midterm

Question 1

Polya’s Four Principles of Problem Solving

Answer 1

Understand the problem, Devise a Plan, Carry out the Plan, and Look Back.

Question 2

Fibonacci Sequence

Answer 2

A sequence where you start with one and one ad add any two consecutive numbers to obtain the next number. For example, the sequence starts with 1,1,2,3,5,8,13,and 21…. The next number would be found by adding 21 + 13 to get 34.

Question 3

This is an arithmetic progression.

Answer 3

The arithmetic progression is defined by the property that every term is a constant difference greater than or less than its predecessor by the same amount. For example, if you took the sequence 2,5,8,11,…, the constant difference is three.

Question 4

The intersection of two sets A and B is the set of elements

Answer 4

common to both A and B. A∩B

Question 5

The union of two sets A and B is

Answer 5

the set of all elements that are in A or B. A∪B

Question 6

A nominal number is a sequence of digits used

Answer 6

as a name or label like a telephone number.

Question 7

An ordinal number is a number that describes

Answer 7

where an object is in an ordered sequence, like first place, second place, etc.

Question 8

A cardinal number is

Answer 8

the number of elements in the set, like 1500 runners in a race.

Question 9

The sum is the answer when two numbers are added.

Answer 9

The expressions which are added are called the addends.

Question 10

Commutative property of addition

Answer 10

Changing the order of addends does not change the sum. For example, 4 + 2 = 2 + 44+2=2+44, plus, 2, equals, 2, plus, 4.

Question 11

Associative property of addition:

Answer 11

Changing the grouping of addends does not change the sum. For example, (2 + 3) + 4 = 2 + (3 + 4)(2+3)+4=2+(3+4)left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.

Question 12

Identity property of addition:

Answer 12

The sum of 000 and any number is that number. For example, 0 + 4 = 40+4=40, plus, 4, equals, 4.

Question 13

closure property

Answer 13

If a and b are any two whole numbers, than a + b is a unique whole number

Question 14

In the equation a x b = c,

Answer 14

a and b are called factors, and c is the product.

Question 15

Commutative property:

Answer 15

When two numbers are multiplied together, the product is the same regardless of the order of the multiplicands. For example 4 * 2 = 2 * 4

Question 16

Associative Property:

Answer 16

When three or more numbers are multiplied, the product is the same regardless of the grouping of the factors. For example (2 * 3) * 4 = 2 * (3 * 4)

Question 17

Multiplicative Identity Property:

Answer 17

The product of any number and one is that number. For example 5 * 1 = 5.

Question 18

Distributive property:

Answer 18

The sum of two numbers times a third number is equal to the sum of each addend times the third number. For example 4 * (6 + 3) = 46 + 43

Question 19

multiplication over division

Answer 19

multiply first

Question 20

A binomial is

Answer 20

an expression with two terms.

Question 21

In the expression , a is the dividend and b is the divisor.

Answer 21

If , c is called the quotient.

Question 22

A number divided BY zero

Answer 22

is undefined.

Question 23

Zero-Exponent Rule:

Answer 23

a0 = 1, this says that anything raised to the zero power is 1.

Question 24

Power Rule (Powers to Powers):

Answer 24

(am)n = amn, this says that to raise a power to a power you need to multiply the exponents.

Question 25

Product Rule: am ∙ an = am + n,

Answer 25

this says that to multiply two exponents with the same base, you keep the base and add the powers.

Question 26

Quotient Rule: Quotient Rule, this says that to divide two exponents with the same base,

Answer 26

you keep the base and subtract the powers.

Question 27

Memorize Roman numerals

Answer 27

DO IT

Question 28

know place values

Answer 28

one, tens, hundreds, ect

Question 29

A number is even

Answer 29

when it is divisible by 2.

Question 30

A prime number is a number that possesses exactly two factors:

Answer 30

one and itself.

Question 31

A composite number is a number

Answer 31

that possesses more than two factors.

Question 32

The number 1 is

Answer 32

neither prime nor composite.

Question 33

The greatest number that divides both a and b is called

Answer 33

the greatest common factor of a and b.

Question 34

The smallest number that is a multiple of both a and b is called

Answer 34

the least common multiple of a and b.

Question 35

divisibility 2

Answer 35

The last digit is even (0,2,4,6,8)

Question 36

divisibility 3

Answer 36

The sum of the digits is divisible by 3

Question 37

divisibility 4

Answer 37

The last 2 digits are divisible by 4

Question 38

dvisibility 5

Answer 38

The last digit is 0 or 5

Question 39

divisibility 6

Answer 39

is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)

Question 40

divisibility 8

Answer 40

The last three digits are divisible by 8

Question 41

divisibility 9

Answer 41

The sum of the digits is divisible by 9

Question 42

divisibility 10

Answer 42

The number ends in 0