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MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS
Curriculum and Instruction
2012-2013
Course Code: 120234002
Page 1 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS
Course Code: 120234002
This Page Was
Intentionally
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Curriculum and Instruction
2012-2013
Page 2 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS
Course Code: 120234002
ESSENTIAL CONTENT NINE WEEK OVERVIEW
1
I.
E.
III.
2nd Nine Weeks
Nine Weeks
Functions, Equations, and Graphs
A.
B.
C.
D.
II.
ST
Linear Functions and Slope
Transformations of Functions
Inverse Functions
Distance and Midpoint
Formulas
Basic Modeling with Functions
IV. Trigonometric Functions
A.
B.
C.
D.
E.
V. Right Triangle Trigonometry
Polynomial and Rational Functions
A. Complex Numbers
B. Polynomial Functions and
Their Graphs
A.
B.
C.
More on Polynomial and Rational
Functions
D.
E.
F.
A. Dividing Polynomials
B. Zeros of Polynomial Functions
C. Rational Functions and Their
Graphs
D. Polynomial and Rational
Inequalities and Modeling
Angles and Radian Measure
Linear and Angular Speed
The Unit Circle
Fundamental Trigonometric Functions
Periodic Functions
Evaluating Trigonometric Functions
Special Angles
Trigonometric Functions and
Complements/Cofunction Identities
Angles of Elevation/Depression
Trigonometric Functions of Any Angle
Reference Angles
VI. Circular Trigonometric Functions
A. Graphs of Sine and Cosine
B. Graphs of Other Trigonometric Functions
C. Inverse Trigonometric Functions
D. Applications of Trigonometric Functions
3rd Nine Weeks
VIII. Additional Topics in Trigonometry
A.
B.
C.
D.
E.
The Law of Sines
The Law of Cosines
Polar Coordinates
Graphs of Polar Equations
Complex Numbers in Polar Form:
DeMoivre’s Theorem
IX. Discrete Mathematics
A. Directed Line Segments and
Geometric Vectors
B. Vectors in The Rectangular
Coordinate System
C. Applications Using Vectors
4th Nine Weeks
XI.
Sequences and Induction
A.
B.
C.
D.
E.
F.
Sequences and Summation Notation
Arithmetic Sequences
Geometric Sequences and Series
Mathematical Induction
Divisibility Statements
Parity Statements
NOT IN TEXT
XII. Introduction to Calculus
A. Limits Using Tables and Graphs
B. Properties of Limits
C. Limits and Continuity
X. Conics and Analytic Geometry
A. The Ellipse
B. The Hyperbola
C. The Parabola
D. Parametric Equations
E. Applications of Conic Sections
VII. Analytic Trigonometry
A. Verifying Trigonometric Identities
B. Identity Formulas
C. Trigonometric Equations
Total Days Allotted for Instruction,
Testing, and “Ketchup” Days:
Traditional (T): 46; Block(B): 23
Topic I:
T: 14/ B:7
Topic II:
T: 12/ B:6
Topic III:
T:20/B:10
Curriculum and Instruction
2012-2013
Total Days Allotted for Instruction,
Testing. and “Ketchup” Days:
Traditional (T): 45; Block(B): 22
Topic: IV
T:10/ B:5
Topic :V
T:14/ B:7
Topic: VI
T:10/ B:5
Topic :VII
T:11/ B:5
Total Days Allotted for Instruction,
Testing. and “Ketchup” Days:
Traditional (T): 41; Block(B): 20
Topic VIII:
T: 12/ B: 6
Topic IX:
T: 14/ B: 7
Topic X:
T: 15/ B: 7
Total Days Allotted for Instruction,
Testing. and “Ketchup” Days:
Traditional (T): 48; Block(B): 24
Topic XI:
T: 23/ B: 12
Topic XII:
T: 25/ B: 12
Page 3 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS
Course Code: 120234002
BENCHMARKS AT A GLANCE
ST
1
Nine Weeks
I. Functions, Equations, and Graphs
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
MA.912.A.2.1
MA.912.A.2.2
MA.912A.2.4
MA.912.A.2.6
MA.912.A.2.10
MA.912.A.2.11
MA.912.G.1.1
II. Polynomial and Rational
Functions
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
III.
MA.912.A.1.6
MA.912.A.4.5
MA.912.A.4.6
MA.912.A.4.7
MA.912.A.4.8
MA.912.A.5.6
MA.912.C.1.12
More on Polynomial and
Rational Functions
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

