Lexington High School Mathematics

Departmental Course Outlines

back to "Departmental Course Outlines" page

Departmental Course Outline for Algebra 2

Courses: 242 Lv1 Algebra 2, 243 Hon Algebra 2

Note: This working document describes our coverage plans, but may be revised somewhat during the year. We hope you will find it useful as an overview of the course and as an approximation of what topics will be covered.

Minimum Topic Coverage

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
(Optional for Lv2) Introduction to 3-dimensional graphing
Arithmetic operations on functions
Inverse of a function
(Optional for Lv2) Piecewise-defined functions
Composition
Inverse functions

Graphical meaning and in terms of ordered pairs
How to compute
Whether an inverse exists

(Optional) Even and odd functions
(Optional) The linear transformations and their effect on graphs
Applications and modeling

Linear functions and relations

Slope-intercept and point-slope form
Graphs and use of a coordinate system
Geometric interpretation of slope and slope as a rate
Solving linear equations
Linear regression
Linear inequalities in one and and two variables
Absolute value equations and inequalities - solved by graphing
Applications and modeling

Systems of linear equations and inequalities

Solving algebraically (substitution and elimination) and by graphing
Use grapher to solvearbitrary systems (not necessarily linear)
Linear programming
(Optional) Graphing in three variables
Applications and modeling

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 row operations by hand
Using rref on calculator
Using inverses (to solve AX = B)
(Optional) Cramer's rule

Selected applications and modeling, e.g.: inventory, cost and profit, area of a triangle, equation of line, cryptography, transformations of the coordinate plane (dilation, reflection, rotation).

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
The 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
(Optional) Arithmetic (add, subtract, multiply, divide) and conjugates
(Optional) The complex plane
(Optional) Absolute value and distance

(Optional) Finding a parabola from three points
Applications and modeling e.g. motion, gravitational constant

Polynomials

Vocabulary: Degree, coefficient, leading coefficient, term, nth degree, term, constant term, root=solution=zero=x-intercept, complete factoring
Multiplying, binomial theorem
Factoring

Common factor
Difference of squares, perfect squares
(Optional) Sum and difference of cubes
(Optional for Lv2) Long division algorithm
(Optional) Synthetic division

Finding roots

The factor/remainder theorem
(Optional) The rational roots theorem
When complete factoring is possible
Use of grapher 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

Powers, roots and radicals

nth roots
Solving radical equations by graphing
Applications and modeling

Rational equations and functions

Inverse, joint and direct variation
Solving rational equations by graphing
Add, subtract, multiply and divide rational expressions
Vertical asymptotes
Applications and modeling

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, with and without calculator
Find an exponential equation from two points
(Optional for Lv1 and Lv2) Base e, ln
Graphs of exponential and logarithmic functions
Applications and modeling e.g. growth and decay, bank interest and depreciation, Ph, Richter scales.

Conic sections

Circles, ellipses, hyperbolas, and parabolas
Algebraic and geometric definitions of each these

Counting principles and probability

Counting problems

Factorials, permutations and combinations, nCr and nPr formulas
With repeated values
Circular arrangements

(Optional for Lv2) Binomial theorem, Pascal's triangle
Simple probability: cards, dice
Rules of probability

Conditional probability
Independent events
Mutually exclusive events

Applications and modeling

(Optional for Lv1 and Lv2) Statistics

("") Random variables, frequency and probability distributions
("") Measures of center (mean, median, mode)
("") Measures of spread (variance, standard deviation)
("") Normal distributions

(Optional) Sequences and series

Calculator Skills

Graph and analyze more advanced functions
Find zeros of functions using tables and graphs
Perform matrix operations (add, subtract, multiply, find inverses)
Solve systems of equations using matrices

Textbook Usage

Hon Algebra 2, course 243: Algebra 2 by Schultz, Ellis, et al. (Holt, Rinehart and Winston, 2001). The course generally covers the contents of Chapters 1, 2.1-2.6, 3.1-3.5, 4, 5.1-5.5, portion of 5.6, 6, 7, 8, 9, 10, and 12.

Lv1 Algebra 2, course 242: Algebra 2 by Larson, Boswell, et al. (McDougall Littell). The course generally covers the contents of Chapters 1.6, 1.7, 2, 3.1-3.4, 4.1-4.2, 4.4 and extension, 5.1-5.3, 5.5, 5.6, 5.8, 6.1-6.5, 7.1-7.4, 7.6, 8.1-8.2, 8.4-8.7, 9.1-9.2, 11.1-11.3, and 12.1-12.5.