quirk of the day

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

?

?