nd
MA.912.A.4.4
MA.912.A.4.5
MA.912.A.4.6
MA.912.A.4.7
MA.912.A.4.8
MA.912.A.4.9
MA.912.A.5.6
MA.912.C.1.12
Total Days Allotted for Instruction,
Testing, and “Ketchup” Days:
Traditional (T): 46; Block(B): 23
Topic I:
T: 14/ B:7
Topic II:
T: 12/ B:6
Topic III:
T:20/B:10
Curriculum and Instruction
2012-2013
2
IV. Trigonometric Functions





MA.912.T.1.1
MA.912.T.1.2
MA.912.T.1.3
MA.912.T.1.4
MA.912.T.1.8
V. Right Triangle Trigonometry




3rd Nine Weeks
Nine Weeks
MA.912.T.1.3
MA.912.T.1.5
MA.912.T.2.1
MA.912.T.2.2
VIII. Additional Topics In Trigonometry

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MA.912.T.2.3
MA.912.T.2.4
MA.912.T.4.1
MA.912.T.4.2
MA.912.T.4.3
MA.912.T.4.4
MA.912.T.4.5
IX. Discrete Mathematics

MA.912.D.9.1

MA.912.D.9.2
 MA.912.D.9.3
VI. Circular Trigonometry



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

MA.912.T.1.6
MA.912.T.1.7
MA.912.T.1.8
MA.912.T.5.1
MA.912.T.5.2
MA.912.T.5.3
X. Conics and Analytic Geometry

MA.912.A.9.1

MA.912.A.9.2

MA.912.A.9.3

MA.912.D.10.1

MA.912.D.10.2

MA.912.D.10.3
4th Nine Weeks
XI. Sequences and Induction







MA.912.D.1.1
MA.912.D.1.2
MA.912.D.1.3
MA.912.D.11.1
MA.912.D.11.2
MA.912.D.11.3
MA.912.D.11.4
XII. Introduction to Calculus










MA.912.A.5.6
MA.912.C.1.1
MA.912.C.1.2
MA.912.C.1.3
MA.912.C.1.4
MA.912.C.1.5
MA.912.C.1.9
MA.912.C.1.10
MA.912.C.1.11
MA.912.C.1.13
VII. Analytic Trigonometry




MA.912.T.3.1
MA.912.T.3.2
MA.912.T.3.3
MA.912.T.3.4
Total Days Allotted for Instruction,
Testing. and “Ketchup” Days:
Traditional (T): 45; Block(B): 22
Topic: IV
T:10/ B:5
Topic :V
T:14/ B:7
Topic: VI
T:10/ B:5
Topic :VII
T:11/ B:5
Total Days Allotted for Instruction,
Testing. and “Ketchup” Days:
Traditional (T): 41;
Topic VIII:
Topic IX:
Topic X:
Block(B): 20
T: 12/ B: 6
T: 14/ B: 7
T: 15/ B: 7
Total Days Allotted for Instruction,
Testing. and “Ketchup” Days:
Traditional (T): 48; Block(B): 24
Topic XI:
T: 23/ B: 12
Topic XII:
T: 25/ B: 12
Page 4 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS
Course Code: 120234002
1st Nine Weeks:
Topics I, II and III
Objectives:
After studying this unit the student will:

Plot points in the rectangular coordinate system.

Graph equations in the rectangular coordinate system.

Interpret information about a graphing utility’s viewing rectangle or
table.

Use a graph to determine intercepts.

Interpret information given by graphs.

Find the domain and range of a relation.

Determine whether a relation is a function.

Determine whether an equation represents a function.

Evaluate a function.

Graph functions by plotting points.

Use the vertical line test to identify functions.

Obtain information about a function from its graph.

Identify the domain and range of a function from its graph.

Identify intercepts from a function’s graph.

Identify intervals on which a function increases, decreases, or is
constant.

Use graphs to locate relative maxima or minima.

Identify even or odd functions and recognize their symmetries.

Understand and use piecewise functions.

Find and simplify a function’s difference quotient.

Calculate a line’s slope.

Write the point-slope form of the equation of a line.

Write and graph the slope-intercept form of the equation of a line.

Graph horizontal or vertical lines.

