48
J.O. Combs Unified School District #44 Honors Algebra 2 with Trigonometry
J.O. Combs Unified School District #44
Honors Algebra 2 with Trigonometry
2
Table of Contents for Honors Algebra 2 with Trigonometry
Linear Functions................................................................................................................................ 3
Absolute Value Functions ................................................................................................................. 5
Characteristics of Functions .............................................................................................................. 7
Graphing Quadratic Functions .......................................................................................................... 9
Application of Quadratic Functions .................................................................................................. 11
Solving Polynomial Functions .......................................................................................................... 13
Application of Polynomial Functions ............................................................................................... 15
Radical Functions.............................................................................................................................. 17
Graphing Rational Functions ............................................................................................................ 19
Application of Rational Functions .................................................................................................... 21
Graphing Exponential Functions....................................................................................................... 23
Application of Exponential Functions .............................................................................................. 25
Simplifying Logarithmic Expressions............................................................................................... 27
Solving and Graphing Logarithmic Functions .................................................................................. 29
Conics................................................................................................................................................ 31
Circles................................................................................................................................................ 33
Sequences and Series ........................................................................................................................ 35
Reasoning .......................................................................................................................................... 37
Graphing Trigonometric Functions................................................................................................... 39
Solutions of Trigonometric Functions .............................................................................................. 41
Inverse Trigonometric Expressions................................................................................................... 43
Writing Trigonometric Equations ..................................................................................................... 45
Application of Trigonometric Relationships..................................................................................... 47
3
Linear Functions
4
Linear Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving linear functions, the student:
• solves linear systems of equations with three equations and three variables
• solves linear systems of inequalities (required: three or more inequalities)
• defines the variables, sets up, solves and analyzes system application problems
(required: linear programming, mixture, distance=rate*time)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o consistent, inconsistent
o dependent, independent
o coinciding
o vertices/intersection point, constraint, feasible region, solution set
o minimum/maximum value, profit, cost, revenue
• recognizes or recalls the accuracy of basic solutions or information and performs
basic operations such as:
o solving basic linear systems
o solving basic inequalities
o identifying accurate statements about system application problems
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
5
Absolute Value Functions
6
Absolute Value Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving absolute value functions, the
student:
• graphs absolute value functions (required: f (x) = ±a±b(x − h) + k )
• graphs and solves absolute value inequalities (required: f (x) ≤ ±a±b(x − h) + k )
• writes the equation of an absolute value function given the graph
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o absolute value
o vertex
o transformations, reflections, translations
o stretches/shrinks (vertical and horizontal)
o interval notation
o scalar multiple
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
7
Characteristics of Functions
8
Characteristics of Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving characteristics of functions, the
student:
• evaluates a function using function notation (required: numeric and algebraic)
• performs operation on functions (required: addition, subtraction, multiplication,
division, and composition)
• finds the inverse function (required: domain restrictions)
• finds the average rate of change given a nonlinear graph, equation, or critical
information
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o inverse function
o function notation
o composition of functions
o slope
o average rate of change
o domain, range, domain restrictions
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
9
Graphing Quadratic Functions
10
Graphing Quadratic Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve graphing of quadratic
functions, the student:
• adds, subtracts, multiplies, and divides complex numbers
• solves quadratic equations (required: by extracting the square root, the quadratic
formula, factoring, completing the square)
• graphs quadratic functions (required: standard form, factored form, and
f (x) = ±a x − h( )2+ k )
• graphs piecewise functions (required: quadratic and linear functions)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o completing the square
o extraction of square roots
o factoring, quadratic formula
o standard form, factored form, vertex form
o piecewise functions
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
11
Application of Quadratic Functions
12
Application of Quadratic Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving application of quadratic
functions, the student:
• writes the equation of a quadratic (required: vertex and a point, x intercepts and a
point)
