Algebra II Syllabus

Overview:

Algebra 2 continues students’ study of advanced algebraic concepts including functions, polynomials, rational expressions, systems of functions and inequalities, and matrices. Students will be expected to describe and translate among graphic, algebraic, numeric, tabular, and verbal representations of relations and use those representations to solve problems. Emphasis should be placed on practical applications and modeling. Appropriate technology, from manipulatives to calculators and application software, should be used regularly for instruction and assessment.

Objectives:

The learner will:

· Simplify and perform operations with rational exponents and logarithms (common and natural) to solve problems.

· Define and compute with complex numbers.

· Operate with algebraic expressions (polynomials, rational, complex fractions) to solve problems.

· Operate with matrices to model and solve problems.

· Model and solve problems using direct, inverse, combined and joint variation.

· Use the composition and inverse of functions to model and solve problems; justify results.

· Use quadratic functions and inequalities to model and solve problems; justify results; solve using tables, graphs, and algebraic properties; interpret the constants and coefficients in the context of the problem.

· Use exponential functions to model and solve problems; justify results; solve using tables, graphs, and algebraic properties; interpret the constants and coefficients in the context of the problem.

· Create and use best-fit mathematical models of linear, exponential, and quadratic functions to solve problems involving sets of data; interpret the constants, coefficients, and bases in the context of the data; check the model for goodness-of-fit and use the model, where appropriate, to draw conclusions or make predictions.

· Use rational equations to model and solve problems; justify results; solve using tables, graphs, and algebraic properties; interpret the constants and coefficients in the context of the problem; identify the asymptotes and intercepts graphically and algebraically.

· Use cubic equations to model and solve problems; solve using tables and graphs; interpret constants and coefficients in the context of the problem.

· Use equations with radical expressions to model and solve problems; justify results; solve using tables, graphs, and algebraic properties; interpret the degree, constants, and coefficients in the context of the problem.

· Use equations and inequalities with absolute value to model and solve problems; justify results; solve using tables, graphs, and algebraic properties; interpret the constants and coefficients in the context of the problem.

· Use the equations of parabolas and circles to model and solve problems; justify results; solve using tables, graphs, and algebraic properties; interpret the constants and coefficients in the context of the problem.

· Use systems of two or more equations or inequalities to model and solve problems; justify results. Solve using tables, graphs, matrix operations, and algebraic properties.

Topic Coverage

Ø Function concepts

§ Definition as a set of ordered pairs, as a rule, compared with relations

§ Function notation

§ Independent and dependent variable; domain and range

§ Graphs of functions and relations

§ Arithmetic operations on functions

§ Inverse of a function

§ Piece-wise defined functions

§ Composition

§ Inverse functions

· Graphical meaning and in terms of ordered pairs

· How to compute

· Whether an inverse exists

§ Even and odd functions

§ Linear transformations and their effect on graphs

§ Applications and modeling

Ø Linear functions and relations

§ Slope-intercept and point-slope form

§ Graphs and use of a coordinate system

§ Geometric interpretation of slope as a rate

§ Solving linear equations

§ Linear regression

§ Linear inequalities in one and two variables

§ Absolute value equations and inequalities - solved by graphing

§ Applications and modeling

Ø Systems of linear equations and inequalities

§ Solving algebraically (substitution and elimination) and by graphing

§ Use calculator to solve arbitrary systems (not necessarily linear)

§ Linear programming

§ Applications and modeling

Ø Matrix algebra

§ Matrix concepts

· Terminology: row, column, identity, inverse

· Calculator use

§ Operations

· Addition, subtraction, and scalar multiplication

· Multiplication by calculator

· Multiplication by hand

§ Identity and inverse matrices

· Finding inverses by calculator

· Finding inverses using formulas and/or by hand

§ Solve systems of equations

· Using inverses to solve AX=B

· Cramer's Rule

§ Selected applications and modeling such as inventory, cost and profit

Ø Quadratics

§ Terminology: intercept, root, zero, solution

§ Graphing: roots, y-intercept, vertex, symmetric points, axis of symmetry

§ Vertex form

§ Solving

· Common factor and quadratic factoring

· Completing the square

· Ways to find the vertex: vertex form, -b/2a, symmetry, graphing calculator

· Quadratic formula

· Relationship between factoring and the quadratic formula

· Relationship between discriminant and roots

§ Complex numbers

· The imaginary unit i

· Solving quadratics with complex roots

· Add, subtract, multiply, divide conjugates

· The complex plane

§ Finding a parabola from three points

§ Applications and modeling such as motion, gravitational constant

Ø Polynomials

§ Vocabulary: degree, coefficient, leading coefficient, term, nth degree, constant term, root, solution, zero, x-intercept, complete factoring

§ Multiplying, binomial theorem

§ Factoring

· Common factor

· Difference of squares, perfect squares

· Sum and difference of cubes

· Long division algorithm

· Synthetic division

§ Finding roots

· The factor/remainder theorem

· The rational roots theorem

· Use of calculator to solve

§ Graphs and curve sketching

· End behavior

· Number of roots/changes in sign

· Turning points

· Finding a function from a graph

§ Applications and modeling

Ø Powers, roots, and radicals

§ nth roots

§ Solving radical equations by graphing

§ Applications and modeling

Ø Rational equations and functions

§ Inverse, joint, combined, and direct variation

§ Solving rational equations by graphing

§ Add, subtract, multiply, and divide rational expressions

§ Vertical and horizontal asymptotes

§ Applications and modeling

Ø Exponents and logarithms

§ Basic laws of exponents, negative and rational exponents, roots

§ Logarithm as the inverse of exponentiation

· Logarithmic notation

· Log rules (product, quotient, power, and change of base rule)

§ Solve exponential equations, with and without calculator

§ Solve log equations

§ Find an exponential equation from two points

§ Base e, ln

§ Graphs of exponential and logarithmic functions

§ Applications and modeling such as growth and decay, bank interest and depreciation

Ø Conic sections

§ Circles

§ Parabolas

Ø Counting principles

§ Counting problems

§ Binomial theorem, Pascal's triangle

Ø Statistics

§ Modeling real world data using scatterplots

§ Prediction equations

§ Correlation

Evaluation

Tests – 60%

Independent Work – 40%

Resources

Prentice Hall Algebra 2

Algebra 2 Indicators NC DPI

Technology Resources

TI-84 Plus Graphing Calculator

Virtual TI Calculator

Interwrite SchoolPad