Pre Calculus with Mrs. Bluell
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- Hilary Wright
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1 Welcome to Pre Calculus with Mrs. Bluell
2 Quick Review Today's Topics include Interval Notation Exponent Rules Quadrants Distance Formula Midpoint Formula Circle Formula
3 Alligator Mouths to Interval Notation
4 Alligator Mouths to Interval Notation with INFINITY
5 Recap: You Try!!! Write the following in inequality notation. [3, 12] ( 45, 13] (5, 67) [17, )
6 Recap Reversed: Write the following in interval notation: 6 < x < 15 x < 24 4 < x < 37
7 Property Example REVIEW of Exponent Rules REALLY IMPORTANT
8 Let's try some properties!
9 QUADRANTS Quadrant 1: Quadrant 2: Quadrant 3: Quadrant 4: What about points like: (0, 5) ( 6, 0)
10 Distance Formula - aka - Pythagorean Theorem
11 Midpoint Formula - aka - average of two values
12 Circle Centered at (0, 0) x 2 + y 2 = r 2 Hmmm...looks like Pythagorean Theorem again.
13 Formulas Recap: Find the distance and midpoint of (3, 6) & ( 5, 11). Write the equation of a circle centered at ( 2, 5) with radius of 4.
14 Summer Review Problems on my web page This week's Assignments Review Work in text book!!!! Do NOT complete every problem. Do some from each section you do not understand. P1 p. 9 #1-52, P2 p.17 # 1-63 P3 p. 25 # 1-68 P4 p. 36 # 1-66 *My advice on comfort level* Very: Choose hardest problem in each section find one NOT like class example Not Sure: Try medium difficulty questions (not first ones in each section) and then try harder questions Not: Try starter questions in each section, then work your way up to "very" in each section
15 Do you have any questions?
16 Quick Review Today's Topics include Simplifying Expressions Combining Fractions Solving Equations
17 Algebra Review
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19 More Algebra Review
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21 This week's Assignments Summer Review Problems on my web page Review Work in text book!!!! **Do NOT complete every problem. Do some from each section you do not understand. P1 p. 9 #1-52, P2 p.17 # 1-63 P3 p. 25 # 1-68 P4 p. 36 # 1-66
22 Questions?
23 Quick Review Today's Topics include Slope Equations of lines Parallel and Perpendicular Quadratic equation
24 How to find slope
25 Equations of lines... Write the equation of this line using: y =mx+b We LOVE this form! Learn it! Know it! Use it!!!! Write the equation of this line using: y y 1 = m(x x 1 )
26 Equations of lines...
27 Parallel and Perpendicular EXAMPLE
28 We use the quadratic formula to find the roots of the equation. What are roots?
29 This week's Assignments Summer Review Problems on my web page Review Work in text book!!!! **Do NOT complete every problem. Do some from each section you do not understand. P1 p. 9 #1-52, P2 p.17 # 1-63 P3 p. 25 # 1-68 P4 p. 36 # 1-66
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31 Today's Topics include P5 5 ways to solve equations Abs equations
32 1. Factoring Solving Equations 2x 2-3x - 2 = 0 2. Extracting Square Roots (algebraically) (2x - 1) 2 = 9 3. Completing the Square 4x 2-20x + 17 = 0
33 4. Using the Quadratic Formula 3x 2-6x - 5 = 0 5. Using Tables 4x 2-4x - 8 = 0
34 Absolute Value Practice... What is abs? t 8 = 2 2x + 5 = 7
35 This week's Assignments P5 p. 46 #1-55mod3, 59, 60 P6 p.52 #1-25odds, 33-43odds P7 p.58 #1-30odds, 33, 34, 36, 37, 42-44
36 How is your homework going????
37 Today's Topics include P6 A quadratic song Complex numbers Operations with Complex Numbers Quadratics and Complex numbers
38 Quadratic Formula So you will NEVER forget it!
39 Complex Numbers A Complex Number is of the form a + bi where a is the real number part and b is the imaginary number part. a + bi is the standard form. Types of Imaginary Numbers: 5i, -5, -7i, 5 i+ 2 1, + 4 i
40 Operations with Complex Numbers Adding & Subtracting Complex Numbers (7-3i) + (4 + 5i) = (2 - i) - (8 + 3i) = Note: 0 = 0 + 0i. Remember given a + bi, -(a+bi) or -a-bi is the additive identity. Multiplying Complex Numbers (2 + 3i)(5 - i) = Note: i 2 =.
41 Complex Conjugate The complex conjugate of the complex number z = a + bi is z = a + bi = a - bi Where we use this: To simplify the quotient of two complex numbers in fraction form, we multiply the numerator and denominator by the complex conjugate- this shows the complex number in standard form. Examples: Write the complex number in standard form i 5 + i 2-3i
42 Complex Solutions of a Quadratic Equation Recall that solutions to quadratic equations of the form ax 2 + bx + c = o where a o, are given by the quadratic formula: x = -b ± b 2-4ac 2a In this formula, b 2-4ac is the discriminant. This tells us whether the solutions are real numbers and how many solutions exist. In general, for ax 2 + bx + c = o where a,b & c are real numbers and a o : *If b 2-4ac 0 there are two distinct, real solutions *If b 2-4ac = 0 *If b 2-4ac 0 there is one repeated real solution there is a complex pair of solutions
43 EXAMPLE Solve the following quadratic equation algebraically. x 2 + x + 1 = 0
44 This week's Assignments P5 p. 46 #1-55mod3, 59, 60 P6 p.52 #1-25odds, 33-43odds P7 p.58 #1-30odds, 33, 34, 36, 37, 42-44
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46 Today's Topics include P7 Absolute Inequalities Quadratics and Absolutes Projectile Motion
47 Solving Absolute Value Inequalities Ex 1: x Ex 2: 3x - 2 5
48 Solving Quadratic Inequalities Ex 1: Solve x 2 - x Hint: Solve with an = and check the graph for the interval solutions. Ex 2: Solve 2x 2 + 3x 20
49 Solving a Quadratic or Cubic Inequalities Graphically Solve x 2-4x graphically
50 Projectile Motion The vertical position s (in feet) of an object t seconds after it's launched can be represented by the equation: s = -16t 2 + v o t + s o Ex: A projectile is launched straight up from the ground with initial velocity of 288 ft/sec. a. Write an equation to represent this situation. b. When will the projectile's height above ground be 1152 ft? c. When will the projectile's height above ground be at least 1152 ft?
51 Projectile Motion The vertical position s (in feet) of an object t seconds after it's launched can be represented by the equation: s = -16t 2 + v o t + s o Ex: A punter kicks a ball from 2 ft above the ground up with an initial velocity of 78 ft/sec. a. Write an equation to represent this situation. b. When will the ball's height above ground be 100 ft? c. When will it hit the ground?
52 This week's Assignments P5 p. 46 #1-55mod3, 59, 60 P6 p.52 #1-25odds, 33-43odds P7 p.58 #1-30odds, 33, 34, 36, 37, 42-44
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56 Warm Up
57 Warm Up Solutions
58
59
60
61 Try These...
62 Review Work!!!! ****Do NOT do complete every problem. Do a some from each section you do not understand. P1 p. 9 #1-52, P2 p.17 # 1-63 P3 p. 25 # 1-68 P4 p. 36 # 1-66
Chapter P. Prerequisites. Slide P- 1. Copyright 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley
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