Math 210 Exam 1

Express a given number in "expanded form" 65,984

6 x 10^4 5 x 10^3 9 x 10^2 8 x 10 4 x 1= 65,984 in Expanded Form

Def: Equivalent Sets

A and B are called elements denoted A *-*B IFF there exists a one-to-one correspondences between the two sets.

Minuend

A number from which another number is subtracted.

Dividend

A number that is divided by another number.

Explain why our base-10 system is called base-10

All numerals are constructed from 10 digits- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Describe the empty set

An empty set is how you describe a set that is empty. For example when there is no intersection between two sets. It is written as { }= 0/

Are these sets equal?

A{1,2,3} B{1,2,3} They are equal because all of the elements are in Set B are in Set A, and all elements in Set A are in Set B.

Are these sets equivalent?

A{1,2,3} B{d,e,f} They are equivalent because there is one-to-one correspondence between the two sets

Arithmetic Ratio 11, 13

Find the common difference 3, 5, 7, 9...

Geometric Sequence ...32, 64

Find the ratio 2, 4, 8, 16...

Use the definition of "Less Than" to show that one number is less than another

If a number is less than a number you should be able to add a number to get the bigger number 3<5 therefore 3+2=5

Def: Equal sets

Let A and B be two sets A and B are called equal IFF every element of A is in and every element of B is in A

Remainder

The amount left over when one number is divided by another.

Determine and describe how to find the intersection of two sets

The intersection of two sets A and B, denotes AnB is the set of all elements that are in both A and B A{2, 4, 6, 8, 10} B {2, 3, 5, 7} AnB{2}

Determine and describe how to find the union of two sets

The union of two sets A and B, denotes AUB is the set of all elements that are in A, in B or in B A{2, 4, 6, 8, 10} B{2, 3, 5, 7} AUB{2, 3, 4, 6, 7, 8, 10}

Compute the number subsets of a given set

To compute the subsets in a given set you need to take 2 and raise it to how ever many elements are in the set EX: A{1,2,3,4,5,6}=2^6=64

Four Step Process

Understand the problem, Devise a plan, Carry out the plan, Looking Back

How to find the number of one-to-one correspondences between two equivalent sets

You line them up vertically and if you can math them up one to one with no left out or left over, them your sets are equivalent

Distributive Property of Multiplication over Addition

a (b + c) = a x b + a x c

Distributive Property of Multiplication over Subtraction

a (b - c) = a x b - a x c

Identity Property of Addition

a + 0 = a

Commutative Property of Addition

a + b = b + a

Factor

a number that is multiplied by another number to find a product

Arithmetic Sequence

a sequence in which each term is found by adding the same number to the previous term

Multiplication Property of Zero

a x 0 = 0

Identity Property of Multiplication

a x 1 = a

Step Four: Looking Back

a. Check results b. Does the answer make sense c. See if there is an easier method to find the solution d. Can method be used for other problems

Step Three: Carry Out the Plan

a. Implement plan from Step two b. Use correct math language and notation c. Make certain to check the logic for each step

Step Two: Devise a Plan

a. Is there a pattern b. Have we done similar problems c. Can we solve an easier similar problem d. Will a Picture or Table help e. Is it possible to work backwards f. Guess and check g. Write some equations

Step One: Understand the Problem

a. What information do we know b. What are the unknowns c. What are we looking for

Commutative Property of Multiplication

ab = ba

Geometric Sequence

is a sequence where each term after the first is otained by multiplying the previous term y a fixed number which is called the ratio

Face Value Def in Base-10 numeration system

is the actual value of a digit in a number

Place Value Def in Base-10 numeration system

is the value represented by a digit in a number according to its position in the number based on powers of 10

Addends

numbers that are added together

Describe how to find the sum of the first 100 natural numbers

sn = n/2(a + l) s100 = 100/2(1 + 100) = 50(101) = 5050.

Quotient

the answer to a division problem

Product

the answer to a multiplication problem

Subtrahend

the number being subtracted

Divisor

the number you divide by

Associative Property of Addition

(a + b) + c = a + (b + c)

Associative Property of Multiplication

(ab)c = a(bc)

The Sequence of triangular number

1, 3, 6, 10

The Sequence of Perfect Squares

1, 4, 9, 16

Fibonacci Sequence add each other number together

1,1,2,3,5,8,13,21,34