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Quirk of the Day

Quirk of the Day. Math. Formulas and practice. Factors. The factors of a number divide into that number without a remainder Example: the factors of 52 are 1, 2, 4, 13, 26, and 52 Practice: What are the factors of 64? 1, 2, 4, 8, 16, 32, 64. Multiples.

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Quirk of the Day

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  1. Quirk of the Day

  2. Math Formulas and practice

  3. Factors • The factors of a number divide into that number without a remainder • Example: the factors of 52 are 1, 2, 4, 13, 26, and 52 Practice: What are the factors of 64? 1, 2, 4, 8, 16, 32, 64

  4. Multiples • the multiples of a number are divisible by that number without a remainder • Example: the positive multiples of 20 are 20, 40, 60, 80, . . . Practice: What are the first 5 multiples of 4? 4, 8, 12, 16, 20

  5. Percents • Use the following formula to find part, whole, or percent: percent 100 • Example: 75% of 300 is what? Solve x = (75/100) × 300 to get 225 Practice: 60% of 200? 120 Part whole = X

  6. Percents cont’d • Example: 45 is what percent of 60? 45 = (p /100) × 60 ÷60 ÷ 60 .75 = (p /100) x 100 x 100 75 = p Practice: 15 is what percent of 75? 20%

  7. Percents cont’d • Example: 30 is 20% of what? 30 = (20/100) × n x (100 / 20) x (100 / 20) 150 = n Practice: 20 is 40% of what? 50

  8. Averages • average = sum of terms ÷ number of terms • Example: the average of 5 + 10 + 15 + 20 + 25 = ? (75 ÷ 5) = 15 Practice: What is the average of 2 + 4 + 6? 4

  9. Average Speed • average speed = total distance ÷ total time • Example: Juan ran 16 miles in 2 hours, what was his average speed? (16 ÷ 2) = 8 miles per hour Practice: Julie drove 30 miles in 17 minutes, stopped for gas, and then drove another 20 miles in 8 minutes. What was her average speed? 2 miles per minute

  10. Sum of Averages • sum = average × (number of terms) • Example: the average is 64, the number of terms is 4, what is the sum? S = 64 × (4) S = 256 Practice: The average is 25, the number of terms is 3, what is the sum? 75

  11. Mode mode = value in the list that appears most often • Example: what is the mode of: {7, 10, 2, 15, 8, 4, 8, 5, 9, 2, 10, 15, 2, 7, 14} 2 Practice: What is the mode of {37, 52, 78, 90, 33, 27, 52, 98, 59, 63, 80, 14} 52

  12. Median median = middle value in the list (which must be sorted) • Example: median of {3, 10, 9, 27, 50} = [3, 9, 10, 27, 50] = 10 • Example: median of {3, 9, 10, 27} = [3, 9, 10, 27] =(9 + 10)/2 = 9.5 • Practice: what is the median of: {7, 10, 2, 15, 8, 4, 8, 5, 9, 2, 10, 15, 2, 7, 14} [2, 2, 2, 4, 5, 7, 7, 8, 8, 9, 10, 10, 14, 15, 15] 8

  13. Probability number of desired outcomes ÷ number of total outcomes • Example: each SAT math multiple choice question has fivepossible answers, one of which is the correct answer. If you guess the answer to a question completely at random, your probability of getting it right is 1 ÷ 5 = 20%. Practice: What is the probability of rolling a 3 or a 5 with a dice? 2/6 = 1/3

  14. Probability of independent events The probability of two different events A and B both happening is P(A and B) = P(A) ・ P(B), as long as the events are independent (not mutually exclusive). • Example: the probability of getting a 3 and a 5 rolling a dice two times. (1/6) x (1/6) = 1/36 Practice: What is the probability of getting a 1, 3, and 4 on 3 dice rolls? (1/6) x (1/6) x (1/6) = 1 / 216

