Download Scope and Sequence AM CC Math 2 Library

Scope and Sequence
AM™ CC Math 2 Library
The Accelerated Math™ scope and sequence is based on extensive mathematics and standards research and
consultation from mathematics educators, mathematicians, and university researchers. You're sure to find objectives that
reinforce the skills you are teaching, regardless of what instructional materials you use. Accelerated Math makes it easy to
select and organize objectives to suit your textbook and your own teaching approach. This Accelerated Math library
provides the following scope and sequence of objectives
Topic 1 - Extending the Number
System
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Apply the product of powers property
to a monomial algebraic expression
Apply the power of a power property
to a monomial algebraic expression
Apply the power of a product property
to a monomial algebraic expression
Apply the quotient of powers property
to monomial algebraic expressions
Apply the power of a quotient property
to monomial algebraic expressions
Apply properties of exponents to
monomial algebraic expressions
Convert between radical notation and
rational exponent notation
Simplify a numerical expression that
includes fractional exponents
Simplify a monomial numerical
expression involving the square root of
a whole number
Simplify a monomial algebraic radical
expression
Add and/or subtract numerical radical
expressions
Add or subtract algebraic radical
expressions
Multiply monomial numerical
expressions involving radicals
Multiply monomial algebraic radical
expressions
Divide monomial numerical
expressions involving radicals
Divide monomial algebraic radical
expressions
Represent an imaginary number in bi
form
Add or subtract complex numbers in a
+ bi form
Add or subtract complex numbers
using the relation i^2 = -1
Multiply complex numbers
Add quadratic polynomials
Subtract quadratic polynomials
•
•
•
•
Multiply two binomials of the form (x
+/- a)(x +/- b)
Multiply two binomials of the form (ax
+/- b)(cx +/- d)
Multiply two binomials of the form (ax
+/- by)(cx +/- dy)
Square a binomial
Topic 2 - Expressions and
Equations
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Factor the GCF from a quadratic
expression
Factor a quadratic expression that
results in factors of the form (x +/a)(x +/- b)
Factor a quadratic expression that
results in factors of the form (ax +/b)(cx +/- d)
Factor a quadratic expression that
results in factors of the form (ax +/by)(cx +/- dy)
Factor a perfect-square trinomial
Factor the difference of two squares
Factor a quadratic expression that has
a GCF and two linear binomial factors
Solve a quadratic equation that can be
written in x^2 = b form and has
rational solutions, no solution, or nonsimplified radical solutions
Solve a quadratic equation that can be
written in x^2 = b form and has a
simplified radical solution or no
solution
Solve a quadratic equation by taking
square roots
Determine the solution(s) of an
equation given in factored form
Solve a quadratic equation by
factoring
Determine the value needed to make a
quadratic expression a perfect square
trinomial
Determine an expression of the form
(x + b)^2 + c that is equivalent to the
given expression
P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com
© 2014 Renaissance Learning, Inc. All rights reserved.
Page 1 of 5
R57259.140114
Scope and Sequence
•
•
•
•
•
•
•
•
•
•
•
•
Solve a quadratic equation by
completing the square
Solve a quadratic equation using the
quadratic formula
Factor a quadratic expression that has
complex roots
Solve a quadratic equation that has
complex solutions
Rearrange a formula to isolate a
variable of interest where the formula
is quadratic in that variable
WP: Represent a situation using a 1variable quadratic equation
WP: Solve a problem that can be
represented by a 1-variable quadratic
equation
WP: Represent a situation using a 2variable quadratic equation
Determine a quadratic equation using
given information
Determine the graph of a quadratic
equation
Determine the solution(s) to a system
of equations represented graphically,
consisting of a linear equation and an
equation in quadratic form
Determine the solution(s) to a system
of equations consisting of a linear
equation and an equation in quadratic
form algebraically
Topic 3 - Quadratic Functions
and Modeling
•
•
•
•
•
•
WP: Determine the graph of a
quadratic function that represents a
situation
WP: Determine a reasonable domain
for a quadratic function in a given
situation using a representative graph
WP: Determine a reasonable domain
for a quadratic function in a given
situation
WP: Calculate the average rate of
change of a quadratic function over a
specified interval given a table or an
equation
WP: Estimate the average rate of
change of a quadratic function over a
specified interval given a graph
Determine the graph of a quadratic
function showing its intercepts and
maximum or minimum
AM™ CC Math 2 Library
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Factor a quadratic function to
determine the zeros of the function
Complete the square of a quadratic
function to determine the vertex
Determine the quadratic function for a
given graph
Determine the graph of a piecewisedefined function
Determine the graph of a step function
Determine the graph of a 2-variable
absolute value equation
Compare the properties of two
quadratic functions, each represented
in a different way
WP: Represent a situation using a
quadratic function
WP: Determine a recursive process for
calculating the values in a situation
that leads to a quadratic function
Combine a quadratic function with a
linear or a quadratic function using
addition or subtraction
WP: Combine a quadratic function with
a linear or a quadratic function using
addition or subtraction
Determine the effect of replacing f(x)
with f(x) + k or f(x + k) on the graph
of a quadratic function
Determine the effect of replacing f(x)
with kf(x) or f(kx) on the graph of a
quadratic function
Determine the quadratic function
resulting from a transformation given
the parent function and graphs of the
parent and transformed functions
Determine the equation of the inverse
of a linear function
Topic 4 - Applications of
Probability
•
•
•
•
•
Determine the probability of
independent events
Represent data using a two-way
frequency table
Approximate conditional probabilities
using a two-way table as a sample
space
Determine the conditional probability
of an event A given an event B
Determine the probability of an event
using the addition rule of probability,
P(A or B) = P(A) + P(B) - P(A and B)
P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com
© 2014 Renaissance Learning, Inc. All rights reserved.
