1. Pre-Calc Unit 1 Equations – Inequalities – Modeling Alg 2 Review Pre-Calc Unit 1 Lessons 1

2. Homework Complete 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? Pre-Calc Unit 1 Lessons2

3. In Class -Syllabus -Text book scavenger hunt Function Gallery page xix Table of Contents Page 95 Highlights Index Answers to ODD problems Summary What was YOUR effort (EEMO) in class today? Leave it better than you found it. Review Functions Graphs http://www.analyzemath.com/Precalculus Tutorials.html Unit 1 Lesson 1 Pre-Calc Unit 1 Lessons3

4. * 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 4

5. * Review * Y = mx + B * In Class * Page 13 - Examples 4 – 8 * Motion * Mixture * Work Summary For thought 1 – 10 EVEN What was YOUR effort (EEMO) in class today? Pre-Calc Unit 1 Lessons 5

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 Lessons6

7. Unit 1 Lesson 3 Review Plotting points {x, y) In Class Page 26 – 30 Example 1: Example 2: Distance Formula Example 3: Midpoint Example 4: Circle pp: 33-36 #s: 9, 21, 47, 71, 83 Summary Plot {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}=.320 X / 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 bats X =.318 Y = 114.(48?)Hits Pre-Calc Unit 1 Lessons7

8. Unit 1 Lesson 4 SEP 12 Do Now: 4a) f (x) = – (1 / 3)x - 1 / 2 Find the Y intercept Find 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 Pre-Calc Unit 1 Lessons 8

9. Unit 1 Lesson 4  Review  DistanceMidpoint  y = mx+B  X & Y Intercepts  CIRCLE Equation  (x - h) 2 + (y - k) 2 = r 2  f(x) = mx + B  f(x) = a x 2 + bx + c In Class  http://www.analyzemath.com/CircleEq/T utorials.htmlhttp://www.analyzemath.com/CircleEq/T utorials.html  Circle Applet: http://www.analyzemath.com/CircleEq/Ci rcleEq.html http://www.analyzemath.com/CircleEq/Ci rcleEq.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 = 49 Center = (, ) Radius = What was YOUR effort (EEMO) in class today? Solution to Example 1: given (h, k ) = (2, - 4) and r = 5 substitute h, k and r in the standard equation (x - 2) 2 + (y - (- 4)) 2 = 5 2 (x - 2) 2 + (y + 4) 2 = 25 Pre-Calc Unit 1 Lessons 9

10. Sep 13 Do Now:15 Minute “Q” pp: 34-36 #s: 11, 31, 40, 55b, 57a Pre-Calc Unit 1 Lessons 10  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: 35-36  4b#s: 47, 55c, 56bc, 57b, 59, 61, 67, 91, 92 Unit 1 Lesson 5

11. Pre-Calc Unit 1 Lessons 11  Review  DistanceMidpoint  y = mx+B  X & Y Intercepts  (x - h) 2 + (y - k) 2 = r 2  f(x) = mx + B  f(x) = ax 2 + bx + c  In Class  C omplete the square  http://www.purplemath.com/modules/sqrquad.htm http://www.purplemath.com/modules/sqrquad.htm  Step 1 Divide all terms by a (the coefficient of x 2 ).  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 Summary Find the roots by completing the square for f (x) = 2x 2 + 4x +3 f (x) = 2x 2 + 4x - 6 x 2 + 2x – 3 = 0 x 2 + 2x = +3 x 2 + 2x + 1 = 3 + 1 (x + 1) 2 = 4

12. Linear Equations in Two Variables Sep 14 Do Now: Graph the circle given by the equation: 16 = (x-3) 2 + (y+2) 2 Pre-Calc Unit 1 Lessons 12  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. Pre-Calc Unit 1 Lessons 13  Review/Practice  In Class  http://www.analyzemath.com /Graphing/GraphingLinearFun ction.html http://www.analyzemath.com /Graphing/GraphingLinearFun ction.html Summary What was YOUR effort (EEMO) in class today? Unit 1 Lesson 6

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 Pre-Calc Unit 1 Lessons 14  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 7 Linear Equations in Two Variables