Recognize and use the general form of a line’s equation.

Use intercepts to graph the general form of a line’s equation.

Model data with linear functions and make predictions.

Find slopes and equations of parallel and perpendicular lines.
Curriculum and Instruction
2012-2013
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Interpret slope as rate of change.
Find a function’s average rate of change.
Recognize graphs of common functions.
Use vertical shifts to graph functions.
Use horizontal shifts to graph functions.
Use reflections to graph functions.
Use vertical stretching and shrinking to graph functions.
Use horizontal stretching and shrinking to graph functions.
Graph functions involving a sequence of transformations.
Verify inverse functions.
Find the inverse of a function.
Use the horizontal line test to determine if a function has an inverse
function.
Use the graph of a one-to-one function to graph its inverse function.
Find the inverse of a function and graph both functions on the same
axes.
Find the distance between two points.
Find the midpoint of a line segment.
Write the standard form of a circle’s equation.
Give the center and radius of a circle whose equation is in standard
form.
Convert the general form of a circle’s equation to standard form.
Construct functions from verbal descriptions.
Construct functions from formulas.
Use the Conjugate Root Theorem to find the zeros of a polynomial
function.
Page 5 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS

Course Code: 120234002
Recognize characteristics of parabolas.
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Identify polynomial functions.
Recognize characteristics of graphs of polynomial functions.
Determine end behavior of polynomial functions.
Use factoring to find zeros of polynomial functions.
Identify zeros and their multiplicities.
Understand and use the Intermediate Value Theorem on a function over a closed interval.
Understand the relationship between degree and turning points.
Graph polynomial functions with and without technology.
Use long division to divide polynomials.
Use synthetic division to divide polynomials.
Evaluate a polynomial using the Remainder Theorem.
Use the Factor Theorem to solve a polynomial equation.
Use the Rational Zero Theorem to find possible rational zeros.
Find zeros of a polynomial function using technology.
Describe the relationships among the solutions of an equation, the zeros of a function, the x-intercepts of a graph, and the
factors of a polynomial expression with and without technology.
Use the Linear Factorization Theorem to find polynomials with given zeros.
Use the Fundamental Theorem of Algebra to find the number of complex roots of a polynomial.
Use Descartes’ Rule of Signs.
Use the Conjugate Root Theorem to find zeros of a polynomial.
Write a polynomial equation for a given set of real and/or complex roots.
Find the domains of rational functions.
Use arrow notation.
Identify vertical asymptotes.
Identify horizontal asymptotes.
Graph rational functions.
Identify oblique/slant asymptotes.
Curriculum and Instruction – Mathematics
2012-2013
Page 6 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
PRECALCULUS
Course Code: 120234002
2nd Nine Weeks
Topics IV, V, VI and VII
Objectives:
After studying this unit the student will:

Recognize and use the vocabulary of angles.

Use degree measure.

Use radian measure.

Convert between degrees and radians.

Draw angles in standard position.
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Find coterminal angles.
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Find the length of a circular arc.

Use linear and angular speed to describe motion on a circular path.

Use a unit circle to define trigonometric functions of real numbers.

Recognize the domain and range of sine and cosine functions.

Find exact values of the trigonometric functions at various radians.

Use even and odd trigonometric functions.

Recognize and use fundamental identities.

Use periodic properties.

Evaluate trigonometric functions with a calculator.

Use right triangles to evaluate trigonometric functions.

Find function values for 30˚ (π/6), 45˚ (π/4), and 60˚ (π/3).

Use equal cofunctions of complements.

Use right triangle trigonometry to solve applied problems.

Use the definitions of trigonometric functions of any angle.

Use the signs of the trigonometric functions.

Find reference angles.

Use reference angles to evaluate trigonometric functions.

Understand the graph and variations of y = sin x.

Understand the graph and variations of y = cos x.

Use vertical shifts of sine and cosine curves.

Model periodic behavior.

Understand the graph and variations of y = tan x.

