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  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

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

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

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

Averages  average = sum of terms ÷ number of terms  Example: the average of = ? (75 ÷ 5) = 15 Practice: What is the average of ? 4

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

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

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

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:  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

Probability number of desired outcomes ÷ number of total outcomes  Example: each SAT math multiple choice question has five possible 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

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

Review Time Yes, there is a possibility for candy

Question 1 35 is 20% of what?

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

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

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

Question 5 What are the first 5 multiples of 3?

Question 6 What are the factors of 48?

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?

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

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?

Question is what percent of 90?

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

Question 12 15% of 60 is what?

Answers Yes, there is a possibility for candy

Question 1 35 is 20% of what? 175

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

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

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

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

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

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?

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

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

Question is what percent of 90? 60%

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

Question 12 15% of 60 is what? 9

Moving on…. Want a quirk of the day?

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

Powers, Exponents, Roots 1. x a ・ x b = x a+b 2. (x a ) b = x a ・ b 3. x 0 = 1 4. x a /x b = x a − b 5. (xy) a = x a ・ y a 6. ( −1 )n = 7. √xy = √x ・ √y 8. 1 /x b = x − b + 1, if n is even; −1, if n is odd.

Practice with Powers, Exponents, & Roots = _____________ 2. √25 x 16 = _____________ ÷ 2 2 = _____________ 4. 1 / 2 4 = _____________ 5. (2 4 ) 2 = _____________ 24−224−2 2−42−4 24・224・2 6. ( −1 ) 3 = _____________ ・ 2 4 _____________ 8. (2 x 4) 2 = _____________ 9. ( −1 ) 8 = _____________ 10. (Make your own) √25 ・ √16 5 ・ 4 = 20 = 20 = 4 = 4 =.0625 =.0625 = 256 = = 64 = ・ ・ 16 = 64 = 64 1

Linear Functions

Distance Formula Consider the line that goes through points A(x 1, y 1 ) and B(x 2, y 2 )  Practice: What is the distance from (2, 3) and (6, 6)? 25

Mid-point Formula Consider the line that goes through points A(x 1, y 1 ) and B(x 2, y 2 )  Practice: What is the midpoint of (2, 4) and (8, 8)? (5, 6)

Slope of the line Consider the line that goes through points A(x 1, y 1 ) and B(x 2, y 2 )  (Slope = m)  Practice: What is the slope of` (4, 4) and (6, 8)? 2

SIN, COS, TAN

SIN = COS = TAN =

Given facts & formulas include…  Area of a triangle  Pythagorean theorem  Special properties of a 30, 60, 90 & a 45, 45, 90 triangle  Area & circumference of a circle  Area & circumference of a rectangle  Volume of a cube  Volume of a cylinder  Number of degrees of an arc in a circle  Sum of degrees of angles in a triangle

Area of a triangle  The area of a triangle is (1/2) base x height

Area of a triangle  What is the area of this triangle?

Pythagorean theorem  Remember the hypotenuse (c) is across from the right angle

Pythagorean theorem  What is the hypotenuse of this triangle? 3 4 ?

Circles Area of a circle

Circles What is the circumference of this circle? What is the area of this circle?

Special Triangles

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