Get a 5! - AP Calculus BC/Calc II in a Month
SAT Score Range
•
26 sessions
•
JM
AI
JM
+17
This series ended on August 12, 2024. All 1:1 and group chats related to this series are disabled 7 days after the last session.
About
I got a 5 on the AP Calculus BC exam, and you can too.
Having previously taught Calculus 1 (the AB curriculum) and now seeing the staggering amount of demand for further maths, I've decided to host this intensive, yet comprehensive series on Calculus 2, including a FULL work-through of a real past exam.
The first two sessions will serve as a review of differential calculus. Below are what we will cover:
INTEGRATION AND APPLICATIONS (UNIT 1)
1. Introduction to accumulation of change
2. Left and right Riemann sums; over and under-approximation
3. Midpoint and trapezoidal sums
4. Definition of indefinite integral using as the limit of Riemann sums
5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals
6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation.
7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds.
8. The reverse power rule, u-substitution, and integration by parts
9. Antiderivatives of all the previously mentioned functions
10. Improper integrals
11. Finding the average value of a function on an interval
12. Connecting position, velocity, and acceleration functions using integrals
13. Using accumulation functions and definite integrals in applied contexts
14. Finding the area between curves expressed as functions of x
15. Finding the area between curves expressed as functions of y
16. Finding the area between curves that intersect at more than two points
17. Volumes with cross sections: squares and rectangles
18. Volumes with cross sections: triangles and semicircles
19. Volume with disc method: revolving around x- or y-axis
20. Volume with disc method: revolving around other axes
21. Volume with washer method: revolving around x- or y-axis
22. Volume with washer method: revolving around other axes
23. The arc length of a smooth, planar curve and distance traveled
24. Calculator-active practice
DIFFERENTIAL EQUATIONS (UNIT 2):
1. Modeling situations with differential equations
2. Verifying solutions for differential equations
3. Sketching slope fields
4. Reasoning using slope fields
5. Approximating solutions using Euler’s method
6. Finding general solutions using separation of variables
7. Finding particular solutions using initial conditions and separation of variables
8. Exponential models with differential equations
9. Logistic models with differential equations
PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS (UNIT 3):
1. Defining and differentiating parametric equations
2. Second derivatives of parametric equations
3. Finding arc lengths of curves given by parametric equations
4. Defining and differentiating vector-valued functions
5. Solving motion problems using parametric and vector-valued functions
6. Defining polar coordinates and differentiating in polar form
7. Finding the area of a polar region or the area bounded by a single polar curve
8. Finding the area of the region bounded by two polar curves
9. Calculator-active practice
INFINITE SERIES (UNIT 4):
1. Defining convergent and divergent infinite series
2. Working with geometric series
3. The nth-term test for divergence
4. Integral test for convergence
5. Harmonic series and p-series
6. Comparison tests for convergence
7. Alternating series test for convergence
8. Ratio test for convergence
9. Determining absolute or conditional convergence
10. Alternating series error bound
11. Finding Taylor polynomial approximations of functions
12. Lagrange error bound
13. Radius and interval of convergence of power series
14. Finding Taylor or Maclaurin series for a function
15. Representing functions as power series
Tutored by
A little about me: I'm about the biggest Indie fan there is, I almost exclusively watch (John Hughes>>) 80s movies or the upcoming Star Wars series, and I read sci-fi in my spare time. I tutor for the sake of those aha moments, and have taken Multivariable Calc, Linear Algebra, Real Analysis, and Complex Analysis. Who knows what I'll tutor next, hope to see you soon.
Schedule
✋ ATTENDANCE POLICY
I try to make the session times as accommodating as possible, however make-up sessions are always available. Please feel free to ask for one if needed!