Understand the graph and variations of y = cot x.
Curriculum and Instruction – Mathematics
2012-2013
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Understand the graphs of and variations of y = sec x.
Understand the graph and variations of y = csc x.
Understand and use the inverse sine function.
Understand and use the inverse cosine function.
Understand and use the inverse tangent function.
Use a calculator to evaluate inverse trigonometric functions.
Find exact values of composite functions with inverse trigonometric
functions.
Solve a right triangle.
Solve problems involving bearings.
Model simple harmonic motion.
Use the fundamental trigonometric identities to verify identities.
Use the formula for the cosine of the difference of two angles.
Use sum and difference formulas for cosines and sines.
Use sum and difference formulas for tangents.
Use the double-angle formulas.
Use the power-reducing formulas.
Use the half-angle formulas.
Use the product-to-sum formulas.
Use the sum-to-product formulas.
Find all solutions of a trigonometric equation.
Solve equations with multiple angles.
Solve trigonometric equations quadratic in form.
Use factoring to separate different functions in trigonometric
equations.
Use identities to solve trigonometric equations.
Use a calculator to solve trigonometric equations.
Page 7 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA II
Course Code: 120033001
3rd Nine Weeks
Topics VIII, IX and X
Objectives:
After studying this unit the student will:
 Use the Law of Sines to solve oblique triangles.
 Use the Law of Sines to solve, if possible, the triangle or triangles in the
ambiguous case.
 Find the area of an oblique triangle using the sine function.
 Solve applied problems using the Law of Sines.
 Use the Law of Cosines to solve oblique triangles.
 Solve applied problems using the Law of Cosines.
 Use Heron’s formula to find the area of a triangle.
 Plot points in the polar coordinate system.
 Find multiple sets of polar coordinates for a given point.
 Convert a point from polar to rectangular coordinates.
 Convert a point from rectangular to polar coordinates.
 Convert an equation from rectangular to polar coordinates.
 Convert an equation from polar to rectangular coordinates.
 Use point plotting to graph polar equations.
 Use symmetry to graph polar equations.
 Use magnitude and direction to show vectors are equal.
 Visualize scalar multiplication, vector addition, and vector subtraction as
geometric vectors.
 Represent vectors in the rectangular coordinate system.
 Perform operations with vectors in terms of i and j.
 Find the unit vector in the direction of v.
 Write a vector in terms of its magnitude and direction.
 Solve applied problems involving vectors.
 Find the dot product of two vectors.
 Find the angle between two vectors.
 Use the dot product to determine if two vectors are orthogonal.
 Find the projection of a vector onto another vector.
 Express a vector as the sum of two orthogonal vectors.
 Graph ellipses centered at the origin.
 Write equations of ellipses in standard form.
Curriculum and Instruction – Mathematics
2012-2013
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Graph ellipses not centered at the origin.
Solve applied problems involving ellipses.
Locate a hyperbola’s vertices and foci.
Write equations of hyperbolas in standard form.
Graph hyperbolas centered at the origin.
Graph hyperbolas not centered at the origin.
Solve applied problems involving hyperbolas.
Graph parabolas with vertices at the origin.
Write equations of parabolas in standard form.
Graph parabolas with vertices not at the origin.
Solve applied problems involving parabolas.
Use point plotting to graph plane curves described by parametric equations.
Eliminate the parameter.
Find parametric equations for functions.
Understand the advantages of parametric representations.
Page 8 of 9
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA II
Course Code: 120033001
4th Nine Weeks
Topics
Objectives:
After studying this unit the student will:
 Find particular terms of a sequence from the general term.
 Use recursion formulas.
 Use factorial notation.
 Use summation notation.
 Find the common difference for an arithmetic sequence.
 Write terms of an arithmetic sequence.
 Use the formula for the general term of an arithmetic sequence.
 Use the formula for the sum of the first terms of an arithmetic
sequence.
 Find the common ratio of a geometric sequence.
 Write terms of a geometric sequence.
 Use the formula for the general term of a geometric sequence.
 Use the formula for the sum of the first n terms of a geometric
sequence.
 Find the value of an annuity.
 Use the formula for the sum of an infinite geometric series.
 Understand the principle of mathematical induction.
 Prove statements using mathematical induction.
 Understand limit notation.
 Find limits using tables.
 Find limits using graphs.
 Find one-sided limits and use them to determine if a limit exists.
 Find limits of constant functions and the identity function.
 Find limits using properties of limits.
 Find one-sided limits using properties of limits.
 Find limits of fractional expressions in which the limit of the
denominator is zero.
 Determine whether a function is continuous at a number.
 Determine for what numbers a function is discontinuous.
Curriculum and Instruction – Mathematics
2012-2013
Page 9 of 9