As a math tutor, the phrase I most commonly hear is: “I don’t know how to study for math.”
Unlike other subjects, there aren’t many vocab words to memorize or books to read. Once you have the formulas down, what else can you do to prepare for your calculus test?
The age-old answer is practice.
Luckily for you, there are thousands of resources available for calculus study. High school calculus hasn’t changed much over the past few years (actually, make that decades), so everything from your current teacher’s homework assignments to AP tests from the 1990s focuses on the same exact material. Therefore, with virtually limitless access to practice problems, you should begin studying with the goal of understanding how to use the formula, rather than just memorizing it.
The when and why of a math formula is just as important as the what.
One of my favorite ways to actually do this is by making a chart that lists the formula, when to use it, an example, and where to find practice problems. You’ll fill out the chart as you study, and you might develop a separate chart for each chapter or unit. For example, it might look like this:
| Formula | When it’s used / What it’s solving for | Example | Where to find more practice |
Taylor Series: |
to approximate the value of an infinite series | Find the Taylor Series for f(x) = e^x about x = 0. | AP Exam – Calculus BC, 2001, #43
Textbook Pg 445 #60-62 |
It is also important to know how to use formulas in reverse. Consider making a second chart like this one:
| What is the question? | What do I need to solve for? | What formulas/concepts will I need? | Where to find more practice |
| A ladder 20 feet long leans against a building. If the bottom of the ladder slides away from the building horizontally at a rate of 4 ft/sec, how fast is the ladder sliding down the house when the top of the ladder is 8 feet from the ground. | the rate of the ladder sliding down
dy/dt |
Related rates
also, Pythagorean Theorem a^2 + b^2 = c^2 |
http://www.mathscoop.com/calculus/derivatives/applications/related-rates-triangle-problems.php
AP Exam – Calculus AB – 1997, #13-14 |
If you don’t know where to start, consider taking an old AP exam for practice and then check your answers (treat it like a diagnostic). Transfer the questions you got wrong (or struggled with) into the second chart. If you find that you missed a lot of questions that dealt with limits, for example, that might be the right place to start your studying. Use that information to fill in the first chart and find corresponding practice questions until you have mastered that concept.
Creating charts like these throughout the year (or during your period of study for the AP Calculus exam) will help you to identify your weaker areas and solidify your overall content knowledge.
