SDC Precalculus TN Ready Performance Standards by Unit Maury County Public Schools 5/8/18 Office of Instruction Pk-12 SDC Precalculus – Curriculum Overview The following Practice Standards and Literacy Skills will be used throughout the course: Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency 1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies. 2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary. 3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas. 4. Model with mathematics. 4. Write mathematical arguments. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. *Unless otherwise noted, all resources are from Glencoe Precaclulus.
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SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
SDC Precalculus – Curriculum Overview
The following Practice Standards and Literacy Skills will be used throughout the course:
Standards for Mathematical Practice Literacy Skills for Mathematical Proficiency
1. Make sense of problems and persevere in solving them. 1. Use multiple reading strategies.
2. Reason abstractly and quantitatively. 2. Understand and use correct mathematical vocabulary.
3. Construct viable arguments and critique the reasoning of others. 3. Discuss and articulate mathematical ideas.
4. Model with mathematics. 4. Write mathematical arguments.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
*Unless otherwise noted, all resources are from Glencoe Precaclulus.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
SDC Precalculus– Curriculum Overview
Quarter 1 Quarter 2 Quarter 3 Quarter 4
Unit 1 12 Days
Unit 2 14 Days
Unit 3 12 Days
Unit 4 16 Days
Unit 5 13 Days
Unit 6 12 Days
Unit 7 16 Days
Unit 8 20 Days
Functions,
Limits, & End
Behavior
Power,
Polynomial, &
Rational
Functions
Exponential &
Logarithmic
Functions
Trigonometric
Functions
Trigonometric
Identities &
Equations
Conic Sections &
Vectors
Polar Graphing
& Vectors
SDC Exam
Review/ Wrap Up
& Short Topics
Standards (By number) 1.E.a
1.E.e
1.E.f
2.I.a
3.F.a
3.PF.a
3.PF.b
3.PF.d
5.F.a
5.F.b
5.F.c
5.F.d
P.MCPS.6
1.E.a
1.E.c
1.E.d
1.E.e
1.E.f
2.I.a
3.PF.c
3.PF.d
4.M.a
4.M.b
4.M.c
1.E.a
1.E.e
1.E.f
1.E.g
1.E.a
6.TF.a
6.TF.b
6.TF.c
7.G.T.a
7.G.T.b
7.G.T.c
8.G.C.d
1.E.a
6.TF.d
6.TF.e
6.TF.f
1.E.a
8.GC.a
8.GC.b
8.GC.c
1.E.a
7.G.T.d
8.G.C.e
Matrices
Partial Fraction
Decomposition
Elipses &
Hyperbolas
Sequences,
Series, & Sigma
Notation
Green=Major Content Blue=Supporting Content
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Unit 1
Functions, Limits, and End Behavior
12 Days
Standards “I Can” Statements
Algebra
1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques.
I can add, subtract, multiply, and divide various expressions.
I can identify the real zeros of the graph of a function (polynomial, rational,
exponential, logarithmic, and trigonometric) in equation or graphical form.
1f.Equations: Identify equations that can’t be solved directly and use graphical or other approximations.
I can explain the relationship between the real zeros and the x-intercept of the
graph of a function (polynomial, rational, exponential, logarithmic, and
trigonometric).
I can use the discriminant to determine the number and types of zeros of
quadratic functions.
2a.Inequalities: Apply various techniques (algebraic and graphical) to solve inequalities involving polynomials (including degree >2), and absolute values, and can express answers using interval notation.
I can solve nonlinear inequalities (quadratic and rational) by graphing
(solutions in interval notation if one-variable), and by using a sign chart.
Functions
3a. Properties of Functions: Express properties and transformations of
functions graphically, and can use a graph to determine function properties.
I can describe the transformation of the graph resulting from the manipulation
of the algebraic properties of the equation (i.e., translations, stretches,
reflections, and changes in periodicity and amplitude).
3b. Properties of Functions: On both the graph and the function can apply
and identify the basic transformations: f(x-a), f(x+a), f(x)+a, f(x)-a, f(ax),
a*f(x).
I can create functions by adding, subtracting, multiplication, division, and
composition of functions.
3d. Properties of Functions: From the graph can locate critical points and
identify if each is a minimum, maximum or point of inflection, and locate
intervals of increasing/ decreasing.
I can locate critical points on the graphs of polynomial functions and
determine if each critical point is a minimum or a maximum.
I can describe and locate maximums, minimums, increasing and decreasing
intervals, and zeroes given a sketch of the graph.
5a. Functions: Manipulate functions and identify their properties. I can form a composite function.
I can create functions by adding, subtracting, multiplication, division, and
composition of functions.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
I can recognize the role that domain of a function plays in the combination of
functions by composition of functions.
5b. Functions: Identify basic properties of functions (definition of function,
domain, range, odd, even, asymptotic behavior).
I can find the domain of a composite function.
