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# Algebra II

Prerequisite Material

Before taking an Algebra II course, students should have successfully completed and
Algebra I course or the Algebra IA and Algebra IB sequence.

Required Material

In order for students to receive credit for having taken an Algebra II course, the following
topics must be covered.

1. Number Systems

a. Counting Numbers, Whole Numbers, Integers, Rational Numbers ,
Irrational Numbers, Real Numbers, and Complex Numbers
b. Properties of Real Numbers (the Field Axioms, reflexive property,
symmetric property…)

2. Linear Equations and Inequalities in One Variable

a. Solving equations that require multiple steps and may have one, none, or
infinitely many solutions
b. Solving simple and compound inequalities
c. Graphing solution sets of simple and compound inequalities

3. Two Variable Functions

a. Definition of relations and functions
b. Domain and range
c. Graphs of functions
d. Function notation
e. Composition of functions
f. Inverse functions

4. Linear Functions in Two Variables

a. Definition
b. Intercepts and slope
c. Horizontal and vertical lines
d. Slope-intercept from, point-slope form, two-point form
e. Graphing linear functions
f. Parallel and perpendicular lines
g. Linear functions as mathematical models

5. Systems of Equations

a. Solutions of two and three variable systems
b. Solving two variable systems by graphing, substitution, and elimination
c. Solving three variable systems by substitution and elimination.
6. Linear Inequalities in Two Variables
a. Graphs of linear inequalities and their solutions
b. Graphs of systems of linear inequalities and their solutions
c. Linear programming

7. Systems of Linear Inequalities

a. Graphs of linear inequalities and their solutions
b. Graphs of systems of linear inequalities and their solutions
c. Linear programming
8. Equations and Inequalities Involving Absolute Value
a. Solving equations involving absolute value
b. Graphing functions involving absolute value
c. Conjunctions and disjunctions

9. Polynomials

a. Exponential expressions with integer exponents
b. Properties of exponents
c. Adding , subtracting , multiplying, and dividing polynomials
d. Factoring polynomials

a. Solving by factoring
b. Solving by the square root method
c. Solving by using the quadratic formula
d. The discriminant and the nature of solutions

a. Definition of a quadratic function
b. Graphing of quadratic functions including finding the equation of the line
of symmetry, the vertex , and the intercepts
c. Quadratic functions as mathematical models

12. Exponential and Logarithmic Functions

a. Definition of exponential function
b. Rational exponents
d. Solving exponential equations using knowledge of powers
e. Definition of a logarithm
f. Common logs , natural logs, and logs with other bases
g. Properties of logs
h. Solving logarithmic equations
i. Solving exponential equations using logs
j. Graphing exponential and logarithmic functions
k. Exponential functions as math models

13. Rational Expressions and Functions

a. Synthetic division
b. Factoring higher degree polynomials using the Factor Theorem (x-b is a
factor of P(x) if and only if P(b) = 0.)
c. Products and quotients of rational expressions
d. Sums and differences of rational expressions
e. Complex rational expressions
f. Equations containing rational expressions
g. Rational functions and their graphs (asymptotes and discontinuities)
h. Variation functions

c. Variation functions with non-integer exponents
d. Functions of more than one independent variable

15. Conic sections

a. Circles , ellipses, parabolas, and hyperbolas
b. Systems of linear and quadratic functions

16. Complex Numbers

a. Definition
b. Addition, subtraction, multiplication , and division
c. Absolute value
d. Equations with complex solutions

17. Sequences and Series

a. Arithmetic and geometric sequences
b. Arithmetic and geometric means
c. Arithmetic and geometric series
d. Convergent geometric series
e. The binomial formula

18. Probability

a. The fundamental counting principle
b. Permutations
c. Combinations
d. Probability

Other Considerations

• There should be an emphasis on the understanding of the underlying concepts.

• Communication, both oral and written, should be emphasized throughout the
course. Written solutions to problems should be expected and evaluated.

• Students should be allowed to use graphing calculators and computers where
appropriate.

• There should be an emphasis on functions as mathematical models.

• At the end of each semester, a summary of the mathematics covered should occur
in which the relationships among concepts are emphasized. Semester exams are
required.

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