Preparing for a calculus course – be it an AP or a general class – requires building a strong foundation in various mathematical concepts. Confidence in your understanding of the previous material (trigonometry, algebra II, geometry) and ability to apply this knowledge to novel problems is one of the most important skills that you will need. Calculus builds upon past concepts and requires proficiency in them in order to properly understand the new material. The following is a brief summary of what you can do in order to be well prepared for when your course begins.
Mastering prerequisites is essential for succeeding in a calculus course. Below is a list of key concepts that you will need in calculus, as well as what mastery entails. Studying I Aced Calculus flashcards and completing the practice questions in the “Prerequisites” deck in IAC app will cover all of these categories.
The foundations for this course are the basic mathematical principles that underlie everything done in calculus. It is critical that there are no holes in your knowledge of these concepts. They include order of operations, proportions, linear and quadratic equations, systems of equations, multi-step word problems, polynomial expansion, factorization, simplification and formula manipulation.
Functions are one of the most fundamental concepts in calculus and advanced mathematics in general. As a way to define relations between numbers, functions will naturally appear everywhere in a course that seeks to understand and model how things change in the real world by analyzing changes between variables. Functions topics include definition of a function, finding domains and ranges, sketching and analyzing graphs of functions, function compositions, piecewise functions, linear, quadratic and polynomial functions, even and odd functions, inverse functions, writing relations as functions.
Many calculus concepts have an intuitive geometric interpretation that is useful when solving problems. The derivative, for instance, is the slope of the line tangent to a function at a point, just as the integral is the area underneath a curve. Applications of Differentiation and Applications of Integration, often have problems that need formulas from the geometry course. The following concepts from geometry will be useful to review in preparation for a calculus course:, areas and volumes of geometric shapes, surface area, Pythagorean theorem, distance between points, missing measurements, similar triangles, basic trigonometric functions, trigonometry word problems, circles and sectors of circles, equations of circles.
As one of the most common precalculus topics, trigonometry is an integral aspect of calculus (pun not intended). In calculus, you will encounter trigonometry in its geometric context, as well as trigonometric functions being manipulated and studied. The topics that will be useful to review are degree to radian conversion, unit circle, calculating trigonometric functions at unit circle angles, trigonometric ratios, graphs of sin, cos and tan, simplifying trigonometric expressions, solving trigonometric equations, word problems, finding trigonometric functions from graphs, and identifying the domain, range and period of trigonometric functions.
Exponential growth and decay are some of the most frequent and fundamental modes of change, and by extension, fundamental to calculus. Although you may have explored algebraic growth and touched upon exponential change, the latter topic will be further fleshed out in calculus. Topics to review include arithmetic of logarithms, quantitative evaluation of logarithms, properties of exponents, exponential equations, logarithmic equations and inequalities, exponential and logarithmic functions, inverses of exponential and logarithmic functions, graphing exponential and logarithmic functions, growth and decay word problems.
Exponents and Logarithms Solutions
The AP Calculus BC course is reasonably more rigorous than the AP Calculus AB course. AP Calculus BC covers all the same topics as AP Calculus AB as well as several extra topics, such as infinite series, parametric equations, polar coordinates, vectors, additional techniques of integration and a few other topics – link to College Board website. The additional topics useful to review for AP Calculus BC course include arithmetic sequences and series, geometric sequences and series, arithmetic and geometric series word problems, partial fraction decompositions, conversions between Cartesian and polar coordinates and functions, parametric functions, graphing polar and parametric functions, basic vector arithmetic, and vector equations.
Reviewing future course material, though it may seem daunting, can help you gain the understanding of the layout of the course, key concepts to focus on, and better understand material in class. You will feel more confident and will grasp more in class if you have already seen the material before and have a vague understanding of it.
Key Strategies:
Before diving into your calculus course, it’s crucial to establish a gameplan to stay organized and focused. Consider the following steps to create a solid foundation for your studies:
Good luck! Let’s Ace Calculus together.
