Review Topics

(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

Relations

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

Introduction to Functions (Chapter2)

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)

Polynomial Functions (Chapter 3)

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

Trigonometric Functions (Chapters 5 & 6)

· Review Pythagorean theorem, Pythagorean triples and Special Right Triangles (Sec 6.2)

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

Sequences and Series (Chapter 10)

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

Differential Calculus

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