pre- calc unit 1
DESCRIPTION
Pre- Calc Unit 1. Equations – Inequalities – Modeling Alg 2 Review. Unit 1 Lesson 1 Do Now: What are the Five Words? What are the Five Principles ?. Homework Complete the EEMO Blank Worksheet Complete the Pre- Calc Pre Test. Objectives - PowerPoint PPT PresentationTRANSCRIPT
2Pre-Calc Unit 1 Lessons
HomeworkComplete the EEMO Blank WorksheetComplete the Pre-Calc Pre Test
Objectives Describe the four levels of effort at Hyde: EEMODescribe the Hyde Learning Process AICRDescribe what it will take to get an HONOR in this classBe able to describe the 4 point grading system used by Mr. RomacBe able to describe the Four P’s
Unit 1 Lesson 1Do Now:What are the Five Words?What are the Five Principles?
3Pre-Calc Unit 1 Lessons
In Class-Syllabus-Text book scavenger hunt
Function Gallery page xixTable of ContentsPage 95 HighlightsIndexAnswers to ODD problems
SummaryWhat was YOUR effort (EEMO) in class today?Leave it better than you found it.
Review Functions Graphs http://www.analyzemath.com/PrecalculusTutorials.html
Unit 1 Lesson 1
Pre-Calc Unit 1 Lessons 4
* Unit 1 Lesson 2 Sep 6Do Now: Solve the formula S = P + Prt for “P”"You cannot teach a man anything; you can only help him find it within himself." Galileo (1564-1642)
*Objectives *Describe the three main categories
of applied problems *Demonstrate the 7-steps of problem
solving*
*Homework*pp: 20-23*#s: 1-22 (all)
Pre-Calc Unit 1 Lessons 5
* Unit 1 Lesson 2
*Review * Y = mx + B
*In Class* In Class*Page 13 - Examples 4 – 8 *Motion*Mixture*Work
SummaryFor thought 1 – 10 EVEN What was YOUR effort (EEMO) in class today?
Pre-Calc Unit 1 Lessons 6
Unit 1 Lesson 3 / 3a /3b
Do Now:David Ortiz had a batting average of .318 at the beginning of a game with the Yankees. After going 2 hits for 4 at bats. At the end of the game his average was .320. How many times has he been at bat for the season and how many hits has he had for the season? Batting averages are found by taking the total number of hits divided by the total number of at bats.
Objectives Graph Points using the Cartesian system Solve for the distance between ordered
pairs Find the midpoint between ordered pairs Write the equation for a circle in
standard form {begin work with “completing the
square”}
Homework Lesson 3 Assigned Wed Sep 6 pp: 34-36 #s: 10, 22, 30, 38, 48, 50, 52, 64
Lesson 3a Assigned Fri Sep 8 pp: 34-36 #s: 12, 16, 29, 32, 36, 38, 55, 56
44
Lesson 3-b Assigned Mon Sep 12 pp: 34-36: #’s (in class) 71, 75, 84, 88 #’s 9, 21, 29, 37, 47, 49, 51, 63, 71,
75, 84, 88
Pre-Calc Unit 1 Lessons 7
Unit 1 Lesson 3Review Plotting points{x, y)
In ClassPage 26 – 30Example 1: Example 2: Distance FormulaExample 3: MidpointExample 4: Circlepp: 33-36#s: 9, 21, 47, 71, 83
SummaryPlot {2, 4} and {5, 30}Find the Distance between the points and the Mid- Point What was YOUR effort (EEMO) in class today?
Do Now Solution:{X + 2}/ {Y+4}= .320X / Y = .318 x = .318 {Y}
{.318 {Y} + 2}/ {Y+4}= .320{.318 {Y} + 2} = {Y+4}{ .320} {.318 {Y} + 2} = {Y}{.320} +1.28 .72 =0.002{Y}Y = 360 at batsX = .318 Y = 114.(48?)Hits
Pre-Calc Unit 1 Lessons8
Unit 1 Lesson 4 SEP 12Do Now:4a) f(x) = – (1 / 3)x - 1 / 2Find the Y interceptFind the X intercept Find the SlopeFind f(6) =
• Objectives Be able to graph a circle free hand
(w/out calculator) from equation Determine circle equation from a graph Know how to “complete the square” Find X and Y Intercepts from Graphing and Analytical methods
• Homework pp: 35-36 4 #s: 49, 51, 53, 63,
74, 76, 86
Pre-Calc Unit 1 Lessons9
Unit 1 Lesson 4
Review Distance Midpoint y = mx+B X & Y Intercepts CIRCLE Equation (x - h)2 + (y - k)2 =
r2
f(x) = mx + B f(x) = a x2 + bx +
c
• In Class
http://www.analyzemath.com/CircleEq/Tutorials.html
Circle Applet: http://www.analyzemath.com/CircleEq/CircleEq.html
Example 1: Find the equation of a circle whose center is
at (2, - 4) and radius 5.
