GOAL I: To use linear equations, inequalities and functions.
LEARNER OUTCOMES
Student will:
1.1


1.2


Use real numbers and perform
number operations.
Use a number line to graph and
order real numbers.
Identify properties and use
operations with real numbers.
Use algebraic expressions and
models.
Evaluate algebraic expressions.
Simplify algebraic expressions.
INDICATORS OF LEARNING
Student will:
 Describe the subsets of real numbers.
 Graph and order real numbers.
 Calculate and explain the steps
involved in adding, subtracting,
multiplying, and dividing real
numbers.
 Conduct operations with real
numbers in real life applications.



1.3


Solve linear equations with one
variable using:
Addition, subtraction, multiplication
and division.
Multiple operations and steps




1.4


Rewrite equations and common
formulas with more than one
variable.
Calculate the value of a variable.
Rewrite and apply formulas.



1.5

Solve problems using algebraic
models.
Use general problem solving and
other strategies to solve real life
problems.


Explain and demonstrate how to
evaluate expressions.
Explain and demonstrate how to
simplify expressions by combining
like terms.
Write and evaluate algebraic models
for real life situations.
Solve and explain the steps used with
linear equations and formulas.
Write and evaluate linear equations
for real life problems.
Write and evaluate a geometric
formula.
Demonstrate how to use the table
feature on a graphing calculator to
solve linear equations.
Solve and describe the steps
involved in equations with more than
one variable.
Solve and write an equation in more
than one variable for real life
problems.
Demonstrate use of rewriting and
applying common formulas.
Write and solve equations using
verbal and algebraic models.
Solve and describe other problem
solving strategies such as diagrams
and patterns.
GOAL I: To use linear equations, inequalities and functions.
LEARNER OUTCOMES
Student will:
INDICATORS OF LEARNING
Student will:
1.6

Solve simple and compound
linear inequalities by using the
properties of inequalities.


1.7
Solve absolute value equations
and absolute value inequalities.


.


Chapter reference: 1.1-1.7
1.8







Graph, evaluate and write
linear equations.
Plot points from a table of values.
Evaluate functions.
Find slope.
Classify parallel and
perpendicular lines.
Use slope-intercept form to graph.
Use standard form to graph.
Use intercepts.






Chapter references: 2.1-2.3

Solve and graph simple as well as
compound inequalities.
Write and solve inequalities to solve
real life problems.
Demonstrate the use of the “Test”
feature of a graphing calculator to
solve an inequality.
Solve and check an absolute value
equation.
Solve, check and graph and absolute
value inequality.
Write and solve a model for tolerance.
Write and solve an absolute value
model for a real life problem.
Create a graph of a relation and tell
whether it is a function.
Create a graph of a function from a
table of values.
Describe how to determine if a
function is linear then evaluate the
function for a given value.
Determine the slope of a line using the
slope formula and determine whether
lines are parallel, perpendicular, or
neither.
Use slope as rate of change to solve
real life problems.
Construct graphs using standard form,
slope intercept form, and intercepts to
solve real life problems.
Demonstrate how to graph equations
using a graphing calculator.
GOAL I: To use linear equations, inequalities and functions.
LEARNER OUTCOMES
Student will:
1.9




Write linear equations.
Slope-intercept form
Point-slope form
Given two points
Parallel and perpendicular lines
INDICATORS OF LEARNING
Student will:




1.10
Correlate data and approximate
a best-fitting line.




1.11
Graph linear inequalities in one
and two variables.


1.12
Use absolute value functions.


Chapter reference: 2.4-2.6, 2.8
Write linear equations using the
three methods.
Write equations of parallel and
perpendicular lines.
Write and use a linear model to
solve real-life problems
Write, identify and use a direct
variation equation.
Draw and describe the correlation
shown by a scatter plot.
Draw a best-fitting line for a data
set.
Correlate data and draw best-fitting
lines with real-life data.
Demonstrate the linear regression
feature on a graphing calculator.
Construct the graph and describe
the steps to graph a linear
inequality.
Write a linear inequality and
construct a graph to solve real-life
problems.
Create an absolute value graph and
explain its’ characteristics.
Write an equation of a given graph.
GOAL II: To use systems of linear equations and inequalities.
LEARNER OUTCOMES
Student will:
2.1 Solve systems of linear equations by
graphing.
INDICATORS OF LEARNING
Student will:




2.2 Solve linear systems (two variables)
of equations algebraically using:
 Substitution
 Linear combination (Elimination)

2.3 Graph and solve a system of linear
inequalities.



2.4 Solve linear program problems.


2.4 Solve systems of linear equations in
three variables using:
 Substitution
 Linear Combination
(Elimination)
Chapter reference: 3.1-3.5


