Algebra 2
This represents a general outline of the course. It details which standards will be covered in what
order, and provides limited explanatory material about the purpose and content of each
section. Implicit within each section is the expectation that students refer back to previous
material. Also implicit is the goal that students solve real-world problems and problems that
require application of multiple standards.
The fundamental guiding principle of the course is the Five Expectations. Students are expected
to use each of the Five Expectations with each class of functions studied and to make
connections between the classes. The course assumes that problem types involving one class of
function are looped appropriately throughout the course. For example: while learning about
exponential functions, students should be asked to solve a system of equations consisting of one
exponential equation and one quadratic equation. Or: while studying rational functions, explicit
connections should be made to polynomial functions and operations. Or: when modeling
problem situations, students should be comfortable using more than one class of function when
appropriate (e.g., 𝑓(𝑥) = 𝑒 𝑥 + 3𝑥 + 1).
Standards listed in purple are my own standards. Standards listed in green refer to both the
Common Core State Standards and the Washington State 2008 standards.
Whole Course Concepts
The following points are intended to be developed and practiced throughout the entire course.
1. The Five Expectations:

Create and solve equations.

Graph functions.

Transform and combine functions. Standards 6, 13 — F.BF.1b, 3; A2.5.A

Describe and interpret functions and their graphs. Standard 12 — F.IF.4

Find and use inverses. Standard 8 — F.BF.4a
2. Know and use correct vocabulary to decompose, understand, and refer to expressions.
Standard 72 — A.SSE.1
3. Use the structure of an expression to identify ways to rewrite it. Standard 73 — A.SSE.2;
F.IF.8
4. Relate the domain of a function to its graph and the quantitative relationship it
describes. Standard 4 — F.IF.5; A1.3.A
5. Estimate, calculate, and interpret the average rate of change of a function over a
specific interval. Standard 5 — F.IF.6
6. Compare properties of two functions, including those represented in different ways.
Standard 9 — F.IF.9
Algebra 2 Course Outline based on WA 2008 and CCSS Standards
Last updated 8/22/2013
7. Recognize and use parent functions to understand more complex functions. Standard 10
8. Find approximate and exact solutions to systems of equations. Standards 42–43 —
A.CED.3; A.REI.11; A2.1.B; A2.7.A
9. The Common Core Standards for Mathematical Practice:

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.
Course Outline
1. Linear functions. Reviewing linear functions and introducing the Five Expectations.
Introducing graphical and algebraic methods for solving systems of equations.

Create and solve linear equations and inequalities. Standard 14 — A.CED.1–3;
A1.4.A

Apply the slope criteria for parallel and perpendicular lines. Standard 15 –
G.GPE.5; G.2.A; G.4.A

Create and solve of three linear equations and three unknowns. Standards 43–44
— A.CED.3; A.REI.11; A2.1.B; A2.7.A
2. Function concepts. Reviewing the concepts that students will be using to understand
functions throughout the course. Introducing the parent functions and transformations.

Students should know the following parent functions: constant, linear, absolute
value, quadratic, cubic, square root, exponential, logarithmic, reciprocal, step,
sine, cosine, and tangent. Standards 10–11 — F.IF.7b; A2.5.D

Determine if a given relation is a function. Standard 1 — F.IF.1; A1.3.A

Determine the domain and range of a function. Standard 2 — F.IF.1; A1.3.A

Use function notation. Standard 3 — F.IF.2; A1.2.B; A1.3.C

Identify the effects of function transformations. Standard 13 — F.BF.3; A2.5.A

Determine whether a given graph or algebraic expression represents an even or
odd function. Standard 7 — F.BF.3
3. A brief mathematical interlude. Formalizing the number systems. Introducing inequality
notations. Reviewing the properties of exponents and square roots.
2

Classify numbers as real, complex, irrational, rational, natural, whole, and/or
integer. Standard 74 — A2.2.A

Write inequalities in interval, set-builder, and inequality notation. Standard 75

Use the properties of exponents to rewrite, simplify, and evaluate exponential
expressions. Standard 77 — N.RN.2; A2.2.B

Simplify square root expressions, including rationalizing the denominator, and
add, subtract, multiply, and divide square roots. Standard 78 — N.RN.2; A1.2.C

Create and solve proportions. Standard 76 — 7.RP.2; 7.2.B
4. Quadratic functions. Developing the mathematics of quadratic functions and complex
numbers.

Create and solve quadratic equations and inequalities. Standards 16–17, 20 —
A.CED.1–4; F.IF.8; N.CN.7; A2.1.A, C; A2.3.C

Graph quadratic equations and inequalities. Standard 21 — F.IF.7a

Factor quadratic expressions. Standards 22, 53, 73 — A.APR.4; A.SSE.2; F.IF.8;
N.CN.8; A1.2.E

Move between the standard form, vertex form, and factored form of a quadratic
function. Standard 18 — F.IF.8; A2.3.A

Determine the number and nature of the roots of a quadratic equation. Standard
19 — F.IF.8; A2.3.B

Know that √−1 = 𝑖 and write the square root of a negative number in terms of 𝑖.
Standard 51 — N.CN.1

Add, subtract, and multiply complex numbers. Standard 52 — N.CN.2
5. Polynomial functions. Developing the mathematics of polynomial functions.