SESSION 1
13
Jul
SESSION 1
Office Hours
Office Hours
Sat 11:45 PM - Sun, 1:00 AM UTCJul 13, 11:45 PM - Jul 14, 1:00 AM UTC
REVIEW OF DIFFERENTIAL CALCULUS (PART 1) (75m)
1. Introduction to derivatives and notation
2. Average rate of change and the secant line
3. Instantaneous rate of change and the tangent line
4. The formal and informal definition of a derivative using limits
5. Equation of the tangent line of a function at a point
6. Estimating derivatives graphically and algebraically
7. Differentiability at a point and over an interval (connection to continuity)
8. Evaluating derivatives using the power rule, sum rule, product rule, quotient rule, and chain rule (including proofs of all the rules)
9. Derivative of sin(x), cos(x), tan(x), csc(x), sec(x), cot(x), ln(x), e^x, a^x, and log_a(x) (including a derivation of all of the formulas)
10. Derivative of inverse functions and inverse trigonometric functions
SESSION 2
14
Jul
SESSION 2
Office Hours
Office Hours
Sun 11:45 PM - Mon, 1:15 AM UTCJul 14, 11:45 PM - Jul 15, 1:15 AM UTC
REVIEW OF DIFFERENTIAL CALCULUS (PART 2) (90m)
11. Second derivatives, implicit differentiation, and related rates
12. Position, velocity, and acceleration problems
13. Local linearity and linear approximations to functions
14. L'Hôpital's rule and the special case of L'Hôpital's rule
15. The Mean Value Theorem for derivatives, the Extreme Value Theorem, and Rolle's Theorem
16. Finding critical points, local minima and maxima, increasing and decreasing intervals of a function
17. Finding absolute extrema over closed intervals and over the entire domain of a function
18. Introduction to concavity
19. The Second Derivative Test and points of inflection
20. Optimization
SESSION 3
15
Jul
SESSION 3
Integration and accumulation of change
Integration and accumulation of change
Mon 11:45 PM - Tue, 1:00 AM UTCJul 15, 11:45 PM - Jul 16, 1:00 AM UTC
Topics covered (75m):
1. Introduction to accumulation of change
2. Left and right Riemann sums; over and under-approximation
3. Midpoint and trapezoidal sums
SESSION 4
16
Jul
SESSION 4
Integration and accumulation of change
Integration and accumulation of change
Tue 11:45 PM - Wed, 1:05 AM UTCJul 16, 11:45 PM - Jul 17, 1:05 AM UTC
Topics covered (80m):
4. Definition of indefinite integral using as the limit of Riemann sums
5. The Fundamental Theorem of Calculus (including the proof), antiderivatives, and definite integrals
6. Interpretation of accumulation functions: negative definite integrals, definite integrals over a single point; graphical interpretation and evaluation.
7. Integrating sums of functions, switching the bounds of integration, and with functions as bounds.
SESSION 5
17
Jul
SESSION 5
Integration and accumulation of change
Integration and accumulation of change
Wed 11:45 PM - Thu, 1:00 AM UTCJul 17, 11:45 PM - Jul 18, 1:00 AM UTC
Topics covered (75m):
8. The reverse power rule, u-substitution, and integration by parts
9. Antiderivatives of all the previously mentioned functions
10. Improper integrals
SESSION 6
18
Jul
SESSION 6
Office Hours
Office Hours
Thu 11:45 PM - Fri, 1:05 AM UTCJul 18, 11:45 PM - Jul 19, 1:05 AM UTC
Khan Academy Unit Test run-through (1h 20m)
Unit Test 6 "Unit 6: Integration and accumulation of change"
*END OF UNIT 1 - INTEGRATION AND APPLICATIONS*
SESSION 7
19
Jul
SESSION 7
Applications of integration
Applications of integration
Fri 11:45 PM - Sat, 1:00 AM UTCJul 19, 11:45 PM - Jul 20, 1:00 AM UTC
(Continuing)
9. Integration by parts and
10. Improper integrals
SESSION 8
20
Jul
SESSION 8