• defines the variables, sets up, solves and analyzes quadratic application problems
(required: position function)
• finds the average rate of change given a nonlinear graph, equation, or critical
information
• approximates the instantaneous rate of change at a given point
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o distributive property of multiplication over addition
o commutative, associative, and the inverse properties of addition and
multiplication
o identity element
o irrational, rational, integer, whole, and natural numbers
o fractions, decimals, percents, ratio
o interval notation 0,∞( ), inequality notation x > 0 o exact solution, approximate solution
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
13
Solving Polynomial Functions
14
Solving Polynomial Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve solving polynomial functions,
the student:
• rewrites polynomial expressions to equivalent forms (required: adding, subtracting,
multiplying and dividing polynomial expressions, and factoring)
• solves polynomial equations (required: factoring, rational root theorem)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o synthetic division
o remainder theorem
o factors
o rational root theorem, complex roots, irrational roots
o Fundamental Theorem of Algebra
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
15
Application of Polynomial Functions
16
Application of Polynomial Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving application of polynomial
functions, the student:
• graphs polynomial functions (required: factored form, standard form, and vertex
form f (x) = ±a x − h( )n+ k )
• writes the equation of a polynomial given the zeroes and the leading coefficient
(required: complex zeros)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o end behavior
o increasing, decreasing intervals
o domain, range
o leading coefficient
o odd degree polynomials, even degree polynomials
o multiplicity
o relative minimums/maximums, absolute minimums/maximums
o inflections points
o concavity intervals
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
17
Radical Functions
18
Radical Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving radical functions, the student:
• simplifies radical expressions to equivalent forms (required: adding, subtracting,
multiplying and dividing radical expressions)
• solves radical equations (required: rational exponents)
• graphs square root and cube root functions (required: f (x) = ±a ±bx − h + k )
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o inverse functions, inverse operations
o domain restrictions
o extraneous solutions
o range restrictions
o verifying inverses through composition
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
19
Graphing Rational Functions
20
Graphing Rational Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve graphing of rational
functions, the student:
• simplifies rational expressions (required: adding, subtracting, multiplying and
dividing rational expressions)
• solves rational equations
• graphs rational functions (required: horizontal and slant asymptotes, removable
discontinuities)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o vertical and horizontal asymptotes, slant asymptotes
o domain restrictions
o end behavior, holes
o relative mins/maxs
o discontinuities (removable and nonremovable)
o factors
o rational root theorem
o compound/complex rational expressions, continuity
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
21
Application of Rational Functions
22
Application of Rational Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving application of rational
functions, the student:
• writes an equation that fits the model of a rational pattern (required: removable
discontinuity)
• defines the variables, sets up, solves, and analyzes direct and inverse (indirect)
variation application problems (required: rational exponents)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o rational exponents
o discontinuity
o direct/indirect variation
o constant of proportionality
o asymptotes
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
23
Graphing Exponential Functions
24
Graphing Exponential Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve the graphing of exponential
functions, the student:
• uses the properties of exponents (required: rational exponents)
• solves exponential equations
• graphs exponential equations (required: f (x) = ±a ⋅b±(x−h ) + k )
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o exponential growth
o exponential decay
o growth/decay factor
o asymptotes
o domain and range
o transformations
o logarithms
o inverse operations
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
25
Application of Exponential Functions
26
Application of Exponential Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving application of exponential
functions, the student:
• writes the equation of an exponential function
• defines the variables, sets up, solves and analyzes exponential application problems
(required: growth, decay, half/double life, continuously compounded interest,
compounded interest)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o compounded interest
o growth, decay
o half/double life
o continuously compounded interest
o systems of equations
o initial quantity
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
27
Simplifying Logarithmic Expressions
28
Simplifying Logarithmic Expressions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve simplifying logarithmic
expressions, the student:
• evaluates logarithmic expressions ( log2 4 )
• condenses and expands logarithmic expressions
• rewrites expressions in equivalent forms (required: exponential and logarithmic form)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o base, change of base
o condensing/expanding logs
o definition of logarithms
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
29
Solving and Graphing Logarithmic Functions
30
Solving and Graphing Logarithmic Functions Honors Algebra II with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving the solving and graphing of
logarithmic functions, the student:
• solves logarithmic equations
• graphs logarithmic functions (required: f (x) = ±a logb[±c(x − h)]+ k )
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o exponentiation
o vertical asymptote
o domain and range
o condensing and expanding logarithms
o transformations
o change of base
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
31
Conics
32
Conics Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving conics, the student:
• graphs conic sections (required: circles, parabolas in the form of
±4 p(x − h) = (y − k)2and ±4 p(y − k) = (x − h)
2 , ellipses, and hyperbolas from standard
and h k form)
