Download Planned Course - Warrior Run School District

WARRIOR RUN SCHOOL DISTRICT
WARRIOR RUN HIGH SCHOOL
MATH CURRICULUM
PRECALCULUS
PREPARED BY:
MATH DEPARTMENT
SUBMITTED:
JUNE 2007
INTRODUCTION
Precalculus builds on previous math courses. It emphasizes comprehensive coverage of algebra,
trigonometry and analytical geometry. The course makes wide use of graphing calculators. Precalculus
also provides an introduction to the skills required in calculus.
EXPECTED LEVELS OF ACHIEVEMENT
The students are expected to:
 maintain an 80% or better average in Precalculus.
 complete all homework assignments. Homework will
Be a part of each nine-week grade.
 master 80% of all written objectives as outlined in
each unit of instruction.
 be prepared for class by having necessary materials
with them.
 follow guidelines of classroom behavior as outlined in the student
Handbook.
PROCEDURES FOR EVALUATION
Student grades will be determined on a percentage basis. Evaluation will be based on the
following:
1. Tests
2. Quizzes
3. Homework
REFERENCES
Textbook:
Algebra and Trigonometry with Analytic Geometry
by:
Earl W. Swokowski
Jeffrey A. Cole
2
UNIT I
FUNDAMENTAL CONCEPTS OF ALGEBRA
OBJECTIVES
Students will be able to:
1. identify integers, rational, irrational, real, and complex numbers.
2. apply the properties of real numbers.
Std. 2.1.11.A
Std. 2.1.11.A
3. simplify numbers written with absolute value.
Std. 2.1.11.A
4. apply the laws of exponents to simplify algebraic expressions with radicals and negative
exponents. Std. 2.1.11.A
5. rationalize denominators.
Std. 2.1.11.A
6. add, subtract, multiply, and divide polynomials.
7. factor polynomials.
Std. 2.8.11.S
8. simplify rational expressions.
Std. 2.8.11.S
CONTENT
1. Real Numbers (Obj. 1, 2, 3)
2. Exponents and Radicals (Obj. 1, 4, 5)
3. Algebraic Expressions (Obj. 1, 6, 7)
4. Fractional Expressions (Obj. 1, 8)
3
Std. 2.8.11.S
UNIT II
EQUATIONS AND INEQUALITIES
OBJECTIVES
Students will be able to:
1. solve applied problems (ex: interest, mixture, distance, and work)
2.3.8.B
Std. 2.8.11.D,
2. solve quadratic equations using factoring and the quadratic formula.
2.11.11.A
Stds. 2.8.11.N,
3. solve applied problems using quadratic equations.
2.11.11.A
4. solve the following types of equations:
 3rd & 4th degree equations by factoring
 absolute value equations
 equations with radicals
 equations with fractional exponents.
Stds. 2.8.11.N, 2.8.11.S
CONTENT
1. Applied problems (Obj. 1)
2. Quadratic Equations (Obj. 2, 3)
3. Other Types of Equations
(Obj. 4)
4
Stds. 2.8.11.N,
UNIT III
FUNCTIONS AND GRAPHS
OBJECTIVES
Students will be able to:
1. apply the distance and midpoint formulas.
2. sketch the graph of circles and semicircles.
Std. 2.3.8.A
Std. 2.10.11.A
3. calculate the equation of a circle given the center and radius.
4. find the center and radius given the equation of a circle.
Std. 2.8.11.E
5. find a general form of an equation given various information.
6. solve applied problems by writing a linear equation.
Std. 2.8.11.E
Std.
Std. 2.8.11.N
7. determine the domain and range of a function given its graph.
8. determine the domain of a function given an equation.
2.8.11.L
Std.
2.8.11.O
Std. 2.8.11.O
9. solve applied problems by writing linear or quadratic equations.
a. 2.8.11.N
Std. 2.8.11.D,
10. graph functions using symmetry, translations, stretching, and compression.
Std. 2.8.11.Q
11. calculate the maximum or minimum value of a quadratic function.
12. solve applied problems by writing quadratic equations.
13. add, subtract, multiply, and divide functions.
14. calculate the composition of functions.
15. calculate the inverse of a function.
Std. 2.8.11.N
Std. 2.8.11.D, 2.8.11.N
Std. 2.8.11.S
2.8.11.S
Strd. 2.8.11.P
16. solve applied problems using direct, inverse, and joint variation.
5
Std. 2.8.8.J
CONTENT
1. Rectangular Coordinate System (Obj. 1, 2)
2. Graphs of Equations
(Obj. 3,4)
3. Lines (Obj. 5, 6, 9)
4. Definition of Functions (Obj. 6, 7, 8, 9, 12)
5. Graphs of Functions (Obj. 10)
6. Quadratic functions (Obj. 9, 11, 12)
7. Operations of Functions (Obj. 13, 14)
8. Inverse Functions (Obj. 15)
9. Variation
Oobj. 16)
UNIT IV
POLYNOMIAL AND RATIONAL FUNCTIONS
OBJECTIVES
Students will be able to:
1. apply the intermediate value theorem to show that a functions has a zero between two
given values. Std. 2.8.11.S
2. determine the values of the domain when the function is less than zero and greater than
zero. Std. 2.8.11.S
3. divide polynomials by long division.
