HONORS ELEMENTARY ANALYSIS
Unit 1: Functions, Graphs and Applications
A. Linear functions
a. Points and lines
b. Slopes of lines
c. Equations of lines
d. Linear functions and models
B. Quadratic functions
a. Complex numbers
b. Solving quadratic equations
c. Quadratic functions and their graphs
d. Quadratic models
C. Polynomial functions
a. Polynomials
b. Synthetic division
i. Remainder theorem
ii. Factor theorem
c. Graphing polynomial functions
d. Finding maximums and minimums graphically
e. Approximating roots of polynomial equations graphically
f. Solving polynomial equations by factoring
D. Inequalities
a. Linear inequalities
b. Absolute value
c. Polynomial inequalities in one variable
d. Polynomial inequalities in two variables
e. Linear programming
E. Functions
a. Properties
b. Operations on functions
c. Graphs
i. Reflecting
ii. Symmetry
iii. Stretching
iv. Translating
v. Inverse functions
d. Function models
F. Exponents and logarithms
a. Exponents
i. Integral
ii. Rational
b. Exponential functions
c. e and e
d. Logarithms
i. Logarithmic functions
ii. Laws
e. Exponential equations
Unit 2: Analytic Geometry
A. Coordinate proofs
B. Conic sections
a. Equations of circles
b. Ellipses
c. Hyperbolas
d. Parabolas
C. Systems of second degree equations
Unit 3: Trigonometry
A. Trigonometric functions
a. Angles, arcs and sectors
i. Measurement of angles
ii. Sectors of circles
b. Sine and cosine
c. Evaluating and graphing sine and cosine
d. Tangent, cotangent, cosecant and secant
e. Inverse trigonometric functions
B. Trigonometric equations and applications
a. Simple trigonometric equations
b. Sine and cosine curves
c. Modeling periodic behavior
d. Relationships among the functions
e. More difficult equations
C. Triangle trigonometry
a. Solving right triangles
b. Area of a triangle
c. Law of Sines
d. Law of Cosines
e. Applications of trigonometry
i. Navigation
ii. Surveying
D. Trigonometric addition formulas
a. Formulas for cos() and sin()
b. Formulas for tan()
c. Double-angle and half-angle formulas
d. Solving trigonometric equations
Unit 4: Discrete Mathematics and Data Analysis
A. Sequences and series
a. Arithmetic and geometric sequences
b. Recursive definitions
c. Arithmetic and geometric series and their sums
d. Limits of infinite sequences
e. Sums of infinite series
f. Sigma notation
g. Mathematical induction
B. Matrices
a. Matrix addition
b. Scalar multiplication
c. Matrix multiplication
d. Applying matrices to linear systems
C. Combinatorics
a. Multiplication Principle
b. Addition Principle
c. Complement Principle
d. Permutations
e. Combinations
f. Binomial Theorem – Pascal’s Triangle
D. Probability
a. Introduction
b. Events occurring together
c. Binomial Probability Theorem
d. Problems involving combinations
e. Conditional probability
f. Expected value
E. Statistics
a. Tables, graphs, and averages
b. Box-and-whisker plots
c. Variability
d. The normal distribution
F. Curve fitting and models
a. Introduction to curve fitting
b. The least-squares line
c. Fitting exponential curves
d. Fitting power curves
References and Materials
Major text
Brown, Richard g. Advanced Mathematics – Precalculus with Discrete Mathematics and Data Analysis. Evanston, Illinois: McDougal Littell Inc., 2003
Reference Books
Stewart, James, LotharRedlin, Saleem Watson. Precalculus- Mathematics for Calculus, 3rd ed. Pacific Grove: Brooks/Cole Publishing Company, 1999