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Pre- Calc Unit 1

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

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Pre- Calc Unit 1

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

  2. Unit 1 Lesson 1Do Now:What are the Five Words?What are the Five Principles? • 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 Pre-Calc Unit 1 Lessons

  3. Unit 1 Lesson 1 • 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/PrecalculusTutorials.html Pre-Calc Unit 1 Lessons

  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) Unit 1 Lesson 2 Sep 6Do Now: Solve the formula S = P + Prtfor “P”"You cannot teach a man anything; you can only help him find it within himself." Galileo (1564-1642) Pre-Calc Unit 1 Lessons

  5. Review • Y = mx + B • In Class • In Class • Page 13 - Examples 4 – 8 • Motion • Mixture • Work Unit 1 Lesson 2 Summary For thought 1 – 10 EVEN What was YOUR effort (EEMO) in class today? Pre-Calc Unit 1 Lessons

  6. Unit 1 Lesson 3 / 3a /3bDo 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 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 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 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? Pre-Calc Unit 1 Lessons

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

  9. Unit 1 Lesson 4 • Review • DistanceMidpoint • 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. • 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 = 52 • (x - 2)2 + (y + 4)2 = 25 • Summary • (x - 4)2+ (y - 3)2= 49 • Center = ( , ) Radius = • What was YOUR effort (EEMO) in class today? Pre-Calc Unit 1 Lessons

  10. Unit 1 Lesson 5 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 fivesteps • 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 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 Summary Find the roots by completing the square for f(x) = 2x2 + 4x +3 f(x) = 2x2 + 4x - 6 x2+ 2x – 3 = 0 x2 + 2x = +3 x2+ 2x + 1 = 3 + 1 (x + 1)2 = 4 Pre-Calc Unit 1 Lessons

  12. Unit 1 Lesson 6 Linear Equations in Two Variables Sep 14Do 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, Pre-Calc Unit 1 Lessons

  13. Unit 1 Lesson 6 • Review/Practice • In Class • http://www.analyzemath.com/Graphing/GraphingLinearFunction.html Summary What was YOUR effort (EEMO) in class today? Pre-Calc Unit 1 Lessons

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

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

  16. Unit 1 HONORS Lesson 8 Scattering Diagrams Curve Fitting: HONORS Do Now: • 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 Pre-Calc Unit 1 Lessons

  17. Unit 1 Lesson 8 • 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? Pre-Calc Unit 1 Lessons

  18. Unit 1 Lesson 9 Quadratic Equations 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 Pre-Calc Unit 1 Lessons

  19. Unit 1 Lesson 9 • 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? Pre-Calc Unit 1 Lessons

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

  21. Unit 1 Lesson 10 • Review / Practice • f (x) = ax2 + bx + c • f (x) = a(x - h)2 + k Quadratic Formula x = {– b+- √(b2 – 4ac) /(2a) Roots  Y =0 h 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 Summary What was YOUR effort (EEMO) in class today? Pre-Calc Unit 1 Lessons

  22. Unit 1 Lesson 12 Linear and Absolute Value Inequalities 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 - 12 • pp: 90 - 92 • #s: 9, 21, 23, 29, 39, 49, 61, 79, 91, 101, 107 Pre-Calc Unit 1 Lessons

  23. Unit 1 Lesson 12 • 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 Summary What was YOUR effort (EEMO) in class today? Pre-Calc Unit 1 Lessons

  24. Unit 1 Lesson 13 Test Review - One Do Now: Graph the solution set for x: if -2*|4 – x| < -4What are the roots for f(x) = x2 – x – 12 • 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, Pre-Calc Unit 1 Lessons

  25. Unit 1 Lesson 13 • 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? Pre-Calc Unit 1 Lessons

  26. Unit 1 Lesson 14 Lesson Do Now:What are the roots for f(x) = x2 – x – 12 • 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 Pre-Calc Unit 1 Lessons

  27. Unit 1 Lesson 14 • 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? Pre-Calc Unit 1 Lessons

  28. Unit 1 Lesson 15 Lesson 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) vocabularyIN YOUR WORDS Pre-Calc Unit 1 Lessons

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

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

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