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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. - PowerPoint PPT Presentation
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Quirk of the Day
MathFormulas 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 ÷ 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 eventsThe 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 TimeYes, 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 10
54 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?
AnswersYes, 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 10
54 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 DayJohn has 32 candy bars. He eats 28. What does he have
now?
Diabetes
Powers, Exponents, Roots1. 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 ・ √ y8. 1/xb = x−b
+1, if n is even; −1, if n is odd.
Practice with Powers, Exponents, & Roots1. 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 ・ √ 165 ・ 4 = 20
= 4
= .0625
= 256
- 11
2 4 + 2 = 64
22 ・ 424 ・ 16 = 64
1
Linear Functions
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
SIN, COS, TAN
SIN, COS, TANSIN =
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
CirclesWhat is the circumference of this circle?
What is the area of this circle?
28.26
63.585
Special Triangles
Special Triangles
?
?