HONORS PRECALCULUS

AKS LIST

 

DESCRIPTION:  This course is a more in depth study of the topics covered in Advanced Algebra with a greater emphasis on preparation for calculus and applications in statistics.  Problem situations include examples from business and finance, economics, engineering and technology, science and medicine, and environmental issues.  Open-ended explorations and investigations provide challenging opportunities for students to move from concrete to abstract levels of understanding.

 

ACADEMIC KNOWLEDGE AND SKILLS:

Curricular goals interwoven throughout the mathematics program are that students will:

            learn to communicate mathematically (QCC)

            learn to use mathematics in their daily lives (QCC)

            become proficient with appropriate computational tools and techniques (QCC)

            learn to reason mathematically (QCC)

            become mathematical problem solvers (QCC)

These goals will provide the direction for assessment and instruction. Attainment of these goals is facilitated by the students’ demonstration of the following Academic Knowledge and Skills (AKS).

 

Chapter P Prerequisites (pp. 1-71):  This chapter will be incorporated into chapters 1-4.

                                                                                                                                                        

Chapter 1 Functions and Their Graphs (pp. 73-134)

·        fit and model linear and nonlinear curves to data (QCC) (MAPC_B2001-12)

·        translate among tabular, symbolic and graphical representation of functions (MAPC_C2001-13)

·        find and graph compositions of functions (QCC) (MAPC_C2001-15)

·        find and graph inverses of functions (QCC) (MAPC_C2001-16)

·        graph and model piecewise functions (QCC) (MAPC_C2001-18)

·        (revised) graph and analyze algebraic and transcendental functions (QCC) (MAPC_2001-19)

·        analyze curves with respect to intervals of increase/decrease, end behavior, and horizontal, vertical and oblique asymptotes (QCC) (MAPC_E2001-27)

 

Chapter 2 Polynomial and Rational Functions (pp. 135-214)                                                     

·        develop algorithms and analyze functions using the Fundamental Theorem of Algebra (QCC) (MAPC_C2001-14)

·        analyze curves with respect to intervals of increase/decrease, end behavior, and horizontal, vertical and oblique asymptotes (QCC) (MAPC_E2001-27)

·        fit and model linear and nonlinear curves to data (QCC) (MAPC_B2001-12)

·        (revised) graph and perform operations with complex numbers (QCC) (MAPC_C2001-21)

 

Chapter 3 Exponential and Logarithmic Functions (pp. 215-282)                                             

·        (revised) solve, graph and model exponential and logarithmic equations and functions (QCC) (MAPC_C2001-17)

·        fit and model linear and nonlinear curves to data (QCC) (MAPC_B2001-12)

 

Chapter 4 Trigonometric Functions (pp. 283-374)                                                                      

·        apply circle and angle relationships (QCC, SAT I) (MAPC_A2001-1)

·        apply special right angle triangle relationships (QCC, SAT I) (MAPC_A2001-2)

·        develop, graph and apply the six trigonometric functions (QCC) (MAPC_A2001-3)

·        explore and apply properties of circular functions (QCC) (MAPC_A2001-5)

·        graph and model circular functions (QCC) (MAPC_A2001-8)

·        apply transformations to graphs of circular functions (MAPC_A2001-9)

·        (revised) solve, graph, and evaluate trigonometric inverses (QCC) (MAPC_A2001-10)

·        fit and model linear and nonlinear curves to data (QCC) (MAPC_B2001-12)

 

Review and Exams

 

Chapter 5 Analytic Trigonometry (pp. 375-426)                                                                         

·        solve trigonometric equations and verify trigonometric identities (QCC) (MAPC_A2001-7)

 

Chapter 6 Additional Topics in Trigonometry (pp 427-486; 739-744)                                       

         *Section 10.6 should be taught before Section 6.5)

·        (revised) apply laws of sines and cosines and determine area of any triangle (QCC) (MAPC_A2001-4)

·        represent complex numbers in trigonometric form (MAPC_A2001-6)

·        perform vector operations algebraically and geometrically (QCC) (MAPC_F2001-29)

·        (revised) graph and apply two- and three-dimensional vector problems (QCC) (MAPC_F2001-30)

 

Chapter 11 Analytic Geometry in Three Dimensions (pp. 769-804)                                         

·         perform vector operations algebraically and geometrically (QCC) (MAPC_F2001-29)

·         graph and perform two- and three-dimensional vector computations (QCC) (MAPC_F2001-30)

 

Chapter 7 Systems of Equations and Inequalities (pp. 487-534)                                               

      *Gaussian elimination, partial fractions, and linear programming are optional topics.

·         graph and analyze both linear and nonlinear systems (QCC) (MAPC_C2001-20)

 

Chapter 8 Matrices and Determinants (pp. 551-616)                                                                

·        (revised) apply sums, products, determinants and inverses of matrices (QCC) (MAPC_G2001-31)

 

Chapter 9 Sequences, Series, and Probability (pp. 617-663; 839-840; 843-845)                      

·         use mathematical induction (QCC) (MAPC_D2001-23)

·         (new) analyze arithmetic and geometric sequences and series and apply the Binomial Theorem (QCC) (MAPC_D2003-1)

 

Chapter 10 Topics in Analytic Geometry (pp. 695-738)                                                             

      *Parametric equations and rotation of axes are optional topics.

·         identify and compare conic sections and sketch their graphs (MAPC_F2001-28)

·         (revised) solve and graph polar equations (QCC) (MAPC_A2001-11)

 

Optional Topics (project), Review and Exams

 

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