Summary (x - 4)2 + (y - 3)2 = 49Center = ( , ) Radius = What was YOUR effort (EEMO) in class today?
Solution to Example 1: given (h , k ) = (2 , - 4) and r = 5substitute h, k and r in the standard equation (x - 2)2 + (y - (- 4))2 = 52
(x - 2)2 + (y + 4)2 = 25
Pre-Calc Unit 1 Lessons
10
Sep 13Do Now:15 Minute “Q”pp: 34-36#s: 11, 31, 40, 55b, 57a
Objectives Be able to graph a circle free hand
(w/out calculator) from equation Determine circle equation from a graph
Know how to “complete the square” in five steps
Find X and Y Intercepts from Graphing and Analytical methods
Homework** changed
pp: 35-364b #s: 47, 55c,
56bc, 57b, 59, 61, 67, 91, 92
Unit 1 Lesson 5
Pre-Calc Unit 1 Lessons
11 Unit 1 Lesson 5 Review Distance Midpoint y = mx+B X & Y Intercepts (x - h)2 + (y - k)2 = r2
f(x) = mx + B f(x) = ax2 + bx + c
In Class Complete the square http://www.purplemath.com/modules/sqrquad.htm Step 1 Divide all terms by a (the coefficient of x2).
Step 2 Move the number term (c/a) to the right side of the equation.
Step 3 Complete the square on the left side of the equation by adding (b/2)2 and balance this by adding the same value to the right side of the equation.
Step 4 Take the square root on both sides of the equation.
Step 5 Add or subtract the number that remains on the left side of the equation to find x.
pp: 35-36 5 in class #s: 49, 54, 61
SummaryFind the roots by completing the square for f(x) = 2x2 + 4x +3
f(x) = 2x2 + 4x - 6x2 + 2x – 3 = 0x2 + 2x = +3x2 + 2x + 1 = 3 +
1(x + 1)2 = 4
Pre-Calc Unit 1 Lessons
12
Linear Equations in Two Variables Sep 14
Do Now: Graph the circle given by the equation:16 = (x-3)2 + (y+2)2
Objectives slope:
definition and methods for solving line equation: standard form line equation: point-slope form line equation: slope-intercept form parallel lines perpendicular lines
Homework pp: 48-49 #s: 5,10, 18, 26,
36, 46, 56,
Unit 1 Lesson 6
Pre-Calc Unit 1 Lessons
13
Review/Practice In Class http://www.analyzemath.com/
Graphing/GraphingLinearFunction.html
SummaryWhat was YOUR effort (EEMO) in class today?
Unit 1 Lesson 6
Pre-Calc Unit 1 Lessons
14
Do Now Q: What is the radius of a circle whose equation is (x + 2)2 + ( y - 3)2 = 9 Is the point “P” (3, 4) inside, outside or on the circle with this equation
Objectives Given a point find a parallel
line to the original linear equation
Given a point find a Perpendicular line to the original linear equation
Find the intersection point (coordinate) of two non parallel lines
Homework pp: 48-49 #’s62, 70, 74, 80, 84,
90 #’s 63 – 83 ODD
Unit 1 Lesson 7Linear Equations in Two Variables
Pre-Calc Unit 1 Lessons
15
Review / Practice
Slope Fractions
pp: 48-49 #’s61, 71, 74, 81,
83, 89
In Class http://www.analyzema
th.com/Graphing/GraphingLinearFunction.html
SummaryWhat was YOUR effort (EEMO) in class today?
Unit 1 Lesson 7
Pre-Calc Unit 1 Lessons
16
Do Now:ObjectivesBe able to classify Scatter
DiagramsFit a line to DataFinding the line of best fitYOU MUST HAVE a
TI-83 / TI- 84
Homework8 HonorsPp: 56 - 57#’s 9 – 17 ALL21, 22
Unit 1 HONORS Lesson 8Scattering Diagrams Curve
Fitting:HONORS
Pre-Calc Unit 1 Lessons
17
Review / Practice
Y= on TI 84 Setting windows Entering Data into
TI
In Class 8 Honors Pp: 56 - 57 #’s 9 – 17 ODD 21, 22
SummaryWhat was YOUR effort (EEMO) in class today?
Unit 1 Lesson 8
Pre-Calc Unit 1 Lessons
18
Do Now:Objectives Write out the quadratic
equation: standard form Demonstrate the square root
property Find the “roots”: Utilize the factoring methods Utilize the completing the
square methods
Homework pp: 76-78 #s: 14, 24, 30, 40,
50, 54, 60, 64, 70, 82, 88, 104
Unit 1 Lesson 9Quadratic Equations
Pre-Calc Unit 1 Lessons
19
Review / Practice Graphing on TI Graphing by hand
“Heavens, by Hand?”
