Precalc Notes

This Semester's Precalc Notes: Fall 2000 Spring 2000 and 2002 Spring 2004

Projects: Project Questions Some Possible Projects

a 1- 3: syntax, numbers, expressions
a4-11: syntax, numbers, expressions:
qb coversheet , number systems , graph paper , calculator express or simplify , calculator solve
a12-13: graphs of ideal and experimental data
basic functions, expressions
odd/even/neither , odd/even , increasing/decreasing, end behavior , asymptote , symmetry ,
basic functions , lines , quadratic quadratic equation
solve a quadratic equation vs. simplify a radical expression ,
solving equations and inequalities: algebraically, graphically technologically in 1, 2, 3 dimensions
solving equations and inequalities: algebraically, graphically, technologically in 1, 2, 3 dimensions: solve linear ,
families of functions, function notation
basic curve shifting and composition of functions: shift square root functions , shift reciprocal function ,
translations, dilations, reflections: algebraically and graphically
more on composition of functions
2nd function quiz, inverse functions
inverse functions: verbally, analytically, algebraically
Inverse Problems Inverse Notes , m29f07d , m29f07e , m29f12b , m28f4c , p28s20 ,
dilation of a line by a constant or a line: animation (note decrease in frequency & increase in slope) , dilation of a function , Dilation ,
animation
quadratic functions: graphs, equations, features, vocabulary , ,
regions bounded by curves: pcdraw , fx8 (precalc drawing required in calc)
polynomial functions , , ,
roots of polynomial functions ,
more on complex numbers: Elizabeth Stapel on Complex Computation I II
rational functions
rational functions
rational functions
exponents and logs: graph exponentials , solve exponential
exponential and natural log are inverse functions (p28s20) ,
simplifying log expressions
graphing log and exponential expressions
solving log and exponential equations
solving log and exponential equations
solving log and exponential equations

Table of Contents for This Page

80 - Order of Operations
130 - Integer (Signed Number) Representation & Computation
210 - Arithmetic & Algebraic Operations with Exponents
230 - GRAPHITI - coordinate geometry, point generation, distance, functions
240 - Lines & Slope
260 - Angles
300 - Functions
320 - Quadratic Equations, Formula, & The Discriminant
330 - Trig Functions
- fractions, degrees, radians
- right triangles and the square
- trig functions
- solving right triangle, inverse trig functions
- the unit circle
- trig funtions in other quadrants
- special angles
- sine, cosine, tangent
- 6 trig functions
- inverse trig functions
- solving basic trig equations
- basic trig identitiies
- simplify trig expressions, factoring
- solving trig equations
- sum and difference identities
- cheat sheet identities
- solving more trig equations
- solving trig equations
340 - How To Appreciate Logs without Feeling Out on A Limb
400 - Varieties, Features and Uses of Calculators
410 - Statistics
420 - Calculus
$library$
$spread sheet notes$ - Spread Sheet Reference List
- Web Use & Wed Page Writing Information
- Word® document techniques

$Tutorials & Lessons$ For Trig material, go to the Lesson 300 on the Lessons Page

fractions, degrees, radians
right triangles and the square
trig functions
solving right triangle, inverse trig functions
the unit circle
trig funtions in other quadrants
special angles
sine, cosine, tangent
6 trig functions
inverse trig functions
solving basic trig equations
basic trig identitiies
simplify trig expressions, factoring
solving trig equations
sum and difference identities
cheat sheet identities
solving more trig equations
solving trig equations
determinants & matrices

Lines, Functions, Slope, Basic Stuff

1/23 - Write equation for a line, compute slope, write TI83 program for slope.
1/23 - 2nd example.
1/24 - Slope of oblique, horizontal, vertical lines.
1/29 - Difference quotient graph.
1/29 - Compute difference quotient.
1/29 - Second example.
1/24 - Identity Fucntion. Opposite Function. Reciprocal Function.
1/31 - Equation of a circle.
1/31 - Since a circle is not a function, it must be stated as two different functions to graph it on the calculator.
2/4 - A function, its opposite, the sum of a function & a constant, the function of the sum of a number and a constant
2/4 -function's reciprocal & inverse.
2/5 -Functions are odd, even, or either.
1/31 -Volume of a box: material , box , math ,
2/5 - Why a cubic "looks" that way -- an example of decomposition of functions
2/7 - Take an inverse function:
using words or order of operations, graphically, or symbolically
2nd example
2/5 - compute difference quotient
2/5 - functions are ODD, EVEN, or NEITHER
2/5 - composition of functions
2/12 - sketch a function by thinking of its reciprocal
2/12 - algebraically & graphically taking an inverse
2/29 - 14a - code geometry into algebra
2/29 - 14b - reciprocal functions with domain changes

Solve Equations w/o Logs

2/29 - 14c - solve a radical equation VS simplify a radical expression
2/29 - 14d - solve a rational (fraction) equation, a cubic VS the cubic equation
2/19 - 19a - graphic SOLVE on TI83 and TI86
2/19 - solve a quadratic by factoring, graphic inspection, quadratic equation
2/21 - solve rational equations, algebra area formula example
2/21 - b - solve a quadratic by factoring, solve a quartic (x⁴) by SUBSTITUTION
2/21 - d - solve (x^4/3) by raising both members to (x^3/4)

