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Prerequisites

Prerequisites. What classes do you need to know: Algebra 1 Geometry Algebra 2 Precalculus is the combination of all previous mathematic classes. Prerequisite #1 Real Number. Review: Real Numbers. Real number : Any number that can be written as a decimal.

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Prerequisites

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  1. Prerequisites What classes do you need to know: Algebra 1 Geometry Algebra 2 Precalculus is the combination of all previous mathematic classes

  2. Prerequisite #1 Real Number

  3. Review: Real Numbers • Real number: Any number that can be written as a decimal. • Activity: Match the corresponding vocab to its correct answer • Integers {1,2,3…} • Natural number(counting number) {0,1,2,3…} • Whole number {…-1,0,1…}

  4. Answer: • Integers {1,2,3…} • Natural number(counting number) {0,1,2,3…} • Whole number {…-1,0,1…}

  5. Review: Real Numbers • What are the difference rational numbers and irrational numbers? • Activity: Identify which of these are rational and irrational. • , -12, 1.75, 7.333… , ,

  6. Answer • Rational Number: number that either terminates or infinitely repeating • , -12, 1.75, 7.333… • Irrational Number: A number is infinitely nonrepeating • ,,

  7. New!!! • {} this represent a set. It encloses the elements or objects. • Example: {0,1,2,3} • Translation: This set includes the solution of 0,1,2,3

  8. Review: Real Number • Inequality • Activity: Match the symbol with the answer • ab a is less than b • ab a is greater than or equal to b • ab a is less than or equal to b • ab a is greater than b

  9. Answer • ab a is less than b • ab a is greater than or equal to b • ab a is less than or equal to b • ab a is greater than b

  10. Bounded Interval Example

  11. Unbounded interval • Graph the following: • (3, • (- • [3, • (-

  12. Properties of Algebra

  13. Example: • Expand: (a+5)8 • Simplify: 9p+ap

  14. Answer • Expand: (a+5)8 • 8a+40 • Simplify: 9p+ap • p(9+a)

  15. Exponential Notation • = a*a*a*a*a… • a = base, n is the exponent • Example: • ( • = • Why is this the case?

  16. Activity: Simplifying expressions

  17. Answer • )

  18. Scientific notation • Scientific notation – related to chemistry where it is written as the product of two factors in the form , where n is an integer and • Activity: Convert the following into scientific notation or expand them out • 3.54 x • 1.29 x • 0.000000459 • 4,970,000

  19. Answer • 3.54 x 3,540,000,000 • 1.29 x 0.00000129 • 0.000000459 4.59 x • 4,970,000 4.97 x

  20. Homework Practice • Pgs 11-12 # 2-44e, 48-54e, 58-64e

  21. Prerequisite #2Cartesian Coordinate System

  22. Given the recent unemployment rate reports in California, describe the trend. What year represent the biggest increase? Decrease? What % can you predict about the future unemployment rate? (Graph it and answer)

  23. Answer • Unemployment rate increasing from year 2006-2010 • Unemployment decreasing from year 2010-2012 • 2008-2009 post the biggest increase • 2011-2012 post the biggest decrease • 10%-12% unemployment rate

  24. Scatter plot: plotting the (x,y) data pair on a cartesian plane • The previous question we just did is an example of a scatter plot

  25. What do you need to graph? • Coordinates • (X,Y), (input, output) • Example (3,-2) • Things to keep in mind: • Always label!!!

  26. Quick Talk: (30 second) • What is absolute value?

  27. Answer • Absolute Value: Always positive, tells distance. • Magnitude: size or distance

  28. Activity • l-4l = • l16-7l= • l9-27l =

  29. Answer • 4 • 9 • 18

  30. Quick talk: How can you find the distance between two places/points?

  31. Answer: • Measure • Use distance formula

  32. Distance Formula • Distance Formula: It is derived from the Pythagorean theorem. D=

  33. Activity: • Distance between (2,-5) and (-7,3) • Distance between (-1,-7) and (-6, 8)

  34. Midpoint Formula • Midpoint Formula: A formula to find the middle of the two points. M=()

  35. Activity: • Find the midpoint between (6,8) and (-4,-10) • Find the midpoint between (-

  36. Review: Geometry Circle • Standard form of a circle: • (h,k) is the center of the circle • r= the radius of the circle • Example: • (-2,9) is the center • 5 is the radius

  37. Quick talk: How do you find the distance from the center to a point on a circle?

  38. Answer • By finding the radius • Use distance formula

  39. Homework Practice • Pgs 20-22 #5, 8, 9, 11, 13, 21, 23, 27, 31, 35, 39, 43, 49, 51, 55, 57

  40. Prerequisite #3Solving Linear equations and inequalities

  41. How do you know if an equation/inequality is linear?

  42. Answer • If the highest power or the highest exponent is 1

  43. Linear Equation • Note: the highest power (exponent) is one

  44. Solving linear equation • Solve for x

  45. Solve for y

  46. Solving inequality • Remember solving inequality is like solving an equation. • There are 3 ways of representing an answer • Example: • X>3 • graphically

  47. Solve

  48. Solve

  49. Solving a sandwich Note: Make 2 separate inequalities

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