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11TH Grade Mathematics [Algebra 2 and Trigonometry]

TABLE OF CONTENTS
  • MAIN OBJECTIVES
  • LINEAR RELATIONS AND FUNCTIONS
    --|Properties Linear Equations
    --|Solving Systems of Equations Algebraically
    --|Linear Programming
  • MATRICES
    --|Adding and Subtracting Matrices
    --|Multiplying Matrices
    --|Matrices and Determinants
    --|Solving Systems of Equations Using Matrices
  • POLYNOMIALS AND RADICAL EXPRESSIONS
    --|Operations with Polynomials
    --|Solving Equations Containing Radicals
    --|Complex Numbers
    --|Simplifying Expressions Containing Complex Numbers
  • EXPONENT AND LOGARITHMIC FUNCTIONS
    --|Properties of Logarithms
    --|Solving Exponential Equations
    --|Growth and Decay
  • TRIGONOMETRIC FUNCTIONS
    --|Trigonometric Functions of General Angles
    --|Law of Sines
    --|Law of Cosines
    --|Trigonometric Identities
    --|Solving Trigonometric Equations
  • REFERENCES
    MAIN OBJECTIVES

    Required Textbook: A Beka Algebra 2, Work-Text, Pensacola, Florida, current edition.

    [a] The relationships among coefficients, exponents, degree and roots of equations.
    [i] Solve and explore equations using the quadratic formula, completing the square, synthetic division, and graphing.
    [ii] Classify solutions of quadratic equations through observations of graphs and through use of the discriminant.
    [iii] Write a polynomial equation when given its roots.

    [b] Systems of equations and inequalities.
    [i] Explore methods of solving systems of equations to include algebraic methods and matrices.
    [ii] Write a system of equations to solve a problem.
    [iii] Interpret by graphing, and solve systems of inequalities.

    [c] Recognize, classify, and perform operations with irrational and complex numbers.
    [i] Explore and describe the complex number system.
    [ii] Explain and apply complex conjugate methods to simplify problems.
    [iii] Perform operations with complex numbers and review radicals.

    [d] Identify and investigate relations and functions.
    [i] Determine the domain, range, roots, and inverse of a function.
    [ii] Recognize and determine graphs of linear, quadratic, absolute value, greatest integer, and piece-wise functions.
    [iii] Develop a complex coordinate plane for complex numbers (a + bi) where reals are represented on the x-axis and imaginary units are represented on the y-axis and model operations of complex numbers.
    [iv] Evaluate functions including composite functions.
    [v] Explore and investigate solutions to compound and absolute value inequalities to include interval notation.
    [vi] Use scatter plots and apply regression analysis to data.
    [vii] Illustrate and apply the relationships between exponential and logarithmic functions.
    [viii] Simplify radical, exponential, and logarithmic expressions. Solve equations involving radicals, exponents, and logarithms.
    [ix] Collect, organize, and interpret data from exponential, logarithmic, and power functions.

    [e] Identify, locate, and apply trigonometric functions to the unit circle.
    [i] Identify and locate angles in radians and degrees based on the unit circle.
    [ii] Convert between degree and radian measurements of angles.
    [iii] Use the definition of the six trigonometric functions to find missing parts of a triangle.
    [iv] Determine the values of inverse trigonometric functions.
    [v] Utilize special right triangle relationships and symmetry as they apply to the unit circle.
    [vi] Relate the unit circle to the right triangle.

    [f] Utilize and extend algebraic and geometric techniques to trigonometric equations and applications.
    [i] Solve for unknown parts of triangles to include Law of Sines and Law of Cosines.
    [ii] State, verify, and utilize trigonometric identities.
    [iii] Find arc length and area of a sector of a circle.
    [iv] Find the area of a triangle using Heronís Formula and/or (1/2)BCsin(A).
    [v] Solve trigonometric equations, using both radians and degrees.
    [vi] Model and apply right triangle formulas, Law of Sines, and Law of Cosines to problem-solving situations.


    1 LINEAR RELATIONS AND FUNCTIONS

    1.1 - Properties of Linear Equations

    ...

    2 MATRICES

    2.1 - Adding and Subtracting Matrices

    ...

    3 POLYNOMIALS AND RADICAL EXPRESSIONS

    3.1 - Operations with Polynomials

    ...

    4 EXPONENT AND LOGARITHMIC FUNCTIONS

    4.1 - Properties of Logarithms

    ...

    5 TRIGONOMETRIC FUNCTIONS

    5.1 - Trigonometric Functions of General Angles

    ...

    REFERENCES

    [1] A Beka Algebra 2, Work-Text, Pensacola, Florida.
    ...