Course
Outline

__Pre-Calculus
Honors (5430) __

__Text: __

__PRECALCULUS
(Mathematics for Calculus 4 ^{th} Edition)__

__(Stewart,
Redlin, Watson)__

* (Chapter 1 in text is a review from Algebra 1
it is expected that all students in pre calculus honors have mastered all
topics in Chapter 1)*

- Real Numbers (Natural, Whole, Integer,
etc.)
**(Text Support: Chapter 1.1)** - Union
and Intersection of sets
**(Text Support Chapter 1.1)** - Graphing
unions and intersections on a number line, set builder notation and
interval notation

- Define a relation/Domain, Range, Mappings and Arrow Diagrams

- Definition and notation

· Graphs of functions and the vertical line test

- Domain and Range, restriction on the domain (i.e. denominator, radicands, etc.)
- 4 ways to represent a function (verbal, table, graphical, and algebraic)

· Composition of functions (notation and mappings)

- Functions and their Inverses

4 step process to finding an inverse; determine if the inverse is a function; check if 2 functions are inverses of each other; horizontal line test, composite of a function and its inverse is the identity; sketching inverses, mirror images across the identity)

- Reintroduce Polynomial Function Notation
_{} - Definition
and notation
- Polynomial Functions of
**Degree Zero (Constant functions**)_{} - Polynomial Functions of
**Degree One (Linear Functions)**:

**1. **Slope, distance, midpoint **(Sec 1.8)**

2.
x-intercepts (Solving an equation
algebraically and graphically)** (Sec 1.9)**

3.
Linear equations (point-slope,
slope-intercept and standard forms) **(Sec 1.10)**

4.
Parallel and perpendicular lines **(Sec
1.10),** equation of perpendicular bisector

5.
Systems of linear equations: solve
by graphing, elimination and substitution **(Sec 8.1)**

·
Polynomial Functions of **Degree
Two (Quadratic Functions)** (limited
use of text)

·
Definitions of quadratic expression, quadratic
function, quadratic equation and quadratic formula

·
Define and graph the 5 major parts
of a parabola (x and y intercepts, axis of symmetry, vertex and point symmetric
to y-intercept) **(Handouts)**

·
Solve for the roots of a quadratic
functions by factoring and the Zero Product Property, by completing the square
or by the Quadratic Formula **(section 1.5)**

·
Derive the Quadratic Formula (find
the 5 key parts of the parabola the algebraic way) **(section 2.6)**

· Solving for the point(s) of intersection of a Quadratic and a Linear, or a Quadratic and a Quadratic

·
Review Complex Numbers **(section 3.4)**

·
Value of the discriminant and
nature of the roots of a quadratic function **(section 1.5 and section 3.4)**

·
Quadratic inequalities **/**Determine
the domain of a quadratic that makes the function positive, negative or zero **(Handouts)**

·
Circles

- Right
triangle trigonometry (SOHCAHTOA)
**(Sec 6.2)** - Degrees,
Minutes and Seconds
**(Sec 6.1)** - Angle of Elevation and Depression

·
Law of Sines and Law of Cosines **(Sec
6.4 and 6.5)**

- Angles
in Standard Position (initial and terminal ray, vertex, positive and
negative angles, angles greater than 180 or 360 degrees, quadrantal
angles, co-terminal angles, reference angles)
**(Sec 6.1)** - Radians
à Degrees and Degree à Radians
**(Sec 6.1)** - Definitions
of 6 trig functions (SOHCAHTOA and reciprocals)
**(Sec 6.2)** - Definitions
of 6 trig functions (in terms of x, y, and r)
**(Sec 6.3)** - “All
Students Take Calculus” Rule
**(Sec 6.3)** - Reference
Angles: given a point on a terminal ray, find all 6 trig functions or
given a trig function and a Quadrant, find remaining 5 trig functions
**(Sec 6.3)** - Graphs
of the 6 trig functions
**(Sec 5.1, 5.2, 5.3 and 5.4)** - Domain,
Range, Period and Amplitude of the 6 trig functions
**(Sec 5.3 and 5.4)** - Trig
Identities (reciprocal, quotient, and Pythagorean identities / Sum and
Difference Identities / Double Angle Formulae, Half Angle formulae)
**(Sec 7.1, 7.2, 7.3)** - Proving
Trigonometric Identities
**(Sec 7.1)** - Inverse
Trigonometric Functions
**(Sec 7.4)** - Trigonometric
Equations and Inequalities
**(Sec 7.5)**

__Polynomial Functions of Degree 3 and Higher (Chapter
3)__

- Positive and Negative
- Increasing and Decreasing
- Concavity

- Synthetic
substitution and division
**(Sec 3.2)** - Remainder
and Factor Theorems
**(Sec3.2)** - Rational
Root Theorem
**(Sec 3.3)** - Fundamental
Theorem of Algebra/Zeros and Their Multiplicities
**(Sec 3.5)** - Roots

- Using
Zeros to graph polynomials of degree 3 and higher
**(Sec 3.1)**

__Exponential and Logarithmic Functions (Chapter 4)__

- Review
rules of exponents (product, quotient, power, and rational exponents)
**(Sec 1.2)** - Graphing
exponential functions
**(Sec 4.1)** - The
natural exponential function
**(Sec4.1)** - Graphing
logarithmic functions (as inverses of exponential functions)
**(Sec 4.2)** - Properties
of logarithms (product, quotient, power, change of base)
**(Sec 4.2 and 4.3)** - Common
Logs and Natural Logs
**(Sec 4.2)** - Solving
Exponential and Logarithmic equations
**(Sec 4.4)** - Exponential
Growth and Decay
**(Sec 4.5)** - Logistic Function

- General
Term method of Generating Terms
**(Sec 10.1)**

· Recursive method of generating terms (Sec 10.1)

__ Limits (Chapter
12)__

· Definition of a Limit of a sequence

- Limit of a function (x goes to infinity)
- Limit of a function (x goes to a number)

1. Left and right sided limits

2. Piecewise defined functions

3. Continuity

- Limits of Rational Functions

- Geometric Interpretation of Derived Function
- Defined
- How to use
- Short Cuts
- Numerical Derivative and Function Derivative
- Equation of the Tangent Line
- nderivative on calculator
- Product Rule
- Quotient Rule
- Derivative of Trigonometric Functions
- Chain Rule