Applications of integration
Applications of integration
Sat 11:45 PM - Sun, 1:00 AM UTCJul 20, 11:45 PM - Jul 21, 1:00 AM UTC
Khan Academy Unit Test run-through (1h 20m)
Unit Test 6 "Unit 6: Integration and accumulation of change"
*END OF UNIT 1 - INTEGRATION AND APPLICATIONS*
SESSION 9
21
Jul
SESSION 9
Applications of integration
Applications of integration
Sun 11:45 PM - Mon, 1:00 AM UTCJul 21, 11:45 PM - Jul 22, 1:00 AM UTC
Topics covered (75m):
11. Finding the average value of a function on an interval
12. Connecting position, velocity, and acceleration functions using integrals
13. Using accumulation functions and definite integrals in applied contexts
14. Finding the area between curves expressed as functions of x
SESSION 10
22
Jul
SESSION 10
Applications of integration
Applications of integration
Mon 11:45 PM - Tue, 1:00 AM UTCJul 22, 11:45 PM - Jul 23, 1:00 AM UTC
Topics covered (75m):
15. Finding the area between curves expressed as functions of y
16. Finding the area between curves that intersect at more than two points
17. Volumes with cross sections: squares and rectangles
SESSION 11
23
Jul
SESSION 11
Applications of integration
Applications of integration
Tue 11:45 PM - Wed, 1:00 AM UTCJul 23, 11:45 PM - Jul 24, 1:00 AM UTC
Topics covered (75m):
18. Volumes with cross sections: triangles and semicircles
19. Volume with disc method: revolving around x- or y-axis
20. Volume with disc method: revolving around other axes
PLEASE BRING YOUR GRAPHING CALCULATORS NEXT session!
(TI-84s preferred!)
SESSION 12
24
Jul
SESSION 12
Applications of integration
Applications of integration
Wed 11:45 PM - Thu, 1:05 AM UTCJul 24, 11:45 PM - Jul 25, 1:05 AM UTC
PLEASE BRING YOUR GRAPHING CALCULATORS! (TI-84s preferred!)
Topics covered (80m):
21. Volume with washer method: revolving around x- or y-axis
22. Volume with washer method: revolving around other axes
23. The arc length of a smooth, planar curve and distance traveled
24. Calculator-active practice
SESSION 13
26
Jul
SESSION 13
Office Hours
Office Hours
Fri 12:00 AM - 1:20 AM UTCJul 26, 12:00 AM - 1:20 AM UTC
Khan Academy Unit Test run-through (1h 20m)
"Unit 6: Integration and accumulation of change"
*END OF UNIT 1 - INTEGRATION AND APPLICATIONS*
SESSION 14
27
Jul
SESSION 14
Differential equations
Differential equations
Sat 11:45 PM - Sun, 1:05 AM UTCJul 27, 11:45 PM - Jul 28, 1:05 AM UTC
Topics covered (80m):
1. Modeling situations with differential equations
2. Verifying solutions for differential equations
3. Sketching slope fields
4. Reasoning using slope fields
5. Approximating solutions using Euler’s method
6. Finding general solutions using separation of variables
SESSION 15
28
Jul
SESSION 15
Differential equations
Differential equations
Sun 11:45 PM - Mon, 1:05 AM UTCJul 28, 11:45 PM - Jul 29, 1:05 AM UTC
Topics covered (80m):
7. Finding particular solutions using initial conditions and separation of variables
8. Exponential models with differential equations
9. Logistic models with differential equations
SESSION 16
29
Jul
SESSION 16
Office Hours
Office Hours
Mon 11:45 PM - Tue, 1:05 AM UTCJul 29, 11:45 PM - Jul 30, 1:05 AM UTC
Khan Academy Unit Test run-through (1h 20m)
"Unit 8: Applications of integration"
*END OF UNIT 2 - DIFFERENTIAL EQUATIONS*
SESSION 17
31
Jul
SESSION 17
Parametric equations, polar coordinates, and vector-valued functions
Parametric equations, polar coordinates, and vector-valued functions
Wed 11:45 PM - Thu, 1:05 AM UTCJul 31, 11:45 PM - Aug 1, 1:05 AM UTC
PLEASE BRING YOUR GRAPHING CALCULATORS NEXT SESSION!