15. Pre-Calc Unit 1 Lessons 15  Review / Practice  Slope  Fractions  pp: 48-49  #’s61, 71, 74, 81, 83, 89  In Class  http://www.analyzemath. com/Graphing/GraphingL inearFunction.html http://www.analyzemath. com/Graphing/GraphingL inearFunction.html Summary What was YOUR effort (EEMO) in class today? Unit 1 Lesson 7

16. Do Now: Pre-Calc Unit 1 Lessons 16  Objectives  Be able to classify Scatter Diagrams  Fit a line to Data  Finding the line of best fit  YOU MUST HAVE a  TI-83 / TI- 84  Homework  8 Honors  Pp: 56 - 57  #’s 9 – 17 ALL  21, 22 Unit 1 HONORS Lesson 8 Scattering Diagrams Curve Fitting : HONORS

17. 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 Summary What was YOUR effort (EEMO) in class today? Unit 1 Lesson 8

18. Do Now: Pre-Calc Unit 1 Lessons 18  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 9 Quadratic Equations

19. 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/Graphin gQuadraticFunction.html http://www.analyzemath.com/Graphing/Graphin gQuadraticFunction.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

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. Pre-Calc Unit 1 Lessons 20  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 10 Quadratic Equations: Roots

21. Pre-Calc Unit 1 Lessons 21  Review / Practice  f (x) = ax 2 + bx + c  f (x) = a(x - h) 2 + k Quadratic Formula x = {– b+- √(b 2 – 4ac) /(2a) Roots  Y =0 h is x vertices = – b / (2a) k is y vertices = – {b 2 – 4ac} / (4a)  where D is the discriminant given by  D = b 2 - 4ac  {D=0: 1 root}  {D<0: no root}  {D>0: 2 roots}  In Class  If is a quadratic function given by  f (x) = 2x 2 + 2 x - 4  JIGSAW  Find the x and y intercepts  Find the vertex  Find the domain and range  Sketch the graph Summary What was YOUR effort (EEMO) in class today? Unit 1 Lesson 10

22. Do Now: A quadratic function given by f (x) = 3x 2 + 3x - 4 Find the x and y intercepts Find the vertex Find the domain and range Sketch the graph Pre-Calc Unit 1 Lessons 22  Objectives  Demonstrate  interval notation  List 3 properties of  linear inequalities  List 2 properties of  absolute value inequalities  Demonstrate  compound inequalities  (∩ and U)  Homework - 12  pp: 90 - 92  #s: 9, 21, 23, 29, 39, 49, 61, 79, 91, 101, 107 Unit 1 Lesson 12 Linear and Absolute Value Inequalities

23. Pre-Calc Unit 1 Lessons 23  Review / Practice  Solve Inequalities With Absolute Value – Tutorial http://www.analyzemat h.com/Absolute_Value_I nequalities/AbsoluteValu eInequalities.html  In Class  pp: 90 - 92  #s: 9, 23, 30, 61, 91 Summary What was YOUR effort (EEMO) in class today? 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) = x 2 – x – 12 Pre-Calc Unit 1 Lessons 24  Objectives  Create a summary Sheet for Chapter ONE  pg 95-96  Chapter 1 review exercises  Homework  Create 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. 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 Summary What was YOUR effort (EEMO) in class today? Unit 1 Lesson 13

26. Do Now: What are the roots for f(x) = x 2 – x – 12 Pre-Calc Unit 1 Lessons 26  Objectives Finish a summary Sheet for Chapter ONE  Homework  Chapter 1 review exercises,  pp 84-87  57 – 61ODD,  63 – 79 ODD  HONORS :  102, 103, 104 Unit 1 Lesson 14 Lesson

27. 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 Summary Are you ready? Unit 1 Lesson 14

28. Do Now: The Test Only Pencil Calculator Summary Sheet on desk Pre-Calc Unit 1 Lessons 28  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 15 Lesson

29. Do Now: Pre-Calc Unit 1 Lessons 29  Objectives   Homework  Unit 1 Lesson blank Lesson

30. Pre-Calc Unit 1 Lessons 30  Review / Practice  In Class  Summary What was YOUR effort (EEMO) in class today? Unit 1 Lesson blank