  15. Review Time Yes, there is a possibility for candy

  16. Question 1 35 is 20% of what?

  17. Question 2 What is the mode of the following list of numbers? {37, 90, 88, 27, 74, 52, 88, 63, 52, 88}

  18. Question 3 What is the median of the following list of numbers? {37, 90, 88, 27, 74, 52, 88, 63, 52, 88}

  19. Question 4 What is the average of the following list of numbers? {37, 90, 88, 27, 74, 52, 88, 63, 52, 88}

  20. Question 5 What are the first 5 multiples of 3?

  21. Question 6 What are the factors of 48?

  22. Question 7 What is the probability of me randomly choosing a boy from this class if I put all of your names into a hat?

  23. Question 8 What is the probability of me rolling a 5 on a dice and flipping heads on a coin?

  24. Question 9 If Joe drives 25 miles in 5 minutes, takes a nap, then drives 45 miles in half an hour, what is his average speed?

  25. Question 10 54 is what percent of 90?

  26. Question 11 The average of terms is 84, the number of terms is 4, what is the sum?

  27. Question 12 15% of 60 is what?

  28. Answers Yes, there is a possibility for candy

  29. Question 1 35 is 20% of what? 175

  30. Question 2 What is the mode of the following list of numbers? {37, 90, 88, 27, 74, 52, 88, 63, 52, 88} 88

  31. Question 3 What is the median of the following list of numbers? {37, 90, 88, 27, 74, 52, 88, 63, 52, 88} 68.5

  32. Question 4 What is the average of the following list of numbers? {37, 90, 88, 27, 74, 52, 88, 63, 52, 88} 65.9

  33. Question 5 What are the first 5 multiples of 3? 3, 6, 9, 12, 15

  34. Question 6 What are the factors of 48? 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

  35. Question 7 What is the probability of me randomly choosing a boy from this class if I put all of your names into a hat?

  36. Question 8 What is the probability of me rolling a 5 on a dice and flipping heads on a coin? 1/12

  37. Question 9 If Joe drives 25 miles in 5 minutes, takes a nap, then drives 45 miles in half an hour, what is his average speed? 2 miles per minute

  38. Question 10 54 is what percent of 90? 60%

  39. Question 11 The average of terms is 84, the number of terms is 4, what is the sum? 336

  40. Question 12 15% of 60 is what? 9

  41. Moving on…. Want a quirk of the day?

  42. Question of the Day • John has 32 candy bars. He eats 28. What does he have now? Diabetes

  43. Powers, Exponents, Roots • √xy = √x ・ √y • 1/xb = x−b • xa ・ xb = x a+b • (xa) b= xa・b • x0 = 1 • xa/xb= xa−b • (xy) a= xa ・ ya • (−1)n = +1, if n is even; −1, if n is odd.

  44. Practice with Powers, Exponents, & Roots • (−1)3 = _____________ • 22・ 24_____________ • (2 x 4) 2 = _____________ • (−1)8 = _____________ • (Make your own) • 20=_____________ • √25 x 16 = _____________ • 24 ÷ 22 = _____________ • 1/ 24 = _____________ • (24) 2 = _____________ - 1 1 5・ 4 = 20 2 4 + 2 = 64 √25 ・ √16 24−2 = 4 = 64 4・ 16 22 ・ 42 2−4 = .0625 1 24・2 = 256

  45. Linear Functions

  46. Distance Formula Consider the line that goes through points A(x1, y1) and B(x2, y2) • Practice: What is the distance from (2, 3) and (6, 6)? 25

  47. Mid-point Formula Consider the line that goes through points A(x1, y1) and B(x2, y2) • Practice: What is the midpoint of (2, 4) and (8, 8)? (5, 6)

  48. Slope of the line Consider the line that goes through points A(x1, y1) and B(x2, y2) • (Slope = m) • Practice: What is the slope of` (4, 4) and (6, 8)? 2

  49. SIN, COS, TAN

  50. SIN, COS, TAN SIN = COS = TAN =

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