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Day 1 of Pre-Calculus! Wohoo !

Day 1 of Pre-Calculus! Wohoo !. Bain’s Daily Procedures: Homework: review from the night before, and turn it in (HW worth 2 pts )

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Day 1 of Pre-Calculus! Wohoo !

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  1. Day 1 of Pre-Calculus! Wohoo! Bain’s Daily Procedures: Homework: review from the night before, and turn it in (HW worth 2 pts) Notes: will be given in the form of power points. You can print these out from my teacher page and bring them to class with you if you would like – choosing a format that works best for note taking. Extended Periods: we will proceed with the next days notes, then add some mind-stretching activities!

  2. Let’s begin exploring (reviewing?!?!) the info in P.1 Interval Notation, Properties of Algebra & Exponents, Scientific Notation

  3. Recall the real number line: Coordinate of a point Origin 13 3 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 Neg. real numbers Pos. real numbers

  4. We can use inequalities to describe intervals of real numbers < (recall the symbols?) > < > Ex: Describe and graph the interval of real numbers for the inequality given 1. x > –2 All real numbers greater than or equal to negative two –2 –1 0 1 –1 0 1 –2 Closed bracket – value included in solution.

  5. We can use inequalities to describe intervals of real numbers < (recall the symbols?) > < > Ex: Describe and graph the interval of real numbers for the inequality given 2. 0 < x < 3 All real numbers between zero and three, including zero –1 0 1 2 3 –1 1 2 3 0

  6. Interval Notation Bounded Intervals of Real Numbers (let a and b be real #s with a < b; a and b are the endpoints of each interval) Interval Notation Interval Type Inequality Notation Graph [a, b] closed a < x < b a b (a, b) open a < x < b a b [a, b) half-open a < x < b a b (a, b] half-open a < x < b a b

  7. Interval Notation Unbounded Intervals of Real Numbers (let a and b be real #s) Interval Notation Interval Type Inequality Notation Graph 8 [a, ) closed x > a a 8 (a, ) open x > a a 8 ( , b] closed x < b b 8 ( , b) open x < b b

  8. More Examples… Convert interval notation to inequality notation or vice versa. Find the endpoints and state whether the interval is bounded, its type, and graph the interval. [–3, 7] 3. –3 < x < 7 Endpoints: –3, 7 Bounded, closed interval –3 0 7

  9. More Examples… Convert interval notation to inequality notation or vice versa. Find the endpoints and state whether the interval is bounded, its type, and graph the interval. x < –9 8 4. (– , –9) Endpoint: –9 Unbounded, open interval –9 0

  10. Some new/old info… Consider the magically appearing expression below: Constants Algebraic Expression Variables

  11. Factored Form Expanded Form Expanded Form Factored Form

  12. Additive inverses are two numbers whose sum is zero (opposites?) Example: Multiplicative inverses are two numbers whose product is one (reciprocals?) Example:

  13. Other Properties from Algebra Let u, v, and w be real numbers, variables, or algebraic expressions. Commutative Property Addition: u + v = v + u Multiplication: uv = vu Associative Property Addition: (u + v) + w = u + (v + w) Multiplication: (uv)w = u(vw)

  14. Inverse Property Addition: u + (– u) = 0 Multiplication: Identity Property Addition: u + 0 = u Multiplication: (u)(1) = u Distributive Property u(v + w) = uv + uw (u + v)w = uw + vw

  15. Exponential Notation Let a be a real number, variable, or algebraic expression and n is a positive integer. Then: n a = a a a … a, n factors n n is the exponent, a is the base, and a is the nth power of a, read as “a to the nth power”

  16. Properties of Exponents (All bases are assumed to be nonzero) m n m + n 1. u u = u u m 2. = m – n u u n 0 3. u = 1 1 – n 4. u = u n

  17. Properties of Exponents (All bases are assumed to be nonzero) m m m 5. (uv) = u v n m mn 6. (u ) = u ( ) u m m u 7. = v m v

  18. Scientific Notation m Where 1 < c < 10, and m is any integer c x 10 Let’s do some practice problems…

  19. Guided Practice • Proctor’s brain has approximately 102,390,000,000 • Neurons (at least before the rugby season). Write this • number in scientific notation 11 1.0239 x 10 – 9 2. Write the number 8.723 x 10 in decimal form 0.000000008723

  20. Guided Practice For #3 and 4, simplify the expression. ( ) 2 3 2 (3x) y 2 ab 3. 4. –1 5 3 12x y b 2 3 a 3x 2 2 b 4y

  21. Guided Practice Use scientific notation to multiply: – 7 6 (3.7 x 10 )(4.3 x 10 ) 5. 7 2.5 x 10 6 6.364 x 10 Homework: p. 11-12 5-31 odd, 37-63 odd Note: Name and assignment should be written on the top line of you paper.

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