Page 2 of 5
R57259.140114
Scope and Sequence
•
•
•
•
•
•
•
•
Determine the probability of an event
using the multiplication rule of
probability, P(A and B) = P(A)P(B|A) =
P(B)P(A|B)
WP: Determine the number of
permutations possible in a given
situation
Determine a probability using
permutations
WP: Solve a probability problem
involving permutations
WP: Determine the number of
combinations possible in a given
situation
Determine a probability using
combinations
WP: Solve a probability problem
involving combinations
Analyze a decision or a strategy using
simple probability concepts
Topic 5 - Similarity, Right
Triangle Trigonometry, and
Proof
•
•
•
•
•
•
•
•
•
•
Determine the midpoint of a line
segment given the coordinates of the
endpoints
Solve a problem involving the midpoint
formula
Determine the point on a line segment
that divides the segment into a given
ratio
Solve a problem using inequalities in a
triangle
Identify similar triangles using triangle
similarity postulates or theorems
Determine the length of a side or the
measure of an angle given two similar
triangles and numeric values for side
lengths or angle measure
Determine the length of a side or the
measure of an angle given two similar
triangles and algebraic expressions for
side lengths or angle measures
Determine a length in a triangle using
a midsegment and given numeric
values for lengths
Determine a length in a triangle using
a midsegment and given algebraic
expressions for lengths
Determine a length in a triangle using
parallel lines and proportional parts
AM™ CC Math 2 Library
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Determine a length given the
perimeters of similar triangles or the
lengths of corresponding interior line
segments
Determine a length using similar
triangles formed by the altitude to the
hypotenuse of a right triangle
WP: Determine a length in a triangle
using similarity
Complete a proof using congruence
and similarity theorems
Determine a length using the
properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle
WP: Determine a length using the
properties of a 45-45-90 degree
triangle or a 30-60-90 degree triangle
Solve a multi-step problem using the
properties of a 45-45-90 degree
triangle and/or a 30-60-90 degree
triangle
Determine a sine, cosine, or tangent
ratio in a right triangle
Determine a length using a sine,
cosine, or tangent ratio in a right
triangle
Determine the measure of an angle
using a sine, cosine, or tangent ratio in
a right triangle
Solve a problem using the
Pythagorean theorem and a sine,
cosine, or tangent ratio in a right
triangle
WP: Solve a problem involving a
complex figure using the Pythagorean
theorem
WP: Determine a length in a right
triangle using a sine, cosine, or
tangent ratio
WP: Determine the measure of an
angle in a right triangle using a sine,
cosine, or tangent ratio
Determine the value of a trigonometric
expression for an acute angle using
the Pythagorean identity
Topic 6 - Circles With and
Without Coordinates
•
Determine the length of a line
segment, the measure of an angle, or
the measure of an arc given a tangent
to a circle
P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com
© 2014 Renaissance Learning, Inc. All rights reserved.
Page 3 of 5
R57259.140114
Scope and Sequence
•
•
•
•
•
•
•
•
•
Determine a length using the
relationship between chords and radii
Determine the measure of an arc or an
angle using properties of an inscribed
triangle or quadrilateral
Determine the measure of an angle
using the relationship between
inscribed angles, circumscribed angles,
and/or central angles
Determine the length of an arc
Determine the area of a sector of a
circle
Determine an equation of a circle
Determine the radius or center of a
circle given an equation
Complete the square to determine the
center or radius of a circle given the
equation
Derive the equation of a vertically
oriented parabola given a focus and a
directrix
AM™ CC Math 2 Library
•
•
•
•
•
•
•
Derive the equation of a horizontally
oriented parabola given a focus and a
directrix
Determine the volume of a right
pyramid or a right cone
Determine a measurement given the
volume of a right pyramid or a right
cone
WP: Determine a measurement given
the volume of a right pyramid or a
right cone
Determine a measurement given the
volume of a sphere
WP: Determine a measurement given
the volume of a sphere
WP: Solve a problem involving the
volume of a complex solid figure
P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com
© 2014 Renaissance Learning, Inc. All rights reserved.
Page 4 of 5
R57259.140114
Scope and Sequence
Accelerated Math Libraries include an almost
unlimited supply of dynamic algorithm-generated
problems for both assisted-response (multiplechoice) and free-response assignments. Twenty
libraries are available:
Kindergarten
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Algebra 1
Algebra 2
Geometry
Math 1
Math 2
Math 3
Probability & Statistics
Pre-Calculus
Calculus
Financial Literacy Math 1
Financial Literacy Math 2
AM™ CC Math 2 Library
Please call us toll-free at 1-800-338-4204 to order
this Accelerated Math library or to request the
Scope and Sequence for other libraries.
Accelerated Math Library
AM CC Math 2 Library
P.O. Box 8036|Wisconsin Rapids, WI 54495-8036|(800) 338-4204|www.renlearn.com
© 2014 Renaissance Learning, Inc. All rights reserved.
Page 5 of 5
R57259.140114