Everything

Question 1

How would you form a box and whisker chart with this data set?

{2, 4, 4, 5, 7, 7, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9}

Answer 1

The box is formed by the bounds Q1 and Q3. M (median) lies within the box. The whiskers extend to the least and greatest values of the set. M = Q2 and divides the set. Q1 and Q3 are the medians of the remaining halves.

Q1=6, Q3=8.5, Q2/M=7

Question 2

List the prime numbers from 0 to 107

Answer 2

{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107}

Question 3

What is the interquartile range?

Answer 3

Typically related to boxplot problems, it is the range between Q3 and Q1.

(ie Q3-Q1)

Question 4

What is the range of a set?

Answer 4

The greatest value of the set minus the least value of the set.

ie {1, 5, 8, 10, 11} -> R=11-1 = 10

Question 5

What is the mode of a set?

Answer 5

The mode of the set is the most common number.

ie. {2, 3, 3, 3, 3, 7, 8, 9, 10, 24, 53, 13,} -> the mode is 3

Question 6

What is the mean (arithmetic) of a set?

Answer 6

Often times identical to the median it is the sum of all of the number in the set divided by the number of terms in the set.

ie. {1, 2, 3, 4, 5} -> M = (1+2+3+4+5)/5 = 15/5 = 3

Question 7

What is the median of a set?

Answer 7

The middle most term or the average of the center two for an even set.

ie. {1, 2, 3, 4, 5, 6} m = 3.5

Question 8

What are the sides of a 30-60-90 triangle?

Answer 8

Question 9

What are the sides of a 45-45-90 triangle?

Answer 9

Question 10

What is the formula for the sum of an arithmetic sequence?

Answer 10

S_n = (n/2)[2a + (n-1)d]

n = # of terms, a = first term in sequence, d = difference between terms

Question 11

What is the formula for the sum of a geometric sequence?

Answer 11

S_n = a[(rⁿ-1)/(r-1)]

a = starting term in sequence, r = common ratio, n = number of terms.

Question 12

What is the general formula for a permutation?

Answer 12

_nP_k = n!/(n-k)!

n = total set, k = subset

Question 13

What is the general formula for a combination?

Answer 13

_nC_k = n!/[k!(n-k)!]

n = total set, k = subset

Question 14

What is the general groups formula (for overlapping sets)?

Answer 14

T = G₁ + G₂ - B + N

Question 15

What is the circumference of a circle?

Answer 15

C = 2πr = πD

Question 16

What is the area of a circle?

Answer 16

A = πr²

Question 17

What is the sum of the internal angles of the pentagon in degrees?

Answer 17

n = # of sides d = degrees

d = (n-2)(180^o)

d = (3)(180^o) = 540^o)

Question 18

What is the area of the parallelogram?

Answer 18

Same as rectangle A = lw = lh = 8(20) = 160

Question 19

What is the area of the trapazoid?

Answer 19

A = 1/2(b₁ + b₂)h , b₁ = 10, b₂ = 18

A = 105

Question 20

What is the least common multiple between 22 and 6?

Answer 20

LCM > smallest number that x and y are both factors of

LCM = 66

Question 21

What is the greatest common factor between 66 and 99?

Answer 21

GFC > greatest shared factor between x and y

GCF = 33

Question 22

How many numbers are in a an ordered list of integers from 1,2,3,4……n

where n = the number of terms in the list?

Answer 22

n = greatest value - least value +1

5,6,7 …. 20

n = 20-5 +1

Question 23

What is the value of the angle C

Answer 23

c = x+y

Question 24

If r = 10 what is the arc length ABC

Answer 24

Length of Arc= (central angle/360)C

(portion of total circumferance that central angle includes)

ABC = 50/360(10π)

Question 25

If r = 10 what is the area of the sector defined by arc ABC

Answer 25

A_sector = A_whole (central angle/360)

A_{sector = π(100)(50/360)}

Question 26

What is the volume and area of a regular cylinder?

Answer 26

V = πr²h

A = 2(πr²) +2πrh

Question 27

How many positive factors does 6600 have

Answer 27

Prime factorize the number. Add one to each exponent. Multiply the exponents together A) (2^3)(5^2)(3^1)(11^1) -> (4)(3)(2)(2) =48

Question 28

How many positive odd factors does 4500 have?

Answer 28

Prime factorize the number. Add one to each exponent. Multiply the exponents together but disregard the factor of 2 A) (5^3)(3^2)-> (4)(3) =12 positive odd factors

Question 29

What is the quadratic formula?

Answer 29

Question 30

Answer 30

B - B is bigger

Question 31

List the Pythagorean triples

Answer 31

3, 4, 5 (and multiples) 6, 8, 10 9, 12, 15 5, 12, 13 8, 15, 17 7, 24, 25