Polynomial and Rational Functions

2/5 - why the graph of a cubic looks the way it does
3/5 - ex. 2., use synthetic or long division to rewrite a rational function
3/5 - displacement formula for projectiles, sketch a polynomial in factored form
3/5 - write statements about what is known about a polynomial function given the equation
3/5 - a rational function and its divisor, quotient, & remainder functions
3/7 - Sketch a polynomial function in factored or a_nxⁿ form
3/7 - Using the p/q, (p) factors of the constant term & (q) factors of the leading coefficient to find roots
3/12 - Why p/q supplies possible roots.
3/12 - polynomial notes page
3/12 - rational functions notes page
3/12 - polynomial spread sheet
3/12 - polynomials on animation, using p/q to find possible roots, exponent examples

Logs, Exponents, exponential and log equations, graphs, functions

2/4 - The natural log function, ln(x), has a restricted domain over the reals.
2/ 4 - Simplify simple log and exponential expressions.
2/6 - Graphs of Exponential Growth & Decay
2/6 - Solve a log equation algebraically. Simplify a log expression.
2/6 - exponential growth and decay
2/6 - solving log equations mentally, algebraically w/logs
3/6 - test answers
3/6 - more test answers
3/11 - more test answers
3/12 - origin of logarithm
3/12 - log vs exponential form
3/12 - simplify simple log expressions, log_b(a) = (log_c(a))/( log_c(b))
3/12 - exponent laws , log laws, examples of how logs work
3/14 - exponential growth & decay in a table and grpah
3/14 - e, sketching exponential curves
3/14 - compound interest
3/14 - compound interest spread sheet
3/14 - more examples of how log expressions/laws work
3/14 - compounding and continuous compounding
2/13 -
2/13 - expanding log expressions, a cubic vs. the cubic function
2/13 - expand log expression, solve log equations

Trig

3/4 - pi = circumference divided by diameter; theta, angle in standard position
3/4 - Oscar/Had A/Heap Of/Apples: sine, cosine, tangent. sine, cosine, tangent of an angle, of 30°, of 60°
3/11 - sine, cosine, tangent. sine, cosine, tangent of an angle, of 30°, of 60°
3/11 - sine & cosecant are reciprocals, sine and cosine of quadrantals, rationalize a denominator

Unit Circle w/6 Trig Functions
central angle
sine & cosine
3/13 - prequiz review of 30°s, 45°s, and 60°s
3/13 - review questions
3/13 - an arc length problem from the book with degrees, minutes, seconds and decimal degrees
3/13 - reference angles, special angles
3/13 - Veronica's Bow Tie, All Students Take Calculus, All Students Try Cheating, All Silver Tea Cups

3/18 - graphs of the sine and cosine function, the sine & cosine of 0°, 90°,180°,270°, w/radian notation
3/18 - graph of the tangent function, given the sine = 5/6, state all other functions.
4/2 - MSH! 330, Trig Lessons Page
4/2 - improper fractions from 0 to 2 sets the stage for radians
4/2 - Oscar/Had A/Heap Of/Apples, sine, cosine, tangent of the quadrantals
4/2 - trig functions of 30°s using Oscar/Had ... and 7th Grade Math
4/2 - trig functions of 60°s using Oscar/Had ... and 7th Grade Math
4/4 - similar figures,
4/4 - circles are similar, arc length
4/4 - sine squared + cosine squared = 1, example using 60°
4/4 - proof than tangent is sine divided by cosine, functions of complements
4/4 - radians to degrees, degrees to radians, degrees-minutes-seconds to decimal degrees
4/11- sin(x), 2sin(x)
4/11- trig functions in other quadrants
4/16 - find the period of a trig function
4/16 - use (1,0), (0,1), (-1,0), (0,-1) to help compute the trig functions of 0°, 90°, 180°, 270°,
- Solve a trig equation graphically
4/18 - Solve cos ( ) = -1 graphically,
- Solve cot ( ) = -1 graphically,
(with a 1-hour review of much of the course in order to graph the cotangent function)
4/18 - chapter 1 -- the composition of functions, opposite of a function, reciprocal of a function,
and inverse of a function
4/18 - chapter 3, polynomial and rational functions, zeros, vertical asymptotes, "holes," and other asymptotes
4/25 - graph cosine and 3sin(2x), review of algebra I prior to chapter 6 & 7
4/25 - arc funtions, inverse trig functions.
4/25 - Graphing Polynomial Functions
4/25 - Graphing Rational Functions
4/30
-- solve trig equations graphically & algebraically
4/30
-- simplifying trig expressions using factoring, substitution of equivalent expression, simple computation
4/30
-- proving trig identities
-- solving trig equations -- by graphing and algebraically by the use of ARC FUNCTIONS
4/30
-- odd and even trig functions
-- sine and cosine of the sum and difference of two angles
4/30
- compute sine of 75° using the sine of the sum formula
-- the sine of a double angle
Solve an equation graphically, analytically