Std. 2.1.11.A
4. divide a polynomial by a first degree polynomial by synthetic division.
6
Std. 2.1.11.A
5. use synthetic division to show a value is a zero of a function.
Stds. 2.8.11.N, 2.8.11.S
6. find a polynomial function given the zeros of the function and a point on the function.
Std. 2.8.11.S
7. use Descartes’ Rule of Signs to determine the possible positive, negative, and nonreal
complex solutions of an equation. Std. 2.8.11.S
8. use the theorem on bounds to determine upper and lower bounds for an equation.
Std. 2.8.11.S
9. apply Descartes’ Rule of Signs and the theorem on bounds for real zeros to calculate the
zeros of third and fourth degree equations. Std. 2.8.11.N
10. solve applied problems using third degree equations.
11. graph rational functions.
Stds.
Std. 2.8.11.N
2.8.8.I, 2.8.11.K
CONTENT
1. Polynomial Functions of Degree Greater than two
(Obj. 1, 2, 3)
2. Properties of Division (Obj. 3,4,5)
3. Zeros of Polynomials
(Obj. 4, 6,7,8)
4. Complex and Rational Zeros of Polynomials
5. Rational Functions
(Obj. 4, 6, 7, 8, 9, 10)
(Obj. 11)
UNIT V
EXPONENTIAL and LOGARITHMIC FUNCTIONS
OBJECTIVES
Students will be able to:
1. solve an equation where the variable is an exponent.
7
Std. 2.8.11.N, 2.8.11.S
2. solve applied problems using exponential equations.
Std. 2.8.11.N
3. use the natural exponential function to solve applied problems.
2.8.11.S, 2.11.11.C
Std. 2.8.11.N,
4. change equations in exponential form to logarithmic form and logarithmic form to
exponential form. Std. 2.8.11.S
5. use logarithmic equations to solve applied problems.
Std. 2.8.11.N, 2.8.11.S
6. apply the properties of logarithms to simplify expressions involving logarithms.
Std. 2.8.11.S
7. solve equations involving logarithms.
Std. 2.8.11.N
8. apply the change of base formula to solve logarithmic equations.
CONTENT
1. Exponential Functions
(Obj. 1, 2)
2. The Natural Exponential Function
3. Logarithmic Functions
(Obj. 3)
(Obj. 4, 5)
4. Properties of Logarithms
(Obj. 4, 6, 7)
5. Exponential and Logarithmic Equations
(4, 7, 8)
8
Std. 2.8.11.N
UNIT VI
THE TRIGONOMETRIC FUNCTIONS
OBJECTIVES
Students will be able to:
1. convert angular measure in degrees to radians and radians to degrees.
2.10.8.A
Stds. 2.3.11.B,
2. calculate the length of an arc subtended by a central angle of given measure.
Std. 2.10.8.A
3. calculate angular and linear speed.
Std. 2.10.8.A
4. find the values of the six trigonometric functions for a given angle in a right triangle.
Std. 2.10.8.B, 2.10.11.A
5. calculate the values of the trigonometric functions of a real number.
Std. 2.10.8.B
6. use a unit circle to calculate trigonometric functions of a real number that falls on an axis.
Std. 2.10.11.B
7. use a reference angle to calculate the exact values of trigonometric functions.
2.10.11.B
Std.
8. use inverse trigonometric functions to calculate the angle in degrees or radians of a given
trig functions. Stds. 2.10.8.A, 2.10.11.B
9. calculate the amplitude, period, phase shift, and vertical translation given a trigonometric
function or the graph of a trig function. Stds. 2.10.8.A, 2.10.11.A
10. graph trigonometric equations with and without graphing calculators.
2.10.11.B
11. solve applied problems using trigonometric equations.
Stds. 2.10.8.A, 2.10.11.B
12. solve applied problems involving bearings using trig equations.
2.10.11.B
9
Stds. 2.10.11.A,
Stds. 2.10.8.A,
CONTENT
1. Angles
(Obj. 1, 2, 3)
2. Trigonometric Functions of Angles
(Obj. 4)
3. Trigonometric Functions of Real Numbers
(Obj. 5, 6)
4. Values of Trigonometric Functions. (Obj. 4, 5, 6, 7, 8)
5. Trigonometric Graphs
6. Applied Problems
(Obj. 9)
(Obj. 4, 5, 6, 7, 8, 10, 11)
UNIT VII
ANALYTIC TRIGONOMETRY
OBJECTIVES
Students will be able to:
1. verify trigonometric identities.
Std. 2.10.11.B
2. use identities to solve for all the solutions trigonometric equations or the solutions on an
interval. Std. 2.10.11.B
3. use calculators to approximate the solutions to trigonometric equations.
Std. 2.10.11.B
4. apply cofunction formulas to rewrite trigonometric expressions.
Std. 2.10.11.B
5. use addition and subtraction formulas to verify identities and to solve trig equations.
2.10.11.B
6. use multiple angle formulas to verify identities and to solve trig equations.
