Geometry/Algebra II Honors: Goals and Course Outline

 

 

DEPARTMENT: Mathematics                                         DATE: 2007-2008

COURSE TITLE: Geometry/Algebra II Honors             COURSE NUMBER:  5250

o YEAR                                                                    QPA: 4.5

o SEMESTER                                                           CREDITS: 5

 

 

TEXTBOOK: (Title, Author, Publisher, Edition)

McDougal Littell Geometry (Both print and electronic editions)Larson, Boswell, Kanold, & Stiff, McDougal Littell Inc., 2007

 

McDougal Littell Algebra 2, Larson, Boswell, Kanold, & Stiff, McDougal Littell Inc., 2001

 

MATERIALS USED:  TI-84 Plus graphing calculators, IBM ThinkPad, supplementary

      materials as supplied by McDougal Littell

 

GOALS:

1.      To complete a comprehensive Geometry course that began in Freshman year.

2.      To provide a comprehensive honors Algebra II course in preparation for Honors Precalculus.

3.      To reinforce the studentsí understanding of patterns, relations, and functions, and the use of symbolic algebra to represent and explain mathematical relationships in the mathematical models they design.

4.      To prepare students for the Math portions of the SAT.

5.      To demonstrate the relevance of algebraic problem solving to the real world.

6.      To use graphing calculators and modern computer graphics to analyze, solve, visualize, and clarify mathematical concepts.

 

 

CONTENT OF COURSE:

 

FIRST SEMESTER

 

Unit 1:  Right Triangles and Trigonometry

1.      Properties of special right triangles (30-60-90 and 45-45-90 triangles)

2.      Trigonometric ratios of an acute angle and their use to solve right triangle problems in real-life applications

 

Unit 2:  Quadrilaterals

  1. Interior and exterior angle measures of polygons
  2. Properties of parallelograms
  3. Properties of rhombuses, rectangles, squares, trapezoids, and kites
  4. Special quadrilaterals

 

Unit 3:  Properties of Circles

      1.   Tangents, chords, and secants of circles

      2.   Properties of arcs, chords, inscribed angles, and inscribed polygons

     

 

Unit 4:  Measuring Length and Area

      1.  Areas of triangles, parallelograms, rectangles, rhombuses, and kites

      2.  Area and circumference of a circle

      3.  Arc lengths and areas of sectors in a circle

      4.  Areas and perimeters of regular polygons

      5.  Geometric probability

 

 

Unit 5:  Surface Area and Volume of Solids

      1.  Finding the surface area of prisms and cylinders

      2.  Calculating volumes of pyramids and cylinders

 

 

Unit 6: Equations and Inequalities

1.      Solving linear inequalities

2.      Solving absolute value equations and inequalities

3.      Using absolute value equations to solve real life problems

 

Unit 7: Linear Equations and Functions

1.      Functions and relations including domain and range

2.      Graphing linear equations using different methods

3.      Slope and rate of change

4.      Writing equations of lines

5.      Linear inequalities in two variables

6.      Piecewise functions

 

Unit 8: Systems of Linear Equations and Inequalities

1.      Solving linear systems graphically and algebraically

2.      Graphing and solving systems of linear inequalities

3.      Solving real-life applications using systems of equations

 

SECOND SEMESTER

 

Unit 9: Introduction to quadratic functions

1.      Introduction of quadratic functions

2.   Graphing quadratic functions

3.   Solving quadratic functions by factoring and taking square roots

4.   Introduction of imaginary and complex numbers 

 

Unit 10: Quadratic Functions

1.      Solving quadratic functions by completing the square and the quadratic formula

2.      Using the discriminant to describe the number and nature of the roots of a qua-dratic function

3.      Modeling quadratic functions

4.      Real applications using quadratic functions

5.      Finding the domain of quadratic inequalities

 

Unit 11: Polynomial Functions

1.      Using properties of exponents

2.      Evaluating and graphing polynomial functions

3.      Multiplying polynomials

4.      Factoring and solving polynomial functions

5.      The remainder and factor theorems

6.      Finding rational zeros

7.      Using the fundamental theorem of algebra

8.      Real applications of polynomial functions

 

Unit 12: Powers, Roots, Radicals and Operations of Polynomial Functions

      1.   Radical form and exponential form

      2.   Radicals, including those with a root index of three or higher

      3.   Operations of polynomial functions, including composition of functions

      4.   Inverse of a function

      5.   Radical equations

 

Unit 13: Exponential and Logarithmic Functions

      1.   Graphs of exponential growth and decay functions

      2.   Logarithmic functions and their graphs

      3.   Properties of logarithms

      4.   Exponential equations and logarithmic equations

      5.   The change of base formula

 

Unit 14: Rational Expressions and Circles  (If time permits)

      1.   Operations of rational expressions

      2.   The LCD of the rational expressions

      3.   Complex fractions

      4.   Solving rational equations

      5.   Equations of circles and graphs

 

 

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