Construct a graph of a linear system,
estimate the solution, and check it
algebraically.
Interpret the graph of a linear
system.
Demonstrate how to solve a linear
system using a graphing calculator.
Write and solve a system by
graphing a real-life problem.
Solve and explain the steps involved
in each algebraic method
Write and solve a linear system of
equations for a real-life problem
Graph, solve and describe the steps
used to graph a system of linear
inequalities.
Write, graph and solve a system of
linear inequalities for a real-life
problem.
Find the minimum and maximum
values of the objective function
subject to the given constraints, and
then graph a feasible region.
Solve real-life problems using linear
programming.
Solve and describe the steps used for
each algebraic method.
Write and solve a linear system of
equations for a real-life problem.
GOAL III: To use quadratic functions, equations and inequalities.
LEARNER OUTCOMES
Student will:
3.1 Graph quadratic functions:
 Vertex form
 Intercept form
 Standard form
INDICATORS OF LEARNING
Student will:
 Create the graph of a quadratic
function using the three forms; label
the vertex, axis of symmetry and x
intercepts.
 Write equations in standard form.
 Demonstrate how to graph a
quadratic function using a graphing
calculator.
 Use real-life models in standard and
vertex form in order to solve reallife problems.
3.2 Solve quadratic equations by
factoring:
 Special patterns
 Find zeros of quadratic functions

3.3 Solve quadratic equations by finding
square roots.





3.4 Solve quadratic equations with
complex numbers.
 Perform operations with complex
numbers
 Find the absolute value of complex
numbers
Chapter reference: 5.1-5.4




Factor and solve quadratic
expressions and equations using
identified methods.
Solve real-life problems using a
quadratic equation.
Describe and use the
product/quotient properties of square
roots.
Solve and explain the steps required
in solving quadratic equations by
finding the square roots.
Solve real-life problems by using a
quadratic model and find the square
roots.
Show how to use a graphing
calculator to solve quadratic
equations.
Solve quadratic equations with
complex numbers.
Demonstrate how to add, subtract,
multiply and divide complex
numbers.
Find the absolute value of a complex
number.
Tell whether a complex number
belongs to the Mandelbrof set.
GOAL III: To use quadratic functions, equations and inequalities.
LEARNER OUTCOMES
Student will:
3.5 Solve quadratic equations by
completing the square.
 Write quadratic functions in
vertex form.
INDICATORS OF LEARNING
Student will:




3.6 Solve quadratic equations using the
quadratic formula.


Chapter reference: 5.5-5.6
Solve and explain the steps used to
solve a quadratic equation by
completing the square.
Use a quadratic equation to model
distance and area problems.
Write a quadratic equation in vertex
form and identify the vertex.
Demonstrate how to find maximum
and minimum values of a quadratic
function.
Demonstrate how to solve quadratic
equations using the quadratic
formula.
Find the discriminant to determine
the number and type of solutions of
a quadratic equation.
GOAL IV: To use polynomials, polynomial equations and polynomial functions.
LEARNER OUTCOMES
Student will:
4.1 Simplify expressions involving
powers by using the properties of
exponents.
INDICATORS OF LEARNING
Student will:


4.2 Evaluate and graph a polynomial
function.





Demonstrate how to evaluate and
simplify numerical and algebraic
expressions using the properties of
exponents.
Use the properties of exponents to
solve real-life problems.
Determine whether a function is a
polynomial function.
Use direct and synthetic substitution
to evaluate a polynomial function.
Construct a graph of a polynomial
function.
Describe the end behavior of
polynomial functions.
Demonstrate how to set a good
viewing window when graphing a
polynomial function on a graphing
calculator.
4.3 Add, subtract and multiply
polynomials.

Demonstrate how to perform
operations with polynomials.
4.4 Factor polynomial expressions and
solve polynomial equations:

Explain and demonstrate at least
three factoring methods used to
factor polynomials.
Explain the steps used to solve a
polynomial equation.
Use polynomial equations to solve
real-life problems.




