Eureka Math Algebra II Study Guide

Major MatheMatICal theMeS In eaCh Grade Band | 9

the signifiCanCe of funCtions

Functions are the central objects in most fields of modern mathematics. They are also
one of the fundamental tools that scientists use to model physical phenomena. A function is a
correspondence between two sets in which each input element of the first set corresponds to
one and only one output element of the second set. This definition generalizes the notion of
proportional and linear relationships that students studied in middle school. In those grades,
these relationships were represented by equations in which there was an independent
variable (usually denoted by x) and a dependent variable (usually denoted by y). In high school,
a linear relationship is represented as a function f from the set of real numbers to the set of
real numbers by fx()=+mx b (where m is the rate of change and b is the initial value). It is then
generalized to exponential, polynomial, rational, trigonometric, and logarithmic functions
throughout high school.

Figure 2.3 Grades 9–12 Year-Long Curriculum Map: A Story of Functions

Grade 9 – Algebra IGrade 10 – GeometryGrade 11 – Algebra II

M1:

Relationships Between

Quantities and Reasoning

with Equations and

Their Graphs

(40 days)

M1:

Congruence, Proof, and

Constructions

(45 days)

M1:

Polynomial, Rational, and

Radical Relationships

(45 days)

M2:

Tr igonometric Functions

(20 days)

M3: Extending to Three

Dimensions (15 days)

M3: Exponential and

Logarithmic Functions

(45 days)

M4: Connecting Algebra

and Geometry through

Coordinates (20 days)

M4:

Inferences and

Conclusions from Data

(40 days)

M4:

Polynomial and

Quadratic Expressions,

Equations, and Functions

(30 days)

M5:

Circles with and Without

Coordinates

(25 days)

M5:

A Synthesis of Modeling

with Equations and

Functions (20 days)

Grade 12 – Precalculus

M1:

Complex Numbers and

Tr ansformations

(41 days)

M2:

Vectors and Matrices

(36 days)

M3:

Rational and Exponential

Functions

(26 days)

M4: Tr igonometry

(21 days)

M5:

Probability and Statistics

(26 days)

M2:

Descriptive Statistics

(25 days)

30 days allotted for

review and examinations**

30 days allotted for

review and examinations**

30 days allotted for

review and examinations**

30 days allotted for

review and examinations**

M2:

Similarity, Proof, and

Tr igonometry

(45 days)

M3:

Linear and Exponential

Functions (35 days)

1st TRIMESTER

2nd TRIMESTER

3rd TRIMESTER

1st QUARTER

2nd QUARTER

3rd QUARTER

4th QUARTER

Key: Number and Quantityand Modeling Geometry andModeling Algebra andModeling Statistics and Probabilityand Modeling Functions andModeling

*The columns indicating trimesters and quarters are provided to give you a rough guideline. Please use your own pacing considerations based

on the specific dates of your academic calender.

**Note that each high school grade accounts for 150 instructional days, allowing 30 days fo r teachers to address concerns and administer end of

course exams.