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Tutoring

Sessions

I started tutoring in high school and never thought to stop. Since then, I've worked with over 300 students, with an emphasis on students studying at or above the level of AP Calculus AB/BC. In particular, I specialize in highly gifted younger students studying far above their grade level -- for example, I've tutored many students in Math Academy, a radically accelerated math program in which highly gifted students master AP Calculus BC in 8th grade and university-level courses in high school. Here are some particularly notable examples of students I've worked with:

colby tutoring icon Colby is a high school student who is studying math at the college level through Math Academy. We started working together when he was a freshman taking linear algebra / multivariable calculus. In the first month of school, he began to fall behind in these classes -- but we met weekly throughout the entire year, and by the end of the course he received not only an A on his transcript, but also the highest score in the class on the final exam. We continued working together through his sophomore year, during which he received another A and the second-highest score on his abstract algebra / differential equations final.
jordan tutoring icon Jordan was a middle school student who, at the age of 12, decided that he wanted to skip high school and enter straight into college to study physics. In order to apply to the Early Entrance Program at Cal State LA, he needed to take the ACT. After meeting weekly with me for 8 months, his ACT math score jumped 12 points from a 16 to a 28, and he was accepted into the program.
malcolm tutoring icon Malcolm is in 6th grade and is studying AP Calculus BC. We started working together when he was 8 years old -- he spent hours on end conducting his own arithmetic experiments, and I helped him state his results using formal mathematical notation. Our discussions quickly ventured into algebra, and before we knew it, we had covered most of high school math. Currently, we are working through AP Calculus BC with a bit of probability thrown in.

My rate is $80/hr, and I normally meet with students via video call. Feel free to contact me if you'd like to chat about potentially working together.

Free-Response Grading

I also offer grading and feedback on AP Calculus AB/BC free response practice exams. My rate is $30 per free response exam. Here is an example of what you can expect from feedback:


L earned 19 out of 41 total points, which equates to 46%. This is right on the borderline between a 3 and a 4.

Does L know how to evaluate an integral on her graphing calculator? It looked like L tried to do these problems entirely by hand, even though they were in the section of the test where she was allowed to use a graphing calculator.

Pointers

Here are some other pointers for L going forward:
  • Whenever a question asks for units, be sure to include the units on your final answer.
  • When determining the interval of convergence of a series using the ratio test, be sure to check the endpoints individually after finding the radius of convergence.

Detailed Feedback

Below is some more detailed feedback about the points L missed, along with links to the exam questions, grading rubric, and photos of L's marked-up answers.


Problem 1 [2 points earned out of 9 possible]
(a) You had the correct integral, but didn't finish computing it.
(b) Your initial amount and number of people who exited were correct. However, the number or people who entered was not. For the amount of people who entered, you evaluated r(300), but this is the rate of people entering at t=300. The amount of people entering is the integral of r(t) from t=0 to t=300.
(c) and (d) Both of these required understanding of part (b).

Problem 2 [1 point earned out of 7 possible]
(a) Your work was correct, but you lost a point for not including the units of p'(25) in your interpretation. The units of p'(25) are millions of cells per cubic meter, per meter.
(b) Your integral wasn't quite correct. It should have been the area (3) times the number of millions of cells per unit area (which would be the integral of p(h) from h=0 to h=300).
(c) This required understanding of part (b).

Problem 3 [7 points earned out of 9 possible]
(b) Your approach was correct, but you only needed to compute the integral from x=1 to x=6. This would have been split up into just two integrals, the integral on [1,3] and the integral on [3,6]. You included additional integrals that were not needed (maybe you were trying to calculate the total area shown).
(d) You had the right point of inflection, but you didn't really explain how you got it. For your explanation, you said that the point of inflection is where f(x) changes concavity, but how did you determine this from the given graph? You'd need to explain that f'' is represented by the slope of the graph, and the slope changes sign at x=4.

Problem 4 [4 points earned out of 9 possible]
(a) Your work was correct, but you lost a point for not including the units of H'(6) in your interpretation. The units of H'(6) are meters per year.
(b) You needed to find an interval where the average rate of change was 2. Then, the MVT would guarantee a point "c" within that interval such that H'(c)=2. The interval [3,5] would have worked for this.
(d) For this problem, you needed to find dG/dt at x=50. You found dG/dx at x=50. To compute dG/dt, you'd use the chain rule: dG/dt = dG/dx * dx/dt. A detailed solution is available in the rubric.

Problem 6 [5 points earned out of 7 possible]
(a) Your method was correct, but incomplete. After you find the radius of convergence, you still need to check the endpoints (in this case, x=-3 and x=3) to determine whether they should be included in the interval. In this case, the function converges for x=3 by the alternating series test, so the final result is (-3,3]. A detailed solution is available in the rubric.