Radnor High School s3

Radnor High School Course Syllabus

Calculus 452

Credits: 1 Grades: 12 Unweighted Prerequisite: Honors Precalculus or Length: Year Trigonometry/Discrete Math with a “B” Format: Meets Daily or teacher recommendation

Overall Description of Course Traditionally, calculus has been the mathematics course taken by college freshmen. There is currently a growing realization that students need to be better prepared in mathematics and science. This need arises because of the ever-increasing role of computing in all disciplines. This course is focused on the student’s understanding of the concepts of calculus from an intuitive point of view. Units from differential and integral calculus provide the main themes of this course, and practical applications of each area will be shown. This course is not intended as preparation for the Advanced Placement Calculus exam. While some students may be eligible for advanced standing in college calculus, all students will be prepared for a beginning college calculus course. A graphing calculator is required.

Topics Marking Period 1: Prerequisites: Solving Equations and Inequalities, Graphs of Equations, Linear Equations Functions and Graphs: Analyzing, Transformations, Combinations, Inverse Functions, Modeling Polynomial & Rational Functions: Quadratic and Higher Degree, Synthetic Division, Complex Numbers, Zeros of Polynomial Functions, Solving Rational Functions Marking Period 2: Limits & Their Properties: Preview of Calculus, Finding Limits Graphically and Numerically, Evaluating Limits Analytically, Continuity & One-Sided Limits, Infinite Limits Differentiation: The Derivative & Tangent Line Problem, Basic Rules & Rates of Change, The Product & Quotient Rules, Higher Order Derivatives, Chain Rule, Implicit Differentiation, Related Rates Marking Period 3: Applications of Differentiation: Extrema on an Interval, Rolle’s Theorem, Mean Value Theorem, Increasing & Decreasing Functions, First Derivative Test, Concavity, Second Derivative Test, Limits at Infinity, A Summary of Curve Sketching, Optimization Problems Integration: Antiderivatives, Indefinite Integration, Area, Riemann Sums, Definite Integrals, The Fundamental Theorem of Calculus, Integration by Substitution, Numerical Integration Marking Period 4: Exponential & Logarithmic Functions and Calculus: Differentiation and Integration Trigonometric Functions and Calculus: Differentiation and Integration

Common Core Standards

Understand the concept of a function and use function notation.

 F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).  F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.  F-IF.3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

Interpret functions that arise in applications in terms of the context.

 F-IF.4. For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.★  F-IF.5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.★  F-IF.6. Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★

Analyze functions using different representations.

 F-IF.7. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★ o a. Graph linear and quadratic functions and show intercepts, maxima, and minima. o b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. o c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. o d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior. o e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.  F-IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. o a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. Keystone Connections:

Student Objectives: 1. To develop the ability to think mathematically. 2. To enhance problem solving ability. 3. To utilize technology appropriately. 4. To be able to work with functions and apply them to the real world. 5. To reason and communicate mathematically. 6. Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems. 7. Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems. 8. To challenge and expand the inquisitive and logical minds of the accelerated mathematics students.

Materials & Texts MATERIALS Graphing Calculator (preferably TI-84+ model) & Appropriate Software Applications

Activities, Assignments, & Assessments ACTIVITIES Computer lab and research activities as needed.

ASSIGNMENTS Assignment sheets will be distributed periodically throughout the school year. Homework will be assigned on a daily basis. Individual assignments for each chapter can be viewed on the Mathematics Department page of Radnor High School’s web site.

ASSESSMENTS Quizzes and tests will be given each chapter to measure understanding. Homework and classwork assignments will also be graded throughout the course. Terminology As listed in topics section.

Media, Technology, Web Resources http://college.cengage.com/mathematics/larson/calculus_precalculus/1e/students/