Midterm 1

Question 1

What are Polyas 4 steps

Answer 1

1. Understand the problem- read it, pick out what you know, figure out what its asking
2. Devise a plan- draw diagram, look for patterns, guess & check, solve a simpler problem, work backwards, use variable
3. Carry out the plan
4. Look back- make sure your answer answered the question being asked, check your work, work backwards, evaluate your strategy
   - come up with a related problem

Question 2

Set definition

Answer 2

a group of objects, called elements

Question 3

what does A = B mean regarding sets

Answer 3

the sets are the same

Question 4

1-1 correspondance

Answer 4

each element in sat A can be matched with one, and only one element in set b

Question 5

subset

Answer 5

every element of A is also an element of B

Question 6

finite

Answer 6

can be counted with an end

Question 7

infinite

Answer 7

never ends

Question 8

union (U)

Answer 8

the set of elements that bring to A or B or Both

Question 9

Intersection

Answer 9

the elements common to A and B

Question 10

Complement

Answer 10

The elements of the universal set that aren’t in A

Question 11

Difference of sets

Answer 11

the set of all elects in A that are not in B

Question 12

Cartesian Product of sets

Answer 12

set of all ordered pairs made from elements in each

Question 13

N

Answer 13

the number of all ordered pairs made. Multiply the total number of elements in each set by each other

Question 14

Roman Numerals

Answer 14

I=1
V=5
X=10
L=50
C=100
D=500
M=1000
Can only subtract from 2 letters up the ladder (I,C,X)
4=IV, 9=1X, 99=XCIX, 40=XL, 90=XC, 400=CD, 900=CM

Question 15

Hindu-Arabic Number system

Answer 15

Ours- 0,1,2,3,4,5,6,7,8,9

Question 16

4 Properties of addition

Answer 16

1. Closure property- the sum of any 2 whole numbers is a whole number
2. Commutative property- a+b=b+a
3. Associative property- (a+b)+c=a(b+c)
4. Identify property- unique whole number such that a+0=0+a=a

Question 17

Closure Property (+)

Answer 17

the sum of any two whole numbers is a whole number

Question 18

Commutative Property (+)

Answer 18

a+b = b+a

Question 19

Associative Property (+)

Answer 19

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

Question 20

Identify Property (+)

Answer 20

There is a unique whole number (usually zero) such that a+0=0+a=a

Question 21

Addition of whole numbers

Answer 21

let a and b be any whole numbers. if A and B are disjoint sets with a=n(A) and b=n(B), then a+b=n(AUB)

Question 22

The Take away approach

Answer 22

let a & b be whole numbers and A & B are sets such that, a=n(A), B=n(B) then a-b=n(A-B)

Question 23

Missing addend approach

Answer 23

let a & b be any whole numbers. then a-b=c if and only if a=b+c

Question 24

2 Subtraction approaches:

Answer 24

The take away approach (If I had