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Welcome to Pre-Calculus!!

Welcome to Pre-Calculus!!. (It’s difficult!! ). College-Prep Class Grades are “curved” A 88 – 100% B 78 – 87% C 65 – 77% D 55 – 64% F Below 54% Tests = 80% of grade HW = 10% Quizzes, Notes, etc = 10% HW every night (almost)

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Welcome to Pre-Calculus!!

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  1. Welcome to Pre-Calculus!! (It’s difficult!!) • College-Prep Class • Grades are “curved” • A 88 – 100% B 78 – 87% C 65 – 77% D 55 – 64% F Below 54% • Tests = 80% of grade • HW = 10% • Quizzes, Notes, etc = 10% • HW every night (almost) • pencil • ALL work shown • 80% HW  drop low test  Posted on website Late HW = ½ credit up until date of test

  2. Supplies • 3-ring binder or Spiral Notebook for notes • Paper (Lined & Graph) • Pencils!! • Scientific Calculator (TI-30XIIS) • Graphing Calculator (TI-84 or free online utilities) Come study with me every day (almost) after school!!

  3. 1.1 Intro to Modeling

  4. Mathematical Model: a mathematical representation of some aspect of a real world system Slope of a line: Given 2 points: (x1, y1) and (x2, y2) x1≠ x2 Eqtns of line: Slope-int form: y = mx + b Point-slope form: y – y1 = m(x – x1)

  5. Ex 1) Find proper dosage, to nearest tenth of mL, for child weighing 39 lbs, given the recommended dosages: Plot pts to see if can assume it’s linear Choose 2 pts to find slope (15, 0.5) and (27, 0.9) Use point-slope form: Check: 39 lb weight:

  6. (Graph is a parabola) Quadratic Function: Ex 2) Find a model that relates Surface Area (A) to body weight (x) Plot pts  Parabola  Quadratic  (0, 0) to find c  c = 0

  7. Ex 2 cont. Choose 2 pts (8, 0.24) & (24, 0.50) 0.24 = a(8)2 + b(8) 0.50 = a(24)2 + b(24) ( )(–3) • 0.24 = 64a + 8b • 0.50 = 576a + 24b • –0.72 = –192a – 24b • 0.50 = 576a + 24b –0.22 = 384a use STO on calc – don’t round until last step! –0.00057292… = a

  8. Ex 2 cont. Plug STO value into ‘a’ & solve for ‘b’ 0.24 = 64(–0.00057292…) + 8b 0.03458333… = b Round ‘a’ and ‘b’ to 5 decimal places & plug into A = ax2 + bx: A = –0.00057x2 + 0.03458x Plug in other pts to check accuracy

  9. Ex 3) Find eqtn for earnings per share in terms of debts/assets ratio Plot pts  quadratic  y = ax2 + bx + c Plug in 3 pts to get a system of 3 eqtns (0, 1.60), (10, 1.85), (20, 2.00) 1.60 = a(0)2 + b(0) + c 1.85 = a(10)2 + b(10) + c 2.00 = a(20)2 + b(20) + c • c = 1.60 • 1.85 = 100a + 10b + 1.60 • 2.00 = 400a + 20b + 1.60

  10. Ex 3 cont. c = 1.60 1.85 = 100a + 10b + 1.60 2.00 = 400a + 20b + 1.60 ( )(–2)  0.25 = 100a + 10b  0.40 = 400a + 20b  –0.50 = –200a – 20b  0.40 = 400a + 20b 0.25 = 100(–0.0005) + 10b 0.03 = b –0.10 = 200a –0.0005 = a y = –0.0005x2 + 0.03x + 1.60

  11. Ex 4) Test model for debts/assets ratio of 60% From Ex 3: y = –0.0005x2 + 0.03x + 1.60 Plug 60 into x: y = –0.0005(60)2 + 0.03(60) + 1.60 y = 1.60 How accurate is our model?

  12. Homework #101 Pg. 8 1 – 11 odd, 12, 14 – 17, 25

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