Add, subtract, multiply, and divide polynomials. Standard 23 — A.APR.1, 6; A1.2.F

Factor polynomials and prove polynomial identities. Standard 22, 53, 73 —
A.APR.4; A.SSE.2; F.IF.8; N.CN.8; A1.2.E

Create and solve polynomial equations. Standard 27 — A.CED.1–3

Identify the zeroes and end behavior of polynomials. Standards 24–25 — A.APR.2–
3; F.IF.7c, 8

Construct a rough graph of the function defined by a polynomial. Standard 26 —
A.APR.3; F.IF.7c
+
Know and apply the Binomial Theorem for expanding a binomial raised to a
power. Standard 28 — A.APR.5; A2.6.D
3
+
Use the Fundamental Theorem of Algebra to number and characterize the roots
of a polynomial. Standard 29 — N.CN.9
6. Exponential and logarithmic functions. Developing the mathematics of exponential and
logarithmic functions.

Evaluate logarithms. Standard 38 — F.LE.4; A2.4.A

Simplify and move between exponential and logarithmic expressions. Standard
39 — F.LE.4; A2.4.A

Create and solve exponential and logarithmic equations and inequalities.
Standards 40–41 — A.CED.1–4; F.IF.8; F.LE.4; A2.1.A, D; A2.4.C

Graph exponential and logarithmic functions. Standard 42 — F.IF.7e; A2.4.B
7. Sequences and Series. Formalizing the mathematics of arithmetic and geometric series.

Find the terms and partial sums of an arithmetic series. Standard 70 — A2.7.B

Find the terms, partial sums, and infinite sum of a geometric series. Standard 71 —
A.SSE.4; A2.7.B
8. Radical functions. Developing the mathematics of radical functions.

Create and solve radical equations and inequalities. Standards 30–31 — A.CED.1–
3; A.REI.2; A2.1.A; A2.5.B

Graph square and cube root functions. Standard 32 — F.IF.7b; A2.5.B
9. Rational functions. Developing the mathematics of rational functions.

Rewrite rational expressions 𝑎(𝑥)/𝑏(𝑥) as 𝑞(𝑥) + 𝑟(𝑥)/𝑏(𝑥). Standard 33 — A.APR.6
+
Add, subtract, multiply, and divide rational expressions. Standard 34 — A.APR.7;
A2.2.C

Create and solve rational equations and inequalities. Standards 35–36 —
A.CED.1–3; A.REI.2; A2.1.A, E; A2.5.C
+
Graph rational functions. Standard 37 — F.IF.7d
10. Probability. Formalizing student understanding of probability. Students should be asked to
make predictions and evaluate situations throughout the section.

Solve problems and find probabilities using combinations and permutations.
Standards 54, 58 — A.APR.5; A2.1.F; A2.6.C–D

Use the Fundamental Counting Principal to calculate probabilities. Standard 55 —
A2.6.A

Determine whether two events are dependent or independent. Standard 56 —
S.CP.2; A2.6.B

Find conditional probabilities. Standard 57 — S.CP.3; A2.6.B
4
+
Use probability concepts to analyze decisions and strategies. Standard 59 —
S.MD.6–7
11. Statistics. Formalizing student understanding of statistics. Students should be asked to
make predictions and inferences and evaluate statistical claims throughout the section.

Understand statistics as a process for making inferences and predictions.
Standard 60 — S.IC.1

Evaluate a report based on data. Standard 61 — S.IC.6

Recognize the purposes of, and differences among, sample surveys, experiments,
and observational studies. Standard 62 — S.IC.3

Determine if a specific model is consistent with given results. Standard 63 — S.IC.2

Determine if a bivariate data set can be better modeled with a linear, quadratic,
exponential function. Standard 64 — S.ID.6; A2.6.E

Find and interpret the mean and standard deviation of a data set. Standard 65
— S.ID.4; A2.6.F

Determine if a normal distribution is appropriate for a given data set, and if so, fit
it to the data set and use it to estimate population percentages. Standards 66–67
— S.ID.4; A2.6.F

Calculate the population mean, margin of error, and confidence interval for a
given data set. Standard 68 — S.IC.4; A2.6.G

Use data to compare two treatments and use simulations to determine if
differences between parameters are significant. Standard 69 — S.IC.5
12. Trigonometric functions. Developing the mathematics of trigonometric functions.

Convert between radian and degree measures of an angle. Standard 45 — F.TF.1

Use trigonometric functions to solve problems. Standard 46 — T.TF.2

Write and solve trigonometric equations. Standard 47 — A.CED.1–3; F.TF.5; A2.1.A

Graph trigonometric functions. Standard 48 — F.IF.7e

Use the Pythagorean identity to solve problems. Standard 49 — F.TF.8
+
Use the addition and subtraction formulas for sine, cosine, and tangent to solve
problems. Standard 50 — F.TF.9
5