I passed the CLEP Calculus exam after about two months of preparation. Was it tough? Yes. But it was also completely doable. No matter what background you have in math, if you enter with the right mindset, plan your studying well, and make good use of resources, you can succeed.
If you haven’t done any math in more than a decade (the position I was in when I started studying for this exam), you’ll probably want to review algebra and trigonometry. For instance, you’ll need to know things like:
I’d forgotten such things. If you’re in that same boat, and you’re overwhelmed and starting to feel like maybe you ought to just cough up money and take a calculus course, don’t give up yet! There are a ton of free resources out there for learning all sorts of math. On Khan Academy, for instance, you can learn all levels of math up to and beyond basic calculus.
To assess where your math skills are, and to alleviate any fear you might have about calculus, I'd suggest starting out by reading Calculus Made Easy. To give you a taste, here’s how the book starts: “The preliminary terror, which chokes off most fifth-form boys from even attempting to learn how to calculate, can be abolished once for all by simply stating what is the meaning--in common-sense terms--of the two principal symbols that are used in calculating.” Thompson's book retains this tone throughout, managing to be both accessible and funny at the same time. After reading a few short chapters, I understood the power rule, product rule, and quotient rule (all important in calculus).I also realized, however, that although I wasn't having trouble with the calculus concepts, I was making basic errors in things like multiplying fractions. So, with regret, I put aside calculus and started reviewing algebra.
If you believe yourself capable, it’s likely that you’ll achieve your goal. Approach calculus as an equal, so to speak, someone you could win against if challenged. It might take a lot of work; it might be humbling, but it will be worth it in the end.
One of the first--and most important--steps is to hone your ability to focus. A book that helped me with this was Deep Work by Cal Newport. It’s all about how to block out distractions, schedule time for serious work, and ramp up efficiency.
Efficiency is definitely your friend on this journey. It’s much better to finish the CLEP earlier rather than later, not just to free up your time for other pursuits but also to give you a chance to retake the test if necessary. There’s a three-month waiting period before you can retake it, if you fail. Trick your brain, if you must, into believing it’s vital that you pass the test, and quickly. Make sure your brain is working with you and not against you. I've gone through stages where I felt down because there was so much more material to cover, because it felt impossible to finish within my timeline, and because I really wanted to be doing things other than studying calculus full-tilt. But whenever I'd drift into one of those moods, my brain was working against me. I had to train myself to snap out of it immediately, or else I'd lose valuable time and productivity. Make sure that the voice in your head is an encouraging, positive one. It all comes back to believing in yourself.
Be ambitious. Be systematic. Work backwards. Set specific goals. You could start by going to the College Board’s website for the Calculus CLEP exam to find out exactly what you’re going to be tested on. That way, you have a checklist; you’ll know how much is left to study and what you already understand. After you get far enough into your studying, start taking practice tests and doing practice questions. Know your goal for each week so that you can assess how on target you are.
For me, at the end of February (I started learning Calculus at the end of January), I still needed to learn about half of the topics, and on top of that I needed to do lots more practice problems, take practice tests, and learn how to use the online calculator that's provided during one section of the exam. I was behind schedule mostly because I had prioritized studying for classes I was getting graded on. Knowing that the only way I'd pass the test by the end of March was to set ambitious goals, I hunkered down and figured out a plan of study.
In the first week, I planned to finish learning about each remaining topic. That ended up taking me the first week and a half, so during the rest of my second week I ramped up the intensity and did as many practice problems as possible, focusing first on limits and integration.
During the third week, I continued doing practice problems, focusing on any area that I was consistently making mistakes in. For instance, I did a lot of u-substitution and practical applications problems. I also made flashcards of things like the derivative of arctan, the average value of a function on an interval, and so on. I’d review them at least twice a day, sometimes more, making use of random bits of down time (like waiting for water to boil to make pasta). I also finally went ahead and scheduled my exam during the third week.
In the last week before the exam, I started doing practice tests. I reviewed any problems I got wrong, and I made flashcards with the problems on one side and a breakdown of how to complete them on the other. I made more flashcards about concepts that I suspected would be important on the exam (such as inflection points and the concavity of graphs). I also set aside a few hours one day to practice calculator questions. Those couple hours proved invaluable, as without them, I would have missed several questions on the calculator portion--not from not knowing calculus but rather from not knowing how to access certain functions on the calculator.
All in all, by the time the morning of the test day rolled around, I felt pretty good. Nervous, but confident. I wouldn’t worry if you’re not getting every single question right on the practice tests, or if there’s one small concept (like linearization, say) that you’re still fuzzy on. The questions are weighted, and though I don’t know how they calculate the scores, I’m pretty sure that if you understand even half of the questions very well, then you’ll be fine. Remember, you don’t have to ace this test to pass it. You just have to truly understand the material. And to do so, I’d recommend the resources listed above.