EL SEGUNDO UNIFIED SCHOOL DISTRICT

EL SEGUNDO HIGH SCHOOL

 

COURSE OF STUDY

 

Course Title:    Algebra 2 and Algebra 2 Honors

Department:      Mathematics

Grade Levels:   9-12

 

COURSE DESCRIPTION

 

ALGEBRA 2

 

This course complements and expands the mathematical content and concepts of Algebra 1 and Geometry.  Students who master Algebra 2 will gain experience with algebraic solutions of problems in various content areas, including the solution of systems of quadratic equations, logarithmic and exponential functions, the binomial theorem, and the complex number system. Students also begin to study trigonometry.

 

ALGEBRA 2 HONORS

 

This course covers the same material; however the depth is more intense, students are required to be able to prove the theorems and derive the formulas, and the projects are more involved; requiring an in depth analysis of the mathematics presented throughout the course.

 

Length:   One Year

Prerequisite for Enrollment for Algebra 2:  A 70% or better in Geometry; Score 79% or below on the placement exam.

Prerequisite for Enrollment for Algebra 2 Honors: 90% or better in Geometry; Score 80% or better on the placement exam.

Recommendation for Enrollment:  Teacher Recommendation

Type of Course:  College preparatory (both courses UC/CSU approved) and meets math graduation requirement.

 

COURSE OUTLINE AND STANDARDS

CALIFORNIA STATE STANDARDS

 

1.0:  Students solve equations and inequalities involving absolute value. (Integration of Core Knowledge)

 

2.0:  Students solve systems of linear equations and inequalities ( in two or three variables) by substitution, with graphs, or with matrices (Integration of Core Knowledge)

 

3.0:  Students are adept at operations on polynomials, including long division. (Integration of Core Knowledge)

 

4.0:  Students factor polynomials representing the difference of squares, perfect square trinomials, and the sum and difference of two cubes. (Integration of Core Knowledge)

 

 

5.0:  Students demonstrate knowledge of how real and complex numbers are related both arithmetically and graphically.  In particular, they can plot complex numbers as points in the plane. (Integration of Core Knowledge)

 

6.0:  Students add, subtract, multiply, and divide complex numbers. (Integration of Core Knowledge)

 

7.0:  Students add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, including those with negative exponents in the denominator. (Integration of Core Knowledge)

 

8.0:  Students solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula.  Students apply these techniques in solving word problems.  They also solve quadratic equations in the complex number system. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

9.0:  Students demonstrate and explain the effect that changing a coefficient has on the graph of quadratic functions; that is, students can determine how the graph of a parabola changes as a, b, and c vary in the equation y=a(x-b)2 + c

 (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

10.0:  Students graph quadratic functions and determine the maxima, minima, and zeros of the function (Integration of Core Knowledge)

 

11.0:  Students prove simple laws of logarithms (Effective Communication; Integration of Core Knowledge)

 

11.1:  Students understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

11.2:  Students judge the validity of an argument according to whether the properties of real numbers, exponents, and logarithms have been applied correctly at each step. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

12.0:  Students know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

13.0:  Students use the definition of logarithms to translate between logarithms in any base. (Integration of Core Knowledge)

 

14.0:  Students understand and use the properties of logarithms to simplify logarithmic numeric expressions and to identify their approximate values. (Integration of Core Knowledge)

 

 

 

 

15.0:  Students determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

16.0:  Students demonstrate and explain how the geometry of the graph of a conic section (e.g., asymptotes, foci, eccentricity) depends on the coefficients of the quadratic equation representing it. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

17.0:  Given a quadratic equation of the form ax2 + by2 +cx+dy+e=0, students can use the method for completing the square to put the equation into standard form and can recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola.  Students can then graph the equation. (Integration of Core Knowledge; Critical Thinking/Problem Solving)

 

18.0:  Students use fundamental counting principals to compute combinations and permutations. (Integration of Core Knowledge)

 

19.0:  Students use combinations and permutations to compute probabilities (Integration of Core Knowledge)

 

20.0:  Students know the binomial theorem and use it to expand binomial expressions that are raised to positive integer powers. (Integration of Core Knowledge)

 

21.0:  Students apply the method of mathematical induction to prove general statements about the positive integers. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

22.0:  Students find the general term and the sums of arithmetic series and of both finite and infinite geometric series. (Integration of Core Knowledge)

 

23.0:  Students derive the summation formulas for arithmetic series and for both finite and infinite geometric series. (Integration of Core Knowledge)

 

24.0:  Students solve problems involving functional concepts, such as composition, defining the inverse function and performing arithmetic operations on functions. (Integration of Core Knowledge)

 

25.0:  Students use properties from number systems to justify steps in combining and simplifying functions. (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

 

Trigonometry Content Standards:

 

1.0:  Students understand the notion of angle and how to measure it, in both degrees and radians.  They can convert between degrees and radians. (Integration of Core Knowledge)

 

2.0:  Students know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.  (Integration of Core Knowledge)

 

4.0:  Students graph functions of the form f(t) Asin(Bt+C) or f(t)=Acos(Bt+C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift. (Integration of Core Knowledge)

 

 

INSTRUCTIONAL METHODS

1.      Lecture and Guided Practice

2.      Investigations (Personal/Social Development)

3.      Manipulatives

4.      Class work and Homework

5.      Individual work, and group work (Personal/Social Development)

6.      Short term projects (Personal/Social Development)

7.      Technology

 

EVALUATION/GRADING OF STUDENT WORK

1.      Quizzes and Chapter tests (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

2.      Semester exam  (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

3.      Comprehensive final exam (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication)

4.      Homework and Classroom participation (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)

5.      Projects (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)

6.      Written Essays (Integration of Core Knowledge; Critical Thinking/Problem Solving; Effective Communication; Personal/Social Development)

 

INSTRUCTIONAL MATERIALS

1.      Text:  ALGEBRA 2, Larson, Kanold, Stiff; D.C. Heath Publishing Co.

c.       1993

2.   Graphing Calculator:  TI-89

 

 

 

 

 

 

 

 

 

 

 

3-26-02