Precalculus. Virginia Standards of Learning for Mathematical Analysis

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1 A Correlation of Precalculus (Blitzer) 4th Edition Virginia Standards of Learning for Mathematical Analysis February 2009

2 INTRODUCTION This document demonstrates how, meets the objectives of the Virginia Standards of Learning and Curriculum Framework for Mathematical Analysis. Correlation page references are Student Edition and Instructor s Edition Manual and are cited at the page level. Blitzer creates intriguing applications that show students the relevance of math. Appealing to a wide range of interests and majors, the program s applications captivate students imagination with his passion for integrating math in worlds of contemporary society, culture, art, and science. Features: Clear and accessible presentation ensures that students can follow the book when they get home from class. o Voice balloons offer the support and guidance of a teacher s voice. These specific annotations clarify procedures and concepts, mimicking what a teacher would say in class when translating the math into plain English. o See it, Hear it, Try it is the consistent format of every textbook example. Extensive exercise sets at the end of each section are organized into six categories: Practice Exercises, Application Exercises, Writing in Mathematics, Technology Exercises, Critical Thinking Exercises, and Group Exercises. This variety lets teachers create well-rounded homework assignments, while holding students interest with an ongoing selection of novel applications. Practice Plus Problems are more challenging problems that test conceptual understanding by requiring students to combine skills and to revisit key concepts in order to solve. New to this edition are Make Sense? Classroom discussion exercises that contain four critical thinking problems that test for conceptual understanding. This is an opportunity for students to express their opinions and for teachers to provide feedback on those thoughts. Assessment includes Mid-Chapter Checkpoints, Cumulative Review Exercises at the end of each chapter, and End-of-chapter tests. These ensure that students remember previously learned material, keeping the fundamental skills and concepts fresh in their minds. Integrated study aids help students make the most of their time outside of the classroom. o Chapter Test Prep Videos (included with the Student Edition) contain worked-out solutions to every exercise in every chapter test. A teacher walks students through all examples step-by-step, allowing students to pause and watch again as needed. o Study Tip boxes appear throughout the book. These offer suggestions for problem solving, point out common student errors, and provide informal tips and suggestions. o Technology boxes illustrate the many capabilities of graphing utilities that go beyond just graphing. This document demonstrates the success students will achieve by using Precalculus by Blitzer. 2

3 Mathematical Analysis The standards below outline the content for a one-year course in Mathematical Analysis. Students enrolled in Mathematical Analysis are assumed to have mastered Algebra II concepts and have some exposure to trigonometry. Mathematical Analysis develops students understanding of algebraic and transcendental functions, parametric and polar equations, sequences and series, and vectors. The content of this course serves as appropriate preparation for a calculus course. Graphing calculators, computers, and other appropriate technology tools will be used to assist in teaching and learning. Graphing utilities enhance the understanding of realistic applications through modeling and aid in the investigation of functions and their inverses. They also provide a powerful tool for solving and verifying solutions to equations and inequalities. MA.1 The student will investigate and identify the characteristics of polynomial and rational functions and use these to sketch the graphs of the functions. This will include determining zeros, upper and lower bounds, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points. Graphing utilities will be used to investigate and verify these characteristics. MA.2 The student will apply compositions of functions and inverses of functions to real-world situations. Analytical methods and graphing utilities will be used to investigate and verify the domain and range of resulting functions. MA.3 The student will investigate and describe the continuity of functions, using graphs and algebraic methods. MA.4 The student will expand binomials having positive integral exponents through the use of the Binomial Theorem, the formula for combinations, and Pascal s Triangle. MA.5 The student will find the sum (sigma notation included) of finite and infinite convergent series, which will lead to an intuitive approach to a limit. MA.6 The student will use mathematical induction to prove formulas and mathematical statements. SE/IE: , , 271, 301, , , , , , SE/IE: , 231, , Additional opportunities to address this standard can be found on the following pages: SE/IE: 228, 230, 241 SE/IE: 303, , SE/IE: , 1030, 1032, Additional opportunities to address this standard can be found on the following pages: SE/IE: SE/IE: , , , , , 1030, 1032, 1034 SE/IE: , 1003, 1030, 1032,

4 MA.7 The student will find the limit of an algebraic function, if it exists, as the variable approaches either a finite number or infinity. A graphing utility will be used to verify intuitive reasoning, algebraic methods, and numerical substitution. MA.8 The student will investigate and identify the characteristics of conic section equations in (h, k) and standard forms. Transformations in the coordinate plane will be used to graph conic sections. MA.9 The student will investigate and identify the characteristics of exponential and logarithmic functions in order to graph these functions and solve equations and real-world problems. This will include the role of e, natural and common logarithms, laws of exponents and logarithms, and the solution of logarithmic and exponential equations. MA.10 The student will investigate and identify the characteristics of the graphs of polar equations, using graphing utilities. This will include classification of polar equations, the effects of changes in the parameters in polar equations, conversion of complex numbers from rectangular form to polar form and vice versa, and the intersection of the graphs of polar equations. MA.11 The student will perform operations with vectors in the coordinate plane and solve realworld problems, using vectors. This will include the following topics: operations of addition, subtraction, scalar multiplication, and inner (dot) product; norm of a vector; unit vector; graphing; properties; simple proofs; complex numbers (as vectors); and perpendicular components. MA.12 The student will use parametric equations to model and solve application problems. MA.13 The student will identify, create, and solve real-world problems involving triangles. Techniques will include using the trigonometric functions, the Pythagorean Theorem, the Law of Sines, and the Law of Cosines. SE/IE: , , , 1083, 1086 SE/IE: , , , , SE/IE: 19-22, 28-30, 41, 43-45, , 133, , , , , , , 457, 726, 949, 1035, 1086 SE/IE: 676, 679, , 684, , , 722, 724, 726 SE/IE: , 696, , , , , 872, 950, 1086 SE/IE: , , 948 SE/IE: , , 564, , 570, , , 642, , , , , 685, 724, 726,

5 MA.14 The student will use matrices to organize data and will add and subtract matrices, multiply matrices, multiply matrices by a scalar, and use matrices to solve systems of equations. SE/IE: , , , , , , , , 949, 1035,

Mathematics. Mathematics

Mathematics. Mathematics Mathematics Program Description Successful completion of this major will assure competence in mathematics through differential and integral calculus, providing an adequate background for employment in