Taking advanced placement, or AP, calculus in high school can be highly advantageous to students considering careers in technical fields such as engineering or computer science. AP calculus courses require a full year of study, culminating in an exam that enables students with passing scores to skip a semester or quarter of college calculus at many schools. Students taking AP calculus usually do so during their senior year, although some advanced students take it earlier.
Obtain Essential Materials
As with any high school course, required materials may differ from teacher to teacher but typically include a notebook or loose-leaf paper in a three-ring binder, grid paper, pencils and erasers. The most notable -- and most expensive -- item required for AP Calculus is a graphing calculator. Because some of the questions on the AP exam cannot be answered within a reasonable amount of time without a graphing calculator, students use these calculators on a regular basis throughout the course. The AP Calculus Development Committee provides a list of approved graphing calculators. However, consult your course's teacher before making a purchase because he or she may prefer specific types, and some districts loan students calculators for the year free of charge.
In order to succeed in AP calculus, students must have a firm grasp of the concepts taught in elementary algebra, which is usually called Algebra 1, as well as intermediate algebra, often referred to as Algebra 2. Two overarching elementary algebra topics are critical to AP calculus: equations and graphing. Students must be able to solve all of the major types of equations, as well as inequalities, including those involving factoring, exponents, radicals and fractions. They must be able to graph linear and quadratic functions and identify domains, ranges, minima and maxima. Topics from intermediate algebra directly correlating to AP calculus include function composition and decomposition, exponential functions and logarithmic functions.
AP calculus students must have solid understanding of concepts from trigonometry, as they resurface in calculus with considerable frequency. Students should be familiar with the graphs of and relationships between the six functions -- sine, cosecant, cosine, secant, tangent and cotangent. They should know how to convert between degrees and radians and the polar coordinate system. Students entering AP calculus also need to be comfortable working with reciprocal and Pythagorean identities, the unit circle, inverse and circular functions, vectors, conic sections and complex numbers.
Preview the Course
As you progress through the course, peruse upcoming topics in your textbook to get acquainted with the basic terminology and notation. Many of the symbols used in calculus will be completely novel to students -- that is, they will not have previously encountered these symbols in pre-calculus, trigonometry or algebra. The first concepts explored in AP calculus are limits, continuity and approximations. Next, students learn to find derivatives and their opposites, integrals. Other major topics include the fundamental theorem of calculus, second derivatives, Riemann sums, partial sums and series.