Quirk of the Day. Math Formulas and practice Factors The factors of a number divide into that...
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Transcript of Quirk of the Day. Math Formulas and practice Factors The factors of a number divide into that...
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:percent100
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 ÷ 60
.75 = (p /100) x 100 x 100 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
Practice: 20 is 40% of what?
50
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
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
Modemode = 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
Medianmedian = 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
Probabilitynumber 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
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 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 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 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 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 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
Powers, Exponents, Roots
1. xa ・ xb = x a+b
2. (xa) b = xa ・ b
3. x0 = 1
4. xa/xb = xa−b
5. (xy) a = xa ・ ya
6. (−1)n =
7. √xy = √x ・ √ y
8. 1/xb = x−b
+1, if n is
even;
−1, if n is
odd.
Practice with Powers, Exponents, & Roots
1. 20 = _____________
2. √25 x 16 = _____________
3. 24 ÷ 22 = _____________
4. 1/ 24 = _____________
5. (24) 2 = _____________
24−2
2−4
24 ・ 2
6. (−1)3 = _____________
7. 22 ・ 24 _____________
8. (2 x 4) 2 = _____________
9. (−1)8 = _____________
10. (Make your own)
√25 ・ √ 16
5 ・ 4 = 20
= 4
= .0625
= 256
- 11
2 4 + 2 = 64
22 ・ 42
4 ・ 16 = 64
1
Distance FormulaConsider 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
Mid-point FormulaConsider 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)
Slope of the lineConsider 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
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