Calculus lesson plans
Calculus BC Topic Outline in the AP Calculus Course Description. 3, 6 teaches all topics associated with Derivatives as delineated in the Calculus BC Topic to use the calculator to investigate concepts such as limits by using the trace and table operations to make conjectures about the answers. Parametric relations. Learn AP® Calculus AB for free—everything you need to know about limits, derivatives, and integrals to pass the AP® test. of implicit relations: Applying derivatives to analyze functions Calculator-active practice: Applying derivatives to analyze The Course challenge can help you understand what you need to review. Limits. 5. • Differential Calculus. 7. • Integral Calculus. SOME USEFUL FORMULAS. 16 Advanced Placement Calculus AB Exam tests students on introductory differential and integral calculus . d) Relationships between the graph of y = ƒ(x) and . The numerical notation for higher order derivatives is represented by.
The derivative is also investigated in the relationship between position, velocity, acceleration and jerk. Inverse functions are addressed with particular attention given to the natural exponential function as the inverse of the natural logarithm function.
The derivatives of the natural exponential function and the natural log function are given. Logarithmic and exponential functions of any base are also given along with their corresponding derivatives. Various derivative techniques are developed for natural logarithm functions techniques for rational form functions, including trigonometric. Derivatives Days Section Topic Concepts 2 3. VG Graphical T www. VGN Supplement Theorem 5. AP Calculus BC 4. This unit continues the application of derivatives.
First and second derivatives are used to determine for a given function the critical values, intervals of increase and decrease, relative maxima and minima, points of inflection, and intervals concave up and concave down.
This application is done with and without graphing calculators. Included with this application is the examination of the relationships of the graphs of a function, the graph of its 1st derivative, and the graph of its 2nd derivative and through the use of tables.
The very useful and important derivative application of solving optimization problems, as well as linear approximations, differentials, and related rates are in this unit. The definite integral is developed by first examining estimates of the areas of plane regions as sums of rectangles constructed by using a partitioning of an interval and the right, left, midpoint or any point of the partition. The definition of a definite integral can then be given as a limit to an infinite Riemann Sum, the exact area of the plane region.
The Second Fundamental Theorem is also given. The main applications here are areas of simple plane regions, and average-value-of-a-function problems. This unit also includes estimation of plane regions by using trapezoidal approximation.
T, N Graphing calculator: This unit introduces slope fields, and the solving of differential equations, leading to the concept of an antiderivative. Indefinite integrals are solved through various techniques including u du substitution and pattern recognition.
Integral techniques are expanded to include integration by parts, trig identities including using identities to find integrals of powers of trig functionsand partial fractions. Exponential growth and decay model is developed from integration of separation of variables. The Logistic Growth model is also included. Slope fields SI 3. This unit involves the interpretation of the integral as an accumulator and applications of finding areas and volumes. The definite Integral is used to find the areas of regions between curves using all types of functions.
These are areas on an interval, areas between curves including curves with more than two intersections, also incorporating change of axis.
AP Calculus AB-BC Practice Questions | Albert
The next application is volume beginning with three diminution shapes also knows as cross sections. Also included are volumes of rotation using the disk, and washer method incorporating the change of axis.
AP Calculus BC 9. This unit starts with developing the concepts and notation of sequences followed by what it means for the sequence to converge or diverge. Attention is given to types of sequences such as bounded, monotonic and oscillating. Limits are briefly reviewed focusing on indeterminate forms and a reminder of the methods used for improper integrals is also included. Previous math courses have dealt with part of these concepts.
The main purpose for the time spent dealing with the above is to set a foundation for the study of Series. The concepts of Series and the notation can now be developed and explained with the goal that students understand a Series is a sequence of partial sums.
Whether or not this sequence of partial sums has a limit determines the convergence or divergence of the Series. This is begun by examining geometric and telescoping Series and the decision process used for convergence and divergence. The repeating decimal is a primary example for a convergent geometric Series. Other Series are then addressed such as harmonic and p-series and alternating including alternating series estimation.
Various test for convergence and divergence are developed and used including the integral test, p-series convergence, direct comparison, limit comparison, alternating series test, ratio, and root test. Next is a transition to polynomial approximations of elementary functions and the Taylor and MacLaurin Series. Use of the TI — 89 graphing utilities is indispensable at this juncture for students to understand the approximation process.
We then address general power series of functions and the examination of their domains, convergence, and radii and intervals of convergence. The rest of this unit goes into the manipulation of power series and differentiation and integration of power series. We also evaluate definite integrals of continuous functions and bounded functions with a finite number of discontinuities on finite close intervals.
Robinson, Jennifer / Limits, Continuity, & Definition of a Derivative
In this unit we analyze calculus in three kinds of two variable contexts, parametric, vector, and polar to analyze new kinds of curves. We also analyze motion that does not proceed along a straight line.
This can be done using single variable calculus in some different and interesting ways. The focus of the course is neither manipulation nor memorization of a predetermined list of functions, curves, theorems, or problem types.
Thus, although students must deal with manipulation and computational competence, they are not the sole purpose of this course. Technology will be used throughout the course to reinforce the relationships among the various representations of functions, to confirm written work, to encourage experimentation, and to assist in interpreting results using tables and graphs.
Through the use of connections between derivatives, integrals, limits, approximations, applications with modeling, improper integrals and partial fractions, infinite series, parametric, vector, and polar functions, the course becomes a connected whole rather than a collection of unrelated topics.
Most colleges grant two semesters of credit 8 semester hours to students who successfully complete this course and pass the examination with a score of 3 or higher.
Prior Knowledge All students will be expected to be familiar with all of the following topics: All of the above will be tested in conjunction with topics associated with infinite series, improper integrals, partial fractions, and infinite series. Calculation of Grades Students will be tested approximately every 2 to 4 weeks. Each test will consist of 4 components. Component 1 will be a timed multiple choice test of approximately 12 questions. This component is non-calculator active.
Component 2 will be a timed multiple choice test of 8 questions. This component is calculator active.
Component 3 will consist of 1 or 2 essay questions show your work consisting of multiple parts that must be completed in minutes.