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AP Calculus Summer Session -

SAT Score Range

•

14 sessions

•

About

Each week, we’ll cover a new unit from the AP Calculus BC curriculum. There will be two sessions per week for lessons and I will run a 3rd optional sessions for questions regarding what we learned during the week. By the end of the camp, you’ll be well-prepared to succeed in the first few months of your AP Calculus BC class. Topics that we cover will include Derivatives, Integrals, Limits, and some essential BC topics like advanced integration techniques.

Tutored by

Jack M 🇺🇸

Certified in 2 topics

View Profile

I'm a high school student from Illinois and I'm interested in helping students with subjects like math and science. In my free time, I enjoy cooking, traveling, and spending time with my friends.

Schedule

✋ ATTENDANCE POLICY

For this AP Calculus Prep course, I have set a few ground rules to maximize our success in the course. These rules include:

1. Let the tutor know if you won't be in attendance for a given lesson. I will hold hours to ask questions, but regardless, please be punctual and try to attend all lessons. You will be withdrawn from the series if you miss any session without giving the tutor prior notice.

2. Homework is optional, but highly recommended. I understand that it is the summer, and many of you will be working on college apps, but front loading work will save you immensely in the long run.

3. Be polite and respectful. We only have so much time together, and I want to use our time effectively to get the most out of this course.

SESSION 2

3

Jul

SESSION 2

Limits and continuity

Limits and continuity

Thu 6:30 PM - 8:00 PM UTCJul 3, 6:30 PM - 8:00 PM UTC

Key Topics:
- What is a limit?
- Graphical and numerical approachesAlgebraic limits (factor, rationalize, special trig limits)
- One-sided and infinite limits
- Continuity and discontinuities (removable, jump, infinite)
- The Intermediate Value Theorem (IVT)
SESSION 3

7

Jul

SESSION 3

Differentiation: definition and basic derivative rules

Differentiation: definition and basic derivative rules

Mon 6:30 PM - 8:00 PM UTCJul 7, 6:30 PM - 8:00 PM UTC

Key Topics:
- Definition of the derivative (limit form)
- Derivative notation (Leibniz, prime, d/dx)
- Basic derivative rules: power, constant, exponential, trig
- Tangent line and rate of change interpretation
SESSION 4

10

Jul

SESSION 4

Differentiation: composite, implicit, and inverse functions

Differentiation: composite, implicit, and inverse functions

Thu 6:30 PM - 8:00 PM UTCJul 10, 6:30 PM - 8:00 PM UTC

Key Topics:
- Chain rule and function composition
- Implicit differentiation: dy/dx with x and y mixed
- Derivatives of inverse functions (including trig inverses)
SESSION 5

12

Jul

SESSION 5

General Calculus Q&A

General Calculus Q&A

Sat 8:00 PM - 9:00 PM UTCJul 12, 8:00 PM - 9:00 PM UTC

This is an optional session for those who have questions regarding previously learned Calculus content.
SESSION 6

21

Jul

SESSION 6

Contextual applications of differentiation

Contextual applications of differentiation

Mon 6:30 PM - 8:00 PM UTCJul 21, 6:30 PM - 8:00 PM UTC

Motion:
- position, velocity, acceleration
- Related rates (classic ladder, cone, shadow problems)
- Optimization: using the first and second derivative
SESSION 7

24

Jul

SESSION 7

Applying derivatives to analyze functions

Applying derivatives to analyze functions

Thu 6:30 PM - 8:00 PM UTCJul 24, 6:30 PM - 8:00 PM UTC

Key Topics:
- Mean Value Theorem (MVT)
- Extreme Value Theorem (EVT)
- Candidates Test

***This session will not have a weekend review sessions. If you have questions, send me a message and I will get back to you as soon as possible.
SESSION 8

31

Jul

SESSION 8

Applying derivatives to analyze functions

Applying derivatives to analyze functions

Thu 6:30 PM - 7:30 PM UTCJul 31, 6:30 PM - 7:30 PM UTC

Key Topics:
- Increasing/decreasing intervals, extrema (1st Derivative Test)
- Concavity and inflection points (2nd Derivative Test)
- Sketching a function given f’ or f’’

***This session will not have a weekend review sessions. If you have questions, send me a message and I will get back to you as soon as possible.
SESSION 9

4

Aug

SESSION 9

Integration and accumulation of change

Integration and accumulation of change

Mon 6:30 PM - 8:00 PM UTCAug 4, 6:30 PM - 8:00 PM UTC

Key Topics:
- Riemann Sums: Left, Right, Midpoint, Trapezoidal
- Definite vs. indefinite integrals
- The Fundamental Theorem of Calculus (FTC Parts 1 & 2)
- Reverse power rule and integrals to remember

SESSION 10

7

Aug

SESSION 10

Integration and accumulation of change

Integration and accumulation of change

Thu 6:30 PM - 8:00 PM UTCAug 7, 6:30 PM - 8:00 PM UTC

Key Topics:
- Partial Fractions
- u substitution
- Integration with long division
- Integration by parts
- Improper Integrals
SESSION 11

9

Aug

SESSION 11

General Calculus Q&A

General Calculus Q&A

Sat 8:00 PM - 9:30 PM UTCAug 9, 8:00 PM - 9:30 PM UTC

This is an optional session for those who have questions regarding previously learned Calculus content. This includes topics such as those discussed in 7 and 8.
SESSION 12

11

Aug

SESSION 12

Differential equations

Differential equations

Mon 6:30 PM - 8:00 PM UTCAug 11, 6:30 PM - 8:00 PM UTC

Key Topics:
- Slope fields (drawing and interpreting)
- Solving separable differential equations
- Exponential growth and decay models
- Logistic growth (basic intro)
SESSION 13

14

Aug

SESSION 13

Applications of integration

Applications of integration

Thu 6:30 PM - 8:00 PM UTCAug 14, 6:30 PM - 8:00 PM UTC

Key Topics:
- Motion with integrals: total distance, displacement
- Average value of a function
- Disk and washer methods
- Area of shapes in coordinate plane
- Arc length of a function
SESSION 14

16

Aug

SESSION 14

General Calculus Q&A

General Calculus Q&A

Sat 8:00 PM - 9:00 PM UTCAug 16, 8:00 PM - 9:00 PM UTC

This is an optional session for those who have questions regarding previously learned Calculus content.

Public Discussion

Please log in to see discussion on this series.

Jun 30 - Aug 16

7 weeks

45 - 90 mins

/ session

Next session on July 3, 2025

SCHEDULE

Mondays

6:30PM

Thursdays

6:30PM

Saturdays

8:00PM