In Class y= 2x y= 2x + 3 y = -1/2 x y = -1/2x + 3
pp: 76-78 #s: 15, 25, 31, 41, 51, 61,
71, http
://www.analyzemath.com/Graphing/GraphingQuadraticFunction.html
Summary:Find a perpendicular line to the equation Y = -1/2 x + 2
What was YOUR effort (EEMO) in class today?
Unit 1 Lesson 9
Pre-Calc Unit 1 Lessons
20
Do Now: What is the equation of the line that goes through the coordinates (3, 5) and (5, 7)?
What is a Linear Equation of a line that is perpendicular to the line above and goes through the point (4, 2)
L.E.T.
Objectives Find the “roots”:
Utilize the factoring solution methods
Utilize the completing the square solution methods**
Utilize the quadratic formula solution methods
Define “Discriminant”
Homework pp: 78 - 79 #s: 101 – 115 ODD,
116
Unit 1 Lesson 10Quadratic Equations: Roots
Pre-Calc Unit 1 Lessons
21 Review / Practice f (x) = ax2 + bx + c f (x) = a(x - h)2 + k
Quadratic Formulax = {– b+- √(b2 – 4ac) /(2a) Roots Y =0h is x vertices = – b / (2a)k is y vertices = – {b2 – 4ac} / (4a)
where D is the discriminant given by
D = b2 - 4ac {D=0: 1 root} {D<0: no root} {D>0: 2 roots}
In Class If is a quadratic function
given by f (x) = 2x2 + 2 x - 4 JIGSAW Find the x and y intercepts Find the vertex Find the domain and range Sketch the graph
SummaryWhat was YOUR effort (EEMO) in class today?
Unit 1 Lesson 10
Pre-Calc Unit 1 Lessons
22
Do Now: A quadratic function given by f (x) = 3x2 + 3x - 4 Find the x and y intercepts Find the vertex Find the domain and rangeSketch the graph
Objectives Demonstrate
interval notation List 3 properties of
linear inequalities List 2 properties of
absolute value inequalities Demonstrate compound inequalities
(∩ and U)
Homework - 12pp: 90 - 92#s: 9, 21, 23, 29, 39,
49, 61, 79, 91, 101, 107
Unit 1 Lesson 12Linear and Absolute Value Inequalities
Pre-Calc Unit 1 Lessons
23
Review / Practice Solve Inequalities
With Absolute Value – Tutorial
http://www.analyzemath.com/Absolute_Value_Inequalities/AbsoluteValueInequalities.html
In Class pp: 90 - 92 #s: 9, 23, 30, 61, 91
SummaryWhat was YOUR effort (EEMO) in class today?
Unit 1 Lesson 12
Pre-Calc Unit 1 Lessons
24
Do Now: Graph the solution set for x: if -2*|4 – x| < -4 What are the roots for f(x) = x2 – x – 12
Objectives Create a summary Sheet for
Chapter ONE pg 95-96 Chapter 1 review exercises
HomeworkCreate Summary
Sheet for Chap 1 pp 97 #’s1 – 7 ODD#’s 11 – 29 ODD#’s 39 – 53 ODD,
HONORS : 85 – 91 ODD,
Unit 1 Lesson 13 Test Review - One
Pre-Calc Unit 1 Lessons
25
Review / Practice
Pp 90 – 91 Highlights
In Class pp 97 #’s1 – 7 ODD #’s 11 – 29 ODD #’s 39 – 53 ODD
SummaryWhat was YOUR effort (EEMO) in class today?
Unit 1 Lesson 13
Pre-Calc Unit 1 Lessons
26
Do Now:What are the roots for f(x) = x2 – x – 12
Objectives Finish a summary Sheet for Chapter ONE
HomeworkChapter 1 review
exercises, pp 84-87 57 – 61ODD, 63 – 79 ODDHONORS :
102, 103, 104
Unit 1 Lesson 14Lesson
Pre-Calc Unit 1 Lessons
27
Review / Practice
For test Linear Quadratic Absolute Value Interval notation(s) Inequalities
Only Pencil Calculator
In Class Chapter 1 review exercises, pp 84-87 57 – 61ODD, 63 – 79 ODD HONORS :
102, 103, 104
SummaryAre you ready?
Unit 1 Lesson 14
Pre-Calc Unit 1 Lessons
28
Do Now:The TestOnly PencilCalculatorSummary Sheet on desk
Objectives Demonstrate knowledge of
equations and modeling
Homework Chapter 2.1 – 2.3 Define ALL
NINE green box (bold) vocabulary IN YOUR WORDS
Unit 1 Lesson 15Lesson