Std. 2.10.11.B
10
Std.
7. use product-to-sum and sum-to-product formulas to verify identities and to solve trig
equations. Std. 2.10.11.B
8. find the exact values of inverse trig functions.
Std. 2.10.11.B
9. use inverse trigonometric functions to find the solutions of equations.
Std. 2.10.11.B
CONTENT
1. Verifying Trigonometric Identities
2. Trigonometric Equations
(Obj. 1)
(Obj. 2, 3)
3. Addition and Subtraction formulas
4. Multiple-Angle Formulas
(Obj. 4, 5)
(Obj. 6)
5. Product-to-Sum and Sum-to-Produce Formulas
6. Inverse Trigonometric Functions
(Obj. 7)
(Obj. 4, 5, 6, 7, 8, 9)
UNIT VIII
APPLICATIONS OF TRIGONOMETRY
OBJECTIVES
Students will be able to:
1. apply the law of sines to solve trigonometric equations.
2. apply the law of cosines to solve trigonometric equations.
11
Std. 2.10.11.B
Std. 2.10.11.B
3. calculate the area of a triangle given two sides and the sine of the angle between them.
Std. 2.10.11.B
4. use Heron’s Formula to calculate the area of a triangle given three sides.
5. solve applied problems using the law of sines and cosines.
Std. 2.10.11.B
Std. 2.10.11.B
CONTENT
1. The Law of Sines
(Obj. 1, 5)
2. The Law of Cosines
(Obj. 2, 3, 4, 5)
UNIT IX
SYSTEMS OF EQUATIONS AND INEQUALITIES
OBJECTIVES
Students will be able to:
1. solve systems of linear equations.
Std. 2.8.11.G
2. solve applications linear programming.
2.8.11.D
3. solve systems of linear equations in more than two variables using matrices.
Stds. 2.8.11.F, 2.8.11.G
4. add, subtract, multiply matrices.
Stds. 2.8.11.I, 2.8.11.G
5. calculate the determinate of a matrix.
Std. 2.8.11.I
12
6. use Cramer’s rule to solve a system of linear equations.
Std. 2.8.11.I
CONTENT
1. Systems of Equations.
2. Linear Programming
(Obj. 1)
(Obj. 2)
3. Systems of Linear Equations in More that Two Variables
4. The Algebra of Matrices
5. Determinants
(Obj. 3)
(Obj. 4)
(Obj. 5)
6. Properties of Determinants
(Obj. 6)
7.
UNIT X
INFINITE SEQUENCES AND SUMMATION NOTATION
OBJECTIVES
Students will be able to:
1. find the terms of a recursively defined infinite sequence.
Std. 2.11.11.D
2. find a sum given an expressions in summation notation.
Std. 2.11.11.D
3. find a specified term of an arithmetic sequence.
Std. 2.11.11.D
4. find the sum of a specified number of terms of an arithmetic sequence.
13
Std. 2.11.11.D
5. solve application problems using an arithmetic sequence.
6. find a specified term of a geometric sequence.
Std. 2.11.11.D
Std. 2.11.11.D
7. find the sum of a specified number of terms of a geometric sequence.
8. find the sum of an infinite geometric sequence.
Std. 2.11.11.D
9. solve application problems using a geometric sequence.
Std. 2.11.11.D
10. use the Binomial Theorem to expand a binomial raised to a power.
11. use permutations to solve application problems.
Stds. 2.7.11.A, 2.7.11.E
CONTENT
2. Arithmetic Sequences
(Ob. 3, 4, 5)
3. Geometric Sequences
(Obj. 6, 7, 8, 9)
4. The Binomial Theorem
(Obj. 10)
5. Permutations
(Obj. 1,2)
(Obj. 11)
6. Distinguishable Permutations and Combinations
7. Probability
(Obj. 14)
14
Std. 2.7.8.A
Std. 2.7.8.A
14. find the probability and odds that an event will occur.
1. Infinite Sequences and Summation Notation
Std. 2.8.11.A
Std. 2.7.8.A
12. use distinguishable permutations to solve application problems.
13. use combinations to solve application problems.
Std. 2.11.11.D
(Obj. 12, 13)
UNIT XI
TOPICS FROM ANALYTIC GEOMETRY
OBJECTIVES
Students will be able to:
1. calculate the vertex, focus, and directrix of a parabola.
Stds. 2.8.11.E, 2.9.11.G
2. find the equation of a parabola given a graph or various conditions.
2.9.11.G
3. find the vertices and foci of an ellipse.
Stds. 2.8.11.E,
Stds. 2.8.11.E, 2.9.11.G
4. find the equation of an ellipse given a graph or various conditions.
2.9.11.G
Std 2.8.11.E,
5. find the vertices, the foci, and the equations of the asymptotes of a hyperbola.
2.8.11.E, 2.9.11.G
6. find the equation of a hyperbola given a graph or various conditions.
2.9.11.G
CONTENT
1. Parabolas
2. Ellipses
(Obj. 1, 2)
(Obj. 3, 4)
3. Hyperbolas
(Obj. 5, 6)
15
Stds.
Stds. 2.8.11.E,