Sum or difference of cubes
Grouping
Quadratic form
Polynomial equations
4.5 Divide polynomials.
Chapter reference: 6.1-6.5



Explain and use the steps necessary
to divide polynomials using long and
synthetic division.
GOAL V: To use radicals and rational exponents, expressions and equations.
LEARNER OUTCOMES
Student will:
5.1 Evaluate nth roots of real numbers
using radical notation and rational
exponent notation.
INDICATORS OF LEARNING
Student will:




5.2 Evaluate and simplify expressions
using properties of rational
exponents.




5.3 Solve radical equations:
 Simple radicals
 Rational exponents
 Equations with one and two
radicals



5.4 Simplify and perform operations
with rational expressions.




Chapter reference: 7.1-7.2, 7.6, 9.4-9.5
Describe and use the properties of
nth roots. Find nth roots.
Evaluate expressions with rational
exponents.
Demonstrate how to use a graphing
calculator to approximate a root.
Solve and explain the steps for
solving equations using nth roots.
Simplify expressions by using the
properties of rational exponents and
radicals.
Perform operations to combine roots
and radicals.
Write variable expressions in
simplest form.
Combine variable expressions.
Solve rational exponent and radical
equations and check for extraneous
solutions.
Solve equations with two radicals
and check for extraneous solutions.
Demonstrate how to use the intersect
feature on a graphing calculator to
solve radical equations.
Simplify rational expressions and
complex fractions.
Add, subtract, multiply and divide
rational expressions and perform
combined operations.
Write and simplify rational models
to solve real-life problems.
Show how to use a graphing
calculator to verify the results of
simplifying rational expressions.
GOAL V: To use radicals and rational exponents, expressions and equations.
LEARNER OUTCOMES
Student will:
5.5 Solve rational equations:
 One solution
 Extraneous solution
 Two solutions
INDICATORS OF LEARNING
Student will:



Chapter reference: 9.6
Add and subtract rational
expressions with like and unlike
denominators.
Demonstrate how to solve rational
equations using the LCD and by
cross-multiplying.
Write and use a rational model to
solve a real-life problem.
GOAL VI: To use trigonometric functions.
LEARNER OUTCOMES
Student will:
6.1 Evaluate trigonometric functions of
acute angles:
 Sine, Cosine, Tangent, Cosecant,
Secant, and Cotangent
INDICATORS OF LEARNING
Student will:



6.2 Measure angles in standard position
using degree and radian measure.




6.3 Evaluate trigonometric functions of
any angle:
 Sine, Cosine, Tangent, Cosecant,
Secant and Cotangent




6.4 Evaluate inverse trigonometric
functions.


Chapter reference: 13.1-13.4
Demonstrate the necessary
procedures to find a missing side
length or angle measure of a right
triangle.
Solve right triangles including
calculator use to solve.
Solve real-life problems using
trigonometric functions.
Draw an angle with a given measure
in standard form.
Find a positive and negative angle
conterminal with a given angle.
Convert measures between degrees
and radians.
Calculate arc lengths and areas of
sectors.
Evaluate trigonometric functions
given a point.
Evaluate trigonometric functions of
any angle.
Evaluate trigonometric angles by
using reference angles.
Use trigonometric functions to solve
real-life problems.
Find angles that correspond to a
given value of a trigonometric
function.
Solve a trigonometric equation.
GOAL VI: To use trigonometric functions.
LEARNER OUTCOMES
Student will:
6.5 Use the Law of Sines
INDICATORS OF LEARNING
Student will:


6.6 Use the Law of Cosines


Chapter reference: 13.5-13.6
Find missing sides and angles of a
triangle given at least one side and
two other parts of a triangle.
Find the area of any triangle by
using the appropriate formula.
Find missing sides and angles of a
triangle when two sides and the
included angle or three sides are
given.
Write and use Heron’s Law to find
the area of a triangle.
GOAL VII: To use exponential and logarithmic functions.
LEARNER OUTCOMES
Student will:
7.1 Graph exponential growth and
decay functions.
INDICATORS OF LEARNING
Student will:



7.2 Use the number e as the base of
exponential functions



7.3 Evaluate and graph logarithmic
functions.





7.4 Use the properties of logarithms


Chapter reference: 8.1-8.5
Create a graph of the function and
state the domain and range.
Use exponential growth and
decay functions to model real-life
problems.
Identify whether a function
represents exponential growth or
decay.
Simplify natural base
expressions.
Construct a graph of a natural
base function and state the
domain and range.
Demonstrate how to evaluate
natural base expressions using a
graphing calculator.
Re-write logarithmic equations in
exponential form.
Evaluate logarithmic expressions.
Demonstrate on a graphing
calculator how to evaluate natural
and common logarithms.
Simplify logarithmic expressions
using inverses and find inverses
of functions.
Construct a graph of a
logarithmic function and state the
domain and range.
Evaluate, expand and condense
logarithmic expressions using the
properties of logarithms.
Demonstrate the use of changeof-base formula to evaluate
common and natural logarithms.
DRAFT
Algebra 2
Curriculum
June 2005