I can determine whether a function is even, odd, or neither algebraically and
graphically.
5c. Functions: Manipulate functions as elements to get new functions via
addition, subtraction, multiplication, division, and composition and can
simplify the resulting expression (e.g. difference quotient).
I can construct the difference quotient for a given function and simplify the
resulting expression.
5d. Functions: Construct and evaluate inverse functions and use domain
and/or range restriction appropriately.
I can calculate the inverse of a function with respect to each of the functional
operations.
I can verify by composition that one function is the inverse of another.
I can identify whether a function has an inverse with respect to composition
and when functions are inverses of each other with respect to composition.
I can find an inverse function by restricting the domain of a function that is
not one-to-one.
I can explain why the graph of a function and its inverse are reflections of one
another over the line y = x.
P.MCPS.6 Develop the concept of the limit using tables, graphs, and
algebraic properties.
I can explore the properties of a limit by analyzing sequences and series.
I can understand the relationship between a horizontal asymptote and the
limit of a function at infinity.
I can determine the limit of a function at a specified number.
I can find the limit of a function at a number using algebra.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Sections/Topics Activities/Resources/Materials
• Pre-assessment
• Section 1 Functions
• Section 2 Analyzing Graphs of Functions
• Section 3 Continuity, End Behavior, and Limits
• Section 4 Extrema and Average Rates of Change
• Quiz
• Section 5 Parent Functions and Transformations
• Section 6 Function Operations and Composition of Functions
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Unit 2
Power, Polynomial, and Rational Functions
14 Days
Standards “I Can” Statements
Algebra
1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques.
I can add, subtract, multiply, and divide polynomial, power, and rational
expressions.
I can simplify complex polynomial, power, radical, and rational expressions.
I can solve complex polynomial, power, radical, and rational equations.
1c.Equations: Solve polynomial equations of degree > 2 for both real and complex roots.
I know the Fundamental Theorem of Algebra and can show it is true for
quadratic polynomials.
1d. Equations: Use synthetic division and other relevant results to identify and simplify the equation.
I can use synthetic division to identify and simplify the equation.
I can identify the real zeros of the graph of a function (polynomial, power,
and rational) in equation or graphical form.
1f.Equations: Identify equations that can’t be solved directly and use graphical or other approximations.
I can explain the relationship between the real zeros and the x-intercept of the
graph of a function (exponential and logarithmic).
I can use the Remainder Theorem to determine roots of polynomials.
I can use the Rational Zero Theorem to determine roots of polynomials.
I can use the Upper and Lower Bound Tests to help determine roots of
polynomials.
I can use Descartes’ Rule of Signs to help find positive and negative roots of
polynomials.
I can use the Rational Root Theorem and the Irrational Root Theorem to
determine roots of polynomials.
2a.Inequalities: Apply various techniques (algebraic and graphical) to solve inequalities involving polynomials (including degree >2), and absolute values, and can express answers using interval notation.
I can solve nonlinear inequalities (quadratic and rational) by graphing
(solutions in interval notation if one-variable), and by using a sign chart.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Functions
3c. Properties of Functions: From the function can identify graphical
functional properties and vice versa: intercepts, asymptotes (vertical,
horizontal, slant), domain, range, and end behavior.
I can graph functions, identifying intercepts, domain, range, asymptotes
(including slant), and holes (when suitable factorizations are available) and
showing end-behavior.
3d. Properties of Functions: From the graph can locate critical points and
identify if each is a minimum, maximum or point of inflection, and locate
intervals of increasing/ decreasing.
I can locate critical points on the graphs of polynomial functions and
determine if each critical point is a minimum or a maximum.
I can describe and locate maximums, minimums, increasing and decreasing
intervals, and zeroes given a sketch of the graph.
Statistics and Probability
4a. Models: Use functions to model behavior described by words and/or data. I can find the regression equation that best fits bivariate data.
4b. Models: Identify and make appropriate models for situations involving
for example, direct and inverse proportionality, average rate of change,
exponential growth and decay, logarithmic relations, and periodic behavior.
I can explain how to determine the best regression equation model that
approximates a particular data set.
4c. Models: Use appropriate units and function properties, like domain, as
needed in function models.
c) Interpret the solutions in terms of the original problem.
I can identify possible considerations such as domain and range regarding the
accuracy of predictions when interpolating or extrapolating.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Unit 3
Exponential and Logarithmic Functions
12 Days
Standards “I Can” Statements
Algebra
1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques.
I can add, subtract, multiply, and divide exponential and logarithmic
expressions.
I can simplify complex exponential and logarithmic expressions.
I can solve complex exponential and logarithmic equations.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Unit 4
Trigonometric Functions
16 Days
Standards “I Can” Statements
Algebra
1a. Equations: Apply various techniques, as appropriate, to simplify
expressions and solve equations. This includes using exact symbolic
(algebraic), approximation and graphical techniques.
