![]() ![]() The AP Calculus BC exam assumes that the calculators students use can do four things: graph functions, solve for functions’ zeros, calculate a function’s derivative, and calculate a definite integral’s value. The second half of the multiple-choice section lasts for fifty minutes and consists of seventeen questions during this section, students should use graphing calculators, as some questions will require them. The first part of the multiple-choice section consists of twenty-eight questions and lasts for fifty-five minutes, and during this section, students may not use calculators. Each of these sections is weighted equally, and each is divided into two parts. The AP Calculus exam lasts for three hours and fifteen minutes and consists of a 45-question, 105-minute multiple-choice section and a six-question, 90-minute free-response section. Students who successfully complete AP Calculus BC courses are invited to take the AP Calculus BC exam to demonstrate what they have learned and potentially earn college credit. Students thus do the work of two introductory calculus classes in one AP course when taking AP Calculus BC, which makes for a course that is extremely challenging, but potentially very rewarding. Because of this, colleges usually grant students credit for whatever course they offer that typically follows their most basic introductory calculus courses. AP Calculus BC courses pertain to single-variable functions, covering all of the information taught in AP Calculus AB courses in addition to more advanced topics. In particular, they should have encountered and mastered advanced concepts in basic functions, analytic geometry, trigonometry, and algebra before attempting to take an AP Calculus course. ![]() Before taking AP Calculus, students should have successfully completed four years of high school math. After reading this guide, you’ll feel less apprehensive about AP Calculus BC and ready to take on its most challenging topics.ĪP Calculus BC is a course that many high school students take in order to earn college credit. If you’re nervous about missing crucial information in your AP Calculus class, need to figure out how the AP Calculus BC exam is structured, or want to find some excellent free resources you can use while studying for AP Calculus BC, you’ve come to the right place. ![]() And above all, know which tools apply in each situation.AP Calculus BC: even the name of the course may strike fear into many students while AP Calculus AB tests easier (“A”) and intermediate (“B”) concepts, AP Calculus BC begins with the intermediate (“B”) concepts and tests the most difficult (“C”) concepts found in an introductory calculus class.Memorize the derivatives of the special functions.Know your basic rules, especially the Chain Rule.Nevertheless, the majority of problems involving derivatives do tend to fall into these basic formats. The five problems above represent just a small sampling of what you’ll find on an AP Calculus AB or BC exam. At what value of x is the slope of the tangent line to g( x) equal to 3? SolutionĪgain, the slope of the tangent line is equal to a derivative value. You’ll need both the Product and Chain Rules for this one. Therefore this function has no inflection points. Use Quotient Rule to help find the second derivative.Īfter simplification, we find that the second derivative is never equal to 0 and never undefined. Don’t forget to rewrite your radical as a power and use Chain Rule. Of course, you must take the first derivative first. You can find inflection points by taking the second derivative. Problem 3įind all inflection points of the curve defined by. V( t) = x '( t) = cos( cos( 4 t ) ) ( -sin( 4 t ) ) (4)Īt time t = π/8, the velocity is equal to: Be careful - we need two applications of the Chain Rule for this one! Findįind velocity by taking the derivative of the position function. ![]() The position of a particle moving along the x-axis at time t is x( t) = sin( cos( 4 t ) ), for 0 ≤ t ≤ π. Then you can find the slope and the equation of the tangent line. Here, we have to use the Power Rule and Sum/Difference Rule. To find a tangent line, first take the derivative. Problem 1įind The tangent line to the curve f( x) = x 4 + 3 x – 10 at the point (1, -6). Now let’s take a look at a few problems involving common derivatives that are modeled after actual AP Calculus problems. Derivatives of inverse trigonometric functionsĬheck out Calculus Review: Derivative Rules and Derivatives on the AP Calculus AB & BC Exams: A Refresher for more. ![]()
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