6.4.3. Practice (around the y-axis)3 min

6.4.4. Practice (around a line)3 min

6.5.1. Volumes of Revolution (Cylindrical Shells)4 min

6.5.2. Practice2 min

6.6.1. Arc Length of a Curve3 min

6.6.2. Practice6 min

6.6.3. Practice4 min

6.7.1. Surface Area of Revolution1 min

6.7.2. Example5 min

6.7.3. Practice

6.8.1. Distribution Functions4 min

6.8.2. Practice: PDF3 min

6.8.3. Practice: CDF2 min

6.8.4. Mean, Median, and Variance3 min

6.8.5. Practice2 min

6.8.6. Practice: Median1 min

6.9.1. Work2 min

6.9.2. Example3 min

6.9.3. Practice

6.Q. Applications of Integration Quiz7 Qns

7. Integration Techniques

2.8hr

7.1.1. Integration by Parts6 min

7.1.2. Practice4 min

7.1.3. Practice (w/

\ln

)2 min

7.1.4. Practice (w/ exp & trig)6 min

7.2.1. Trigonometric Integrals3 min

7.2.2. Practice (odd power of

\cos x

)3 min

7.2.3. Practice (odd power of

\sin x

)3 min

7.2.4. Practice (even powers of

\sin x

&

\cos x

)2 min

7.2.5. Practice (even power of

\sec x

)4 min

7.2.6. Practice (w/

\sec x \tan x

)3 min

7.2.7. Practice (

\sin (mx)

&

\sin(nx)

)1 min

7.2.8. Practice (special case

\sec x

)3 min

7.2.9. Practice (special case

\sec^3x

)5 min

7.2.10. Reduction Formula2 min

7.2.11. Practice5 min

7.2.12. Practice3 min

7.3.1. Trigonometric Substitution10 min

7.3.2. Practice6 min

7.3.3. Practice5 min

7.3.4. Practice (w/ completing the square)6 min

7.4.1. Partial Fractions Decomposition7 min

7.4.2. Practice (linear factors only)4 min

7.4.3. Practice (w/ quadratic factors)7 min

7.4.4. Practice (w/ long division)6 min

7.5.1. Strategies for Integration3 min

7.5.2. Practice (rationalizing substitution)4 min

7.5.3. Practice: Mixed Integrals4 min

7.6.1. Improper Integrals4 min

7.6.2. Practice (type 1)2 min

7.6.3. Practice (type 1)5 min

7.6.4. Practice (Type 2)5 min

7.7.1. The Midpoint Rule1 min

7.7.2. Example2 min

7.7.3. The Trapezoid Rule 1 min

7.7.4. Example2 min

7.7.5. Practice

7.7.6. Simpson's Rule1 min

7.7.7. Example2 min

7.7.8. Practice

7.7.9. Error Bounds for Approximations2 min

7.7.10. Practice

7.7.11. Numerical Integration (Summary)

7.Q. Integration Techniques Quiz18 Qns

8. Parametric and Polar Curves

1.8hr

8.1.1. Parametric Curves6 min

8.1.2. Practice (Cartesian equations)2 min

8.1.3. Practice (graphs)4 min

8.1.4. Practice (graphs)3 min

8.2.1. Tangents/Derivatives of Parametric Curves2 min

8.2.2. Practice (derivatives)2 min

8.2.3. Practice (horizontal/vertical tangents)5 min

8.2.4. Practice (horizontal/vertical tangents*)6 min

8.2.5. Arc Length, Area, and Surface Area2 min

8.2.6. Practice (arc length)3 min

8.2.7. Practice (area)3 min

8.2.8. Practice (surface area)6 min

8.2.9. Practice (surface area)5 min

8.3.1. Polar Coordinates7 min

8.3.2. Graphing Polar Curves6 min

8.3.3. Practice (graphs)6 min

8.3.4. Practice (polar coordinates)2 min

8.3.5. Practice (matching graphs)4 min

8.4.1. Tangents/Derivatives of Polar Curves2 min

8.4.2. Practice (derivative)4 min

8.4.3. Practice (horizontal/vertical tangents)7 min

8.4.4. Arc Length, Area Under & Between Curves2 min

8.4.5. Practice (arc length)3 min

8.4.6. Practice (area inside curve)2 min

8.4.7. Practice (area inside curve)4 min

8.4.8. Practice (area between curves)8 min

8.Q. Parametric and polar curves Quiz6 Qns

Mock Exam

ME.1. Final Exam - Mock Assessment20 Qns

MATH 117

Course Overview

1. Functions and Other Fundamentals

2. Limits & Continuity

3. Differentiation

4. Applications of Differentiation

5. Integration

6. Applications of Integrals

7. Integration Techniques

8. Parametric and Polar Curves

Mock Exam

ME.1 Final Exam - Mock Assessment

Included in Wizeprep Plus

Final Exam - Mock Assessment

Timer