(TI-84s preferred!)
Topics covered (80m):
1. Defining and differentiating parametric equations
2. Second derivatives of parametric equations
3. Finding arc lengths of curves given by parametric equations
SESSION 18
1
Aug
SESSION 18
Parametric equations, polar coordinates, and vector-valued functions
Parametric equations, polar coordinates, and vector-valued functions
Thu 11:45 PM - Fri, 1:05 AM UTCAug 1, 11:45 PM - Aug 2, 1:05 AM UTC
Topics covered (80m):
4. Defining and differentiating vector-valued functions
5. Solving motion problems using parametric and vector-valued functions
6. Defining polar coordinates and differentiating in polar form
7. Finding the area of a polar region or the area bounded by a single polar curve
SESSION 19
3
Aug
SESSION 19
Other Topics
Other Topics
Sat 11:45 PM - Sun, 1:00 AM UTCAug 3, 11:45 PM - Aug 4, 1:00 AM UTC
Topics covered (75m):
PLEASE BRING YOUR GRAPHING CALCULATORS! (TI-84s preferred!)
8. Finding the area of the region bounded by two polar curves
9. Calculator-active practice
*END OF UNIT 3 - PARAMETRIC EQUATIONS AND VECTOR-VALUED FUNCTIONS*
We'll start our next unit:
1. Defining convergent and divergent infinite series
SESSION 20
4
Aug
SESSION 20
Other Topics
Other Topics
Sun 11:45 PM - Mon, 1:00 AM UTCAug 4, 11:45 PM - Aug 5, 1:00 AM UTC
Topics covered (75m):
2. Working with geometric series
3. The nth-term test for divergence
4. Integral test for convergence
SESSION 21
6
Aug
SESSION 21
Other Topics
Other Topics
Tue 12:15 AM - 1:30 AM UTCAug 6, 12:15 AM - 1:30 AM UTC
Topics covered (75m):
5. Harmonic series and p-series
6. Comparison tests for convergence
7. Alternating series test for convergence
8. Ratio test for convergence
SESSION 22
7
Aug
SESSION 22
Other Topics
Other Topics
Wed 11:45 PM - Thu, 1:05 AM UTCAug 7, 11:45 PM - Aug 8, 1:05 AM UTC
Topics covered (80m):
9. Determining absolute or conditional convergence
10. Alternating series error bound
11. Finding Taylor polynomial approximations of functions
SESSION 23
9
Aug
SESSION 23
Other Topics
Other Topics
Fri 1:15 AM - 2:35 AM UTCAug 9, 1:15 AM - 2:35 AM UTC
Topics covered (80m):
12. Lagrange error bound
13. Radius and interval of convergence of power series
14. Finding Taylor or Maclaurin series for a function
15. Representing functions as power series
SESSION 24
9
Aug
SESSION 24
AP Calculus
AP Calculus
Fri 11:45 PM - Sat, 1:15 AM UTCAug 9, 11:45 PM - Aug 10, 1:15 AM UTC
Topics covered (80m):
11. Finding Taylor polynomial approximations of functions
12. Lagrange error bound
SESSION 25
11
Aug
SESSION 25
AP Calculus
AP Calculus
Sun 12:45 AM - 2:15 AM UTCAug 11, 12:45 AM - 2:15 AM UTC
Topics covered (80m):
13. Radius and interval of convergence of power series
14. Finding Taylor or Maclaurin series for a function
15. Representing functions as power series
SESSION 26
12
Aug
SESSION 26
AP Calculus
AP Calculus
Mon 1:15 AM - 2:45 AM UTCAug 12, 1:15 AM - 2:45 AM UTC
COURSE CHALLENGE (90m)
THE SERIES WILL END IN A WEEK; IN THAT TIME I WILL ACCEPT ANY PRACTICE EXAMS AND RETURN THEM WITH FEEDBACK.