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Algebra II Power Standards
AMA ESD
Based on MDE Algebra II course description revised 9-3-09
These power standards represent the most important mathematical ideas and skills of Algebra II, the concepts
that all students need to learn for life (endurance) as well as for on-going education (leverage).
Expressions and equations
Expressions and equations
Students in Algebra II represent real-world situations
mathematically, evaluate expressions, and solve
equations involving polynomials, rational expressions,
and exponential and logarithmic expressions.
I can put real-world situations into mathematical
expressions and equations. (L1.2.1, A1.1.1)
I can evaluate expressions for a given value of the
variable. (A1.1.1)
PS 1: Solve polynomial equations, equations involving I can solve polynomial equations, by adding,
rational expressions, exponential equations and
subtracting, multiplying, dividing and simplifying
logarithmic equations. A1.2.5, A1.2.7
polynomials. (A1.2.5, A1.1.4, A1.1.5)
Related content expectations: L1.2.1, A1.1.1,
I can solve rational equations, by adding, subtracting,
A1.1.4, A1.1.5, A1.1.6, A1.2.2, L2.1.3 (rules of
multiplying and simplifying rational expressions.
logarithms are post-MME)
(A1.2.5, A1.1.4)
PS 2: Solve an equation involving several variables
I can solve exponential and logarithmic equations, by
(with numerical or letter coefficients) for a designated transforming exponential and logarithmic expressions
variable, and justify steps in the solution. A1.2.8
into equivalent forms using their properties and
knowing that logarithms are the inverse of exponents.
(A1.2.7, A1.1.6, A3.2.3 – logarithms are post-MME)
I can solve equations by graphing the related function
and finding the zeros. (A1.2.2)
I can solve an equation that has several variables for a
chosen variable. (A1.2.8)
Functions
Functions
Students in Algebra II use exponential, logarithmic
and rational functions to model real-world situations
and solve problems.
I understand logarithmic measurements scales such as
the Richter scale, the pH scale, and decibel
measurements, and I can solve problems that use these
measuring scales. (L2.3.2 – post-MME.)
PS 3: Describe and interpret logarithmic relationships
in such measurement contexts as the Richter scale, the
pH scale, or decibel measurements; solve applied
problems. L2.3.2 – Real-world examples of
logarithmic relationships are post-MME.
I can decide which family of functions can be used to
represent (model) a real-world situation. In Algebra I,
those functions include linear, quadratic and
exponential functions. In Algebra II they include
exponential, logarithmic, and rational functions.
PS 4: Identify the family of functions (exponential,
logarithmic, rational) best suited for modeling a given (A2.4.1)
real-world situation. Identify a function as a member I can look at a written function or graph and tell what
of a family of functions from its symbolic form or
family of functions it belongs to. (A2.3.1, A3.2.2)
graph. A2.4.1, A2.3.1, A2.3.3, A3.2.2 (exponential
I can write the general form of the function for each
and logarithmic), A3.6.1 (rational)
family of functions. (A2.3.3, A3.6.1)
PS 5: Adapt the general symbolic form of a function to
one that fits the specifications of a given situation by
using the information to replace arbitrary constants
with numbers, A2.4.2; identify and interpret the key
features of a function from its graph or its formula(s);
apply transformations to parent functions, A2.1.7,
A2.2.2; solve problems with functions, A2.4.3.
I know what each constant means in a general form
for exponential functions. I can customize a general
mathematical function to fit a specific real-world
situation by using information from the situation to fill
in each constant in the general function. (A2.4.2)
Related content expectations:
Exponential and Logarithmic functions: A3.2.2-3
– logarithmic functions are post-MME.
Rational functions: A3.6.2
PS 6: Theory of functions: Interpret function notation
(A2.1.2); is it a function? (A2.1.1); what are its zeros?
(A2.1.6); where is it increasing/decreasing? (A2.1.6);
combine functions (A2.2.1); find inverse of functions
(A2.2.3)
I can look at a graph and identify the key features of
the function. (A2.1.7, A3.2.2, A3.6.2 – logarithmic
functions are post-MME.)
I can graph basic exponential, logarithmic and rational
functions. (A2.1.3, A3.2.2, A3.6.1 – logarithmic
functions are post-MME.)
I can transform a function in different ways by
changing its constants and I can show what that does
to its graph. (A2.2.2)
I can solve problems with functions. (A2.4.3)
I understand recursive formulas for linear and
PS 7: Relate sequences of values to recursive formulas exponential functions and I can relate them to
for linear and exponential functions; find nth term.
sequences of values. (L2.2.1 – post MME.)
L2.2.1 – Sequences are post-MME.
I can find the nth term of a sequence and the sum of
Related content expectations:
Sums of finite arithmetic and geometric
sequences: L2.2.2 – post-MME
PS 8: Use iterative processes in such examples as
computing compound interest or applying
approximation procedures. L2.2.3 – Iterative
processes are post-MME.
Statistics
finite arithmetic and geometric sequences. (L2.2.1 –
post MME.)
I can use iterative processes for things like computing
compound interest or approximating answers to
complex problems. (L2.2.3 – post-MME.)
Statistics
Students in Algebra II represent and analyze data sets I can gather information from dot plots, histograms,
related to real-world situations and identify sources of relative frequency histograms, bar graphs, basic
bias.
control charts, and box plots and I can make them,
using appropriate labels and scales. (S1.1.1)
PS 9: Construct and interpret dot plots, histograms,
relative frequency histograms, bar graphs, basic
control charts, and box plots with appropriate labels
and scales; determine which kinds of plots are
appropriate for different types of data; compare data
sets and interpret differences based on graphs and
summary statistics. S1.1.1
Related content expectations:
Measures of center: S1.2.1
I can decide which kind of plot is the most appropriate
to use for the given data. (S1.1.1)
I can compare data sets and interpret differences based
on graphs and summary statistics. (S1.1.1)
I can find mean, median, mode and range of a data set.
I can identify outliers. (S1.2.1)
Probability
Probability
Students in Algebra II understand basic probability
concepts and apply them to real-world situations.
I can use counting techniques as needed. (L1.3.1 –
post-MME)
PS 10: Describe, explain, and apply various counting
techniques; relate combinations to Pascal’s triangle;
know when to use each technique. L1.3.1 – Counting
techniques are post-MME.
These topics are included in the HSCE document for Algebra II, but our criteria of endurance and
leverage don’t apply to them, so they are not part of the power standards:
Conic sections – G1.7.1 is recommended if there is time; G1.7.2 and G1.7.3 are extensions (pre-calculus).
Conic sections are not tested on the MME.
Complex numbers (L2.1.5) are “nice to know” and may appear as solutions to some polynomial equations.
Complex numbers are not tested on the MME