• writes the equation of a conic section given critical information (required: circles,
ellipses, hyperbolas, and ellipses)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o conic section
o parabola
o hyperbola
o standard form
o h k form
o asymptotes
o completing the square
o directrix, focus, vertex, center, covertex
o midpoint formula, distance formula
o major/minor axis
o transverse axis
• performs basic processes
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
33
Circles
34
Circles Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving circles, the student:
• converts between radian measure and degree measure
• sketches angles in radian measure
• finds the arc length
• finds the reference angle
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o radian measurement
o arc length
o degree measure
o angle sweep
o coterminal
o complementary, supplementary, reference angle
o circumference, diameter
o radius, revolution, standard position of an angle, negative angles, period,
quadrants, axes
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
35
Sequences and Series
36
Sequences and Series Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving sequences and series, the
student:
• (A) determines the type and the nth term of a sequence (required: arithmetic and
geometric)
• (A) evaluates a finite and infinite geometric series
• (A) evaluates a finite arithmetic sum
• (B) evaluates a finite sum in summation notation
• (B) evaluates a sum using the summation formulas (required: a constant, i,i 2)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o geometric/arithmetic sequences and series
o finite and infinite geometric series
o summation notation
o summation formulas
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
37
Reasoning
38
Reasoning Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving reasoning, the student:
• simplifies trigonometric expressions (required: half angle, double angle, sum and
difference, Pythagorean identities, reciprocal identities, quotient identities, cofunction
identities, even and odd identities)
• evaluates trigonometric expressions (required: half angle, double angle, sum and
difference, reciprocal identities, quotient identities, cofunction identities, even and
odd identities)
• verifies trigonometric identities (required: half angle, double angle, sum and
difference, Pythagorean identities, reciprocal identities, quotient identities, cofunction
identities, even and odd identities, 2-column proof format)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o half angle, double angle
o Pythagorean identities, reciprocal identities, quotient identities, co-
function identities, even and odd identities
o 2-column proof
o coordinates of angles on the unit circle
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
39
Graphing Trigonometric Functions
40
Graphing Trigonometric Functions Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve graphing of trigonometric
functions, the student:
• graphs all six trigonometric functions with transformations (e.g.,
f (x) = ±a sin[±b(x − c)]+ d )
• describes the graphs of the arcsine, arccosine, and arctangent functions, giving
domain and range
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o transformations
o amplitude
o period
o domain and range, domain restrictions
o asymptotes
o inverse functions
o axis
o critical points
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
41
Solutions of Trigonometric Equations
42
Solutions of Trigonometric Equations Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving solutions of trigonometric
equations, the student:
• solves trigonometric equations (required: with and without domain restrictions)
• solves inverse trigonometric equations (required: unit circle angle solutions, and
calculator approximations, inverse cosecant, secant, and cotangent equations)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o finite and infinite solution sets
o inverse operations
o periodic solutions
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
43
Inverse Trigonometric Expressions
44
Inverse Trigonometric Expressions Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving inverse trigonometric
expressions, the student:
• evaluates inverse trigonometric expressions
• simplifies and evaluates the composition of trigonometric and inverse trigonometric
expressions
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o composition
o domain restrictions
o signs of trigonometric expressions in the quadrants
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
45
Writing Trigonometric Equations
46
Writing Trigonometric Equations Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks that involve writing trigonometric
equations, the student:
• writes the equation of any transformed periodic function (required: given the graph,
critical information)
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o no terminology for this topic
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
47
Application of Trigonometric Relationships
48
Application of Trigonometric Relationships Honors Algebra 2 with Trigonometry
Level 4.0 In addition to Level 3.0, in-depth inferences and applications that go beyond what was taught.
Level 3.5 In addition to Level 3.0 performance, in-depth inferences and applications with partial
success.
Level 3.0 While engaged in grade appropriate tasks involving application of trigonometric
relationships, the student:
• solves application problems of right and oblique triangles (required: bearings)
• finds the area of right and oblique triangles
• defines the variables, sets up an equation, and analyzes a trigonometric equation from
an application problem
• analyzes an application problem given trigonometric equation
The student exhibits no major errors or omissions. Level 2.5 No major errors or omissions regarding the simpler details and process and partial
knowledge of the more complex ideas and processes.
Level 2.0 There are no major errors or omissions regarding the simpler details and processes
as the student:
• recognizes or recalls specific terminology such as:
o bearings
o angle of elevation/depression
• performs basic operations
However, the student exhibits major errors or omissions regarding the more
complex ideas and processes. Level 1.5 Partial knowledge of the simpler details and processes but major errors or omissions
regarding the more complex ideas and procedures.
Level 1.0 With help, a partial understanding of some of the simpler details and processes and some of the more
complex ideas and processes.
Level 0.5 With help, a partial understanding of some of the simpler details and processes but not the
more complex ideas and processes.
Level 0.0 Even with help, no understanding or skill demonstrated.
