College Math Clep

Front 1

What does the following statement indicate?
6 ∈ S

Back 1

6 is an element of set S

Front 2

What does the following statement indicate?
2 ∉ S

Back 2

2 is not an element of set S

Front 3

How is a union of two sets written?

Back 3

A ∪ B

Front 4

Given two sets:
A={4,6,12,65}
B={6,15,42,87}
How is a union of the two sets written?

Back 4

A ∪ B = {4,6,12,15,42,65,87}

Front 5

Describe a union of two sets.

Back 5

Numbers common to both sets are listed once in a new set.

Front 6

Describe an intersection of two sets.

Back 6

Intersections combine two sets but only contain numbers that were present in both sets.

Front 7

Given two sets:
A={3,4,6,12,65}
B={3,6,13,65,87}
What is the intersection of the two sets?

Back 7

A ∩ B = {3,6,65}

Front 8

What symbol is used to represent an intersection of two sets?

Back 8

A ∩ B

Front 9

Describe the Cartesian Product of two sets.

Back 9

Every element in a set multiplied by every element in another set.

Front 10

Given two sets:
A = {1,5,6}
B = {2,5,8}
How do you write the Cartesian Product of the two sets?

Back 10

A x B ={(1,2),(1,5),(1,8),(5,2),(5,5),(5,8),(6,2),(6,5),(6,8)}

Front 11

In reference to logical statements, what is an implication?

Back 11

Used to imply something. If A is true, then B is true.

Front 12

In reference to logical statements, how is an implication written?

Back 12

A -> B
or
A IMPLIES B

Front 13

In reference to logical statements, what is a conjuction?

Back 13

Known as the AND operator. Both A and B must be true for the statement to be true.

Front 14

In reference to logical statements, how is a conjuction written?

Back 14

A /\ B

Front 15

In reference to logical statements, what is a disjunction?

Back 15

Means that either A or B must be true for the statement to be true.

Front 16

In reference to logical statements, how is a disjunction written?

Back 16

A \/ B

Front 17

In reference to logical operations, what is negation?

Back 17

Negation is an operation on one logical value, that produces a value of true when its operand is false and a value of false when its operand is true.

Front 18

What is a symbol for negation?

Back 18

~

Front 19

In reference to logical operations, what is equivalence?

Back 19

Simply means equals

Front 20

How is equivalence of two logical operators written?

Back 20

As a two or three line equal sign

Front 21

What is a logical converse?

Back 21

Means to switch the variables in a statement.
Ex: If A then B or A -> B, the converse would be If B then A or B -> A

Front 22

In reference to logical operations, what is an inverse?

Back 22

Means to changes variables to their inverse values.
Ex: If A then B or A -> B, the inverse would be If ~A then ~B or ~A -> ~B

Front 23

In reference to logical operations, what is a contrapositive?

Back 23

Means to take the negation of the converse.
Ex: If A then B or A -> B, then the converse would be If B then A or B -> A, then the contrapositive would be If ~B then ~A or ~B -> ~A

Front 24

In reference to logical operations, what is a counter example?

Back 24

Situation where the hypothesis is true but the conclusion is false.
Ex: All odd whole numbers between 1 and 11 are prime. For number 9, the hypothesis (odd whole number between 1 and 11) is true but the conclusion (are prime) is false.

Front 25

Describe rational numbers

Back 25

Can be written out easily as a fraction.
Can be infinite on the right of the decimal if written as a fraction. (Ex: 2/3)

Front 26

Describe irrational numbers

Back 26

Cannot be written nicely as a fraction AND are infinite on the right of the decimal if written as a fraction.

Front 27

What is a relation?

Back 27

A set of ordered pairs where the first components of the ordered pairs are the input values and the second set are the output values.

Front 28

What is a function?

Back 28

A relation that assigns to each input number EXACTLY ONE output number.

Front 29

Describe the domain of ordered pairs.

Back 29

The set of all input values, also called the independent variables. They correspond to the first components of the ordered pairs.

Front 30

Describe the range of ordered pairs.

Back 30

The set of all output values, also called dependent variables. They correspond to the second components of the ordered pairs.

Front 31

What is the Vertical Line Test?

Back 31

If no vertical line can be drawn on a graph so that it intersects the graph more than once, it is a graph of a function.

Front 32

For a function, the output values are also called what?

Back 32

Functional values

Front 33

For function f(0), what is the function name and what is the value of the input value, x?

Back 33

The name of the function is "f" and the value of x is 0.

Front 34

What is the mean?

Back 34

The average

Front 35

What is the median?

Back 35

The value in the middle of a set.

Front 36

How do you determine the percent change?

Back 36

Divide the difference by the old value.

Front 37

What is standard deviation?

Back 37

Describes how tightly values are concentrated around the mean.

Front 38

The probability of event A can be written as what notation?

Back 38

P(A)

Front 39

What is the mode?

Back 39

The value that appears most often in the data.

Front 40

What is the range?

Back 40

The difference between the min and max values.

Front 41

Complex numbers consists of what two parts?

Back 41

Real and imaginary

Front 42

How are imaginary numbers identified?

Back 42

i

Front 43

What is the standard format used for complex numbers?

Back 43

a + bi. The real number is represented by "a" and the imaginary number is represented by "bi", with the "i" indicating imaginary.

Front 44

In reference to imaginary numbers, what does "i" equal?

Back 44

The square root of -1

Front 45

What is the result of the following:
2i X 3i =

Back 45

5i

Front 46

What is the result of the following:
(3i)(4i)=

Back 46

(3i)(4i) =12 x i squared =12 x -1 = -12

Front 47

How do you calculate a high power or i? (Ex: i to the 99th power)

Back 47

Extract a portion of the exponent that is a multiple of 4 (96) and utilize the remaining (3) to calculate the result. i = -1

Front 48

What is -6 squared?

Back 48

-6 x 6 = -36

Front 49

What is (-6) squared?

Back 49

(-6) x (-6) = 36

Front 50

What is the result of any number with a square root of zero?

Back 50

1

Front 51

What is the base of a natural logarithm?

Back 51

2.71828...

Front 52

What lower case letter denotes the base of a natural logarithm?

Back 52

e

Front 53

What is the result of Log 100?

Back 53

2

Front 54

What is the result of ln 100?

Back 54

4.605

Front 55

How do you calculate the circumference of a circle?

Back 55

Circumference = Pi x diameter

Front 56

How do you find the length of the long side (hypotenuse or "c") of a triangle?

Back 56

a squared + b squared = c squared