Download Advanced Algebra/PreCalculus Semester Overview

Advanced Algebra/PreCalculus Semester Overview
1st Semester
Unit 1 – Functions
AII.2 (reference)
AII.4
AII.7
Unit 2 – Conic Sections
AA.3
AA.4
Unit 3 – Matrices
AA.1
AA.2
Unit 4 – Trigonometry (Continued into Semester 2)
AA.5
AA.7
AA.5
AA.6
AA.5
AA.8
AA.9
AA.11
AA.12
AA.8
AA.10
42 blocks
2nd Semester
Unit 4 – Trigonometry (Continued from Semester 1)
AA.11
AA.13
Unit 5 – Exponential and Logarithmic Functions
AA.14
Unit 6 – Polynomial and Rational Functions Review
Unit 7 – Sequences and Series
AA.15
AA.16
AA.17
Unit 8 – Topics from Calculus: Limits
43 blocks
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and
representations as they engage in mathematics activities throughout the year.
Advanced Algebra/PreCalculus
Curriculum Guide 2013-2014
Last updated: August 21, 2013
1
Advanced Algebra/PreCalculus Scope & Sequence
Semester 1: 42 blocks total
Number
Standard
Topic
of blocks
Unit 1 – Functions
3
AII.2
One-to-one functions (new)
AII.4
Inverse Functions
AII.7
Transformations (connect to graphs and equations)
Domain and range (interval notation)
Even and odd functions (new)
Factoring
Completing the square
Converting between standard form and vertex form (h, k) form
1 block – Suggested assessment, enrichment, and remediation for this unit.
Unit 2 – Conic Sections
2
AA.3
Parabola
AA.4
Define a parabola using the focus and the directrix
Identify whether the parabola is horizontal or vertical and how it opens
Graph a parabola, identify the vertex, focus, directrix, and latus rectum
Write the equation of a graph given the vertex, focus, directrix, or latus rectum
1
Circle
Graph the standard form
Write the equation of a circle given information about its center, radius, or diameter
Graph a circle from general form
Find the x- and y- intercepts of the circle
Convert between standard form and general form
Satellite dishes (parabola)
2
Ellipse
Define an ellipse using the foci
Identify whether the ellipse is horizontal or vertical
Graph the ellipse, identify the major/minor axes, the center, the vertices, and the foci
Write the equation of the ellipse given the center, foci, vertices, or axes
Find the x- and y- intercepts of the ellipse
Convert between standard form and general form
Orbits, whispering galleries (ellipses)
Advanced Algebra/PreCalculus
Curriculum Guide 2013-2014
Last updated: August 21, 2013
2
Semester 1: 42 blocks total (continued)
Number
of blocks
Standard
Topic
Unit 2 – Conic Sections (continued)
2
AA.3
AA.4
Hyperbola
Define a hyperbola using the foci
Identify whether the hyperbola is horizontal or vertical
Graph the hyperbola, identify the center, vertices, foci, and the equations of the asymptotes
Write the equation of the hyperbola given information about the center, vertices, foci, or the
equations of the asymptotes
Find the x- and andy- intercepts of the hyperbola
Convert between standard form and general form
LOng RAnge Navigation system (LORAN) (hyperboa)
Applications of Conics
Solving systems of conics
1
4 blocks – Suggested assessment, enrichment, and remediation for this unit.
Advanced Algebra/PreCalculus
Curriculum Guide 2013-2014
Last updated: August 21, 2013
3
Semester 1: 42 blocks total (continued)
Number
of blocks
Standard
Topic
Unit 3 – Matrices
2
2
AA.1
AA.2
Writing a Matrix
Dimension
Matrix Operations
Addition
Subtraction
Scalar Multiplication
Matrix Multiplication
Larger than a 3 x 3 on a calculator only
Recommended that matrix multiplication for matrices smaller than 3 x 3 are done without the
assistance of a calculator
Determinants
Meaning of a determinant of zero
Larger than a 2 x 2 on a calculator only, recommending that all others are calculated without the aid
of a calculator
Area of a triangle (Application)
Inverses
Larger than a 2 x 2 on a calculator only, recommending that all others are calculated without the aid
of a calculator
When an inverse does not exist
Solving Systems of Equations
Write the system as a matrix
Solve using an inverse matrix
Matrices larger than a 2 x 2 on a calculator only, but write the matrix equation
Applications Involving Matrices
Determine if points are collinear
Cryptography
Equation of Parabola given 3 points
2 blocks – Suggested assessment, enrichment, and remediation for this unit.
Advanced Algebra/PreCalculus
Curriculum Guide 2013-2014
Last updated: August 21, 2013
4
Semester 1: 42 blocks total (continued)
Number
Standard
Topic
of blocks
1
AA.5
2
AA.7
AA.6
4
AA.5
AA.8
AA.9
AA.11
AA.12
Advanced Algebra/PreCalculus
Unit 4 – Trigonometry
Introduction to Trigonometry: Angles
Define angle, including its initial and terminal sides
Identify the direction of rotation for angles to be positive and negative
Define standard position of an angle, direction of rotation, quadrant in which an angle lies, and
quadrantal angles
Draw angles of varying measures
Angle Measurements
Define radian
Use the arc length and area of a sector to solve problems
Convert from radians to degrees and back
Use unit analysis to solve problems involving linear speed, rotational speed, and angular speed
Unit Circle
Use the concepts of the special right triangles to create the unit circle
Reproduce the unit circle without the aid of a calculator
Define the six trigonometric functions
Determine the signs of the trigonometric functions in each quadrant
Find the six trigonometric functions
• In terms of the coordinates of any point on the unit circle
• Using a calculator
• In terms of the coordinates of any point on a circle of radius, r
• Given the coordinates of any point on the terminal side of an angle
Write the following fundamental identities:
• Reciprocal identities
• Quotient identities
• Pythagorean identities
Solve problems by finding values of the six trigonometric functions
• Using even-odd properties to find the exact values of the trigonometric functions
• Using fundamental trigonometric identities
• Given one of the functions and the quadrant of the angle
Curriculum Guide 2013-2014
Last updated: August 21, 2013
5
Semester 1: 42 blocks total (continued)
Number
Standard
Topic
of blocks
4
4
Unit 4 – Trigonometry (continued)
AA.10
Graphing Trigonometric Functions
State the domain, range, and periodicity of the trigonometric functions
Graph the sine, cosine and tangent functions as parent functions
• Identify the properties of the sine, cosine, and tangent graphs
• Use the sine, cosine, and tangent graphs to develop and explain the graphs of the remaining
trigonometric functions (i.e. sec, csc, cot)
Use knowledge of transformations to graph general form of trigonometric equations in the form
y = A sin( Bx − C ) + D
• Describe how changes in amplitude, period, phase shifts, and vertical shifts affect sine and cosine
graphs from a practical application standpoint
• Determine the amplitude, period, phase shift, and vertical shift of trigonometric functions and
their graphs
Write a sine or cosine function that satisfies a given data set allowing for amplitude, period, phase
shift, and vertical shift.
4 blocks – Suggested assessment, enrichment, and remediation for this unit.
AA.11
Inverse Trigonometric Functions
Define the inverse of each of the six trigonometric functions, to include restricted domain and range
Find the exact value of the inverse trigonometric functions using
• Graphing calculators
• Unit circle
Composite trigonometric functions
1 block – Suggested assessment, enrichment, and remediation for this unit.
Advanced Algebra/PreCalculus
Curriculum Guide 2013-2014
Last updated: August 21, 2013
6
Advanced Algebra/PreCalculus
Curriculum Guide 2013-2014
Last updated: August 21, 2013
7