I can add, subtract, multiply, and divide trigonometric expressions.
I can simplify complex trigonometric expressions.
I can solve complex trigonometric equations.
Functions
6a. Trig Functions: Use trigonometric functions and identities to find specific results.
I can add, subtract, multiply, and divide trigonometric expressions.
I can simplify complex trigonometric expressions.
I can solve complex trigonometric equations.
6b. Trig Functions: Relate values on the unit circle to trig function values, and vice-versa, with numerical values at specific angles (0, π/6, π/4, π/3, π/2) and their periodic extensions.
I can find the reference angle of any angle on the unit circle. I can evaluate
the trig functions of any angle of the unit circle using reference angles.
6c. Trig Functions: Graph the six trigonometric functions and identify characteristics such as period, amplitude, phase shift, and asymptotes.
I can graph the six trigonometric functions (sin, cos, tan, csc, sec, cot) and
identify characteristics such as period, amplitude, phase shift, and
asymptotes.
I can determine the difference made by choice of units for angle measurement
when graphing a trigonometric function.
I can determine identify and list the appropriate domain and corresponding
range for each of the inverse trigonometric functions.
I can graph the inverse trigonometric functions and identify their key
characteristics.
Geometry
7a. Triangles: Solve right triangle problems including applications. I can use the definitions of the six trigonometric ratios as ratios of sides in a
right triangle to solve problems about lengths of sides and measures of
angles.
7b. Triangles: Solve right triangle problems involving angles of elevation and depression and angles using compass notation (e.g. 30o
North) using trigonometric identities and rules.
I can solve right triangle problems involving angles of elevation and
depression.
I can convert from degree measure to compass notation (i.e. degree-minutes-
seconds).
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
7c. Triangles: Use the Law of Cosines and Sines for all triangle types. I can prove the Law of Sines and Cosines and apply them to solve problems.
I can apply the Law of Sines (including the ambiguous case) and Cosines in
order to solve right and oblique triangles.
I can solve real work problems (e.g. surveying, navigation.)
I can determine how many solutions are possible for the Ambiguous case of
the Law of Sines.
I can determine when it is appropriate to use A = ½ ab sin C and Heron’s
Law.
I can find areas of triangles using the two area formulas A = ½ ab sin C and
Heron’s Law.
8d. Circles: Calculate basic geometric properties like area of a sector, arc length, and the relation between the area of a sector and the inscribed triangle.
I can derive and apply the formulas for the area of sector of a circle.
I can calculate the arc length of a circle subtended by a central angle.
I can apply linear and angular velocity formulas in real world applications.
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Sections/Topics Activities/Resources/Materials
• Pre-assessment
• Section 1 Right Triangle Trigonometry
• Section 2 Degrees and Radians, Arc Length, Area of a Sector, Linear
and Angular Speed
• Section 3 Trigonometric Functions on the Unit Circle
• Quiz
• Section 4 Graphing Sine and Cosine Functions
• Section 5 Graphing Tangent, Cosecant, and Secant
SDC Precalculus TN Ready Performance Standards by Unit
Maury County Public Schools 5/8/18 Office of Instruction Pk-12
Unit 5
Trigonometric Identities and Equations
13 Days
Standards “I Can” Statements
Algebra
1a. Equations: Apply various techniques, as appropriate, to simplify expressions and solve equations. This includes using exact symbolic (algebraic), approximation and graphical techniques.
I can add, subtract, multiply, and divide trigonometric expressions.
I can simplify complex trigonometric expressions.
I can solve complex trigonometric equations.
Functions
6d. Trig Functions: Use trigonometric identities to evaluate numerical
values, simplify expressions and solve equations. (E.g. use sum/difference
identities to evaluate sin (π/12), simplify (sin(x) + cos(x))2 .)
I can recognize and use the following trigonometric identities to verify
identities and solve trigonometric equations: Pythagorean, Reciprocal,
Quotient, Sum/Difference, Double Angle.
I can prove the sum and difference formulas for sine, cosine, and tangent and
apply them in solving problems.
6e. Trig Functions: Apply multiple identities to simplify expressions and
solve equations, including ones involving inverse functions.
I can use various trigonometric identities and combinations of trigonometric
identities to simplify and solve trigonometric equations.
I can use various trigonometric identities and combinations of trigonometric
identities to find inverses of trigonometric functions.
6f. Trig Functions: Solve trigonometric equations by factoring, by using
identities, and by graphing.
I can solve trigonometric equations by factoring and using trigonometric
identities.
Sections/Topics Activities/Resources/Materials
• Pre-assessment
• Section 1 Trigonometric Identities
• Section 2 Verifying Trigonometric Identities
• Quiz
• Section 3 Solving Trigonometric Equations
• Section 4 Sum and Difference Identities
• Section 5 Multiple-Angle and Product-to-Sum Identities