Course Outline

Pre-Calculus Honors (5430)

Text:

PRECALCULUS (Mathematics for Calculus 4th Edition)

(Stewart, Redlin, Watson)

 

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)

 

 

Relations

 

 

Introduction to Functions (Chapter2)

·         Graphs of functions and the vertical line test

·         Composition of functions (notation and mappings)

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)

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)

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

 

 

Polynomial Functions of Degree 3 and Higher (Chapter 3)

 

 

Exponential and Logarithmic Functions (Chapter 4)

 

 

Sequences and Series (Chapter 10)

·         Recursive method of generating terms (Sec 10.1)

 

 

 Limits (Chapter 12)

·         Definition of a Limit of a sequence

1.        Left and right sided limits

2.        Piecewise defined functions

3.        Continuity

 

Differential Calculus