pre-calc unit 1 equations – inequalities – modeling alg 2 review pre-calc unit 1 lessons 1

Pre-Calc Unit 1 Lessons1

Pre-Calc Unit 1

Equations – Inequalities – Modeling

Alg 2 Review

2Pre-Calc Unit 1 Lessons

HomeworkComplete the EEMO Blank Worksheet

Complete the Pre-Calc Pre Test

Objectives Describe the four levels of effort at Hyde: EEMO

Describe the Hyde Learning Process AICR

Describe what it will take to get an HONOR in this class

Be able to describe the 4 point grading system used by Mr. Romac

Be able to describe the Four P’s

Unit 1 Lesson 1

Do 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 xix

Table of Contents

Page 95 Highlights

Index

Answers 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)


* 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?


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


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


Unit 1 Lesson 4 SEP 12Do Now:4a) f(x) = – (1 / 3)x - 1 / 2Find the Y interceptFind the X intercept Find the Slope

Find 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


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



http://www.analyzemath.com/CircleEq/CircleEq.html

http://www.analyzemath.com/CircleEq/CircleEq.html

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


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

http://www.purplemath.com/modules/sqrquad.htm




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


13

Review/Practice In Class http://www.analyzemath.com/

Graphing/GraphingLinearFunction.html


Unit 1 Lesson 6

http://www.analyzemath.com/Graphing/GraphingLinearFunction.html




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


15

Review / Practice

Slope Fractions

pp: 48-49 #’s61, 71, 74, 81,

83, 89

In Class http://www.analyzema

th.com/Graphing/GraphingLinearFunction.html


Unit 1 Lesson 7






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 8

Scattering Diagrams Curve Fitting:HONORS


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


Unit 1 Lesson 8


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


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

http://www.analyzemath.com/Graphing/GraphingQuadraticFunction.html





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


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


Unit 1 Lesson 10


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


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


Unit 1 Lesson 12







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


25

Review / Practice

Pp 90 – 91 Highlights

In Class pp 97 #’s1 – 7 ODD #’s 11 – 29 ODD #’s 39 – 53 ODD


Unit 1 Lesson 13


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


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


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


29

Do Now:

Objectives

Homework

Unit 1 Lesson blankLesson


30

Review / Practice In Class


Unit 1 Lesson blank

pre-calc unit 1 equations – inequalities – modeling alg 2 review pre-calc unit 1 lessons 1

Documents