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AIMS Math Potpourri

AIMS Math Potpourri . Spring, 2008. Natural Numbers: 1, 2, 3, 4… Whole Numbers: 0, 1, 2, 3, 4, …. Integers: …, -3, -2, -1, 0, 1, 2, 3, … Rational Numbers: fractions, terminating decimals, numbers that can be written as ratios

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AIMS Math Potpourri

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  1. AIMS Math Potpourri Spring, 2008

  2. Natural Numbers: 1, 2, 3, 4… Whole Numbers: 0, 1, 2, 3, 4, …. Integers: …, -3, -2, -1, 0, 1, 2, 3, … Rational Numbers: fractions, terminating decimals, numbers that can be written as ratios Irrational Numbers: Square root of a non-perfect square, pi (), and non-ending,non-repeating decimals Period 1 • Infinite or Finite? • Infinite means…. • Finite means… • Are the following sets finite or infinite? • Integers between 1 and 10. • Natural numbers between 1 and 10. • Rational numbers between 1 and 10.

  3. Natural Numbers: 1, 2, 3, 4… Whole Numbers: 0, 1, 2, 3, 4, …. Integers: …, -3, -2, -1, 0, 1, 2, 3, … Rational Numbers: fractions, terminating decimals, numbers that can be written as ratios Irrational Numbers: Square root of a non-perfect square, pi (), and non-ending,non-repeating decimals Period 1ANSWERS • Infinite or Finite? • Infinite means….cannot be counted, endless • Finite means…can be counted, even if difficult (such as counting the grains of sand on a beach) • Are the following sets finite or infinite? • Integers between 1 and 10.finite {2, 3, 4, 5, 6, 7, 8, 9} • Natural numbers between 1 and 10. finite {2, 3, 4, 5, 6, 7, 8, 9} • Rational numbers between 1 and 10. infinite because it contains all fractions and decimals between 1 & 10

  4. Period 2 • Absolute Value • Absolute value is defined as the distance a number is from _____. • |3| 3. |-5| 4. - | -2| • |-2| - |4| 6. |-2| - |4| + |3 – 10| • |-3| + |-2| 8. - |3| + |-2| 9. -|3| - |2| 10. |-3 + 2|

  5. Period 2 ANSWERS • Absolute Value • Absolute value is defined as the distance a number is from ___ 0 (zero)__. • |3| 3 3. |-5| 5 4. - | -2| -2 • |-2| - |4| -2 6. |-2| - |4| + |3 – 10| 5 • |-3| + |-2| 5 8. - |3| + |-2| -1 9. -|3| - |2| -1 10. |-3 + 2| 1

  6. Period 3 - Combinations • Jennifer wants to make a sandwich. She has 5 types of meat, 3 types of cheese, and 2 types of sandwich spreads. If Jennifer chooses 1 meat, 1 cheese, and 1 sandwich spread, how many different combinations are possible for her sandwich. • Pizza Putz has 4 types of crust, 3 types of sauces, and 6 kinds of toppings. How many one-topping pizzas are possible? • Jose is selecting an outfit from amount 2 pairs of pants, 4 shirts, and 3 pairs of shoes. How many different outfits consisting of 1 pair of pants, 1 shirt, and 1 pair of shoes are possible?

  7. Period 3 – CombinationsANSWERS • Jennifer wants to make a sandwich. She has 5 types of meat, 3 types of cheese, and 2 types of sandwich spreads. If Jennifer chooses 1 meat, 1 cheese, and 1 sandwich spread, how many different combinations are possible for her sandwich. 5*3*2=30 sandwich combinations • Pizza Putz has 4 types of crust, 3 types of sauces, and 6 kinds of toppings. How many one-topping pizzas are possible? 4 * 3 * 6 = 72 one-topping pizzas • Jose is selecting an outfit from amount 2 pairs of pants, 4 shirts, and 3 pairs of shoes. How many different outfits consisting of 1 pair of pants, 1 shirt, and 1 pair of shoes are possible? 2*4*3 = 24 outfits

  8. Period 4 – Special Triangles • An isosceles triangle has 2 equal ____ and 2 equal ___. • An equilateral triangle has ___ equal sides and ___ equal angles. Each angle is __ degrees. • The angles of a triangle add up to _ degrees. • Find the missing side or angle measures. a. b. c. 32° 8 c° t 5 c 3 r 61° m b

  9. Period 4 – Special Triangles ANSWERS • An isosceles triangle has 2 equal _ angles_ and 2 equal _ sides_. • An equilateral triangle has _ 3 _ equal sides and _ 3 _ equal angles. Each angle is _ 60 _ degrees. • The angles of a triangle add up to _ 180 degrees. • Find the missing side or angle measures. a. b. c. 32° 8 c° t 5 c 3 r 61° m b c=5 m=61° b = 60° r = 3 c = 116° t = 8

  10. Period 5 • Marissa has $20.00. A six-pack of soda costs $2.29, including tax. What is the greatest number of six-packs of soda she can buy? • Jeffrey has $10.00. A candy bar cost $0.65. What is the greatest number of candy bars he can buy?

  11. Period 5 ANSWERS • Marissa has $20.00. A six-pack of soda costs $2.29, including tax. What is the greatest number of six-packs of soda she can buy? $20  $2.29 = 8 six-packs • Jeffrey has $10.00. A candy bar cost $0.65. What is the greatest number of candy bars he can buy? $10  $0.65 = 15 candy bars

  12. Period 6 Given the expression , what is the value given 1. x = 3, y = -1 2. x = 8, y = 5 3. x = 8, y = 4 4. x = 0, y = -12 5. x = 5, y = 2 Estimate the value to the nearest whole number of the following.

  13. Period 6 ANSWERS Given the expression , what is the value given 1. x = 3, y = -1 3 2. x = 8, y = 5 1 3. x = 8, y = 4 2 4. x = 0, y = -12 6 5. x = 5, y = 2 2 Estimate the value to the nearest whole number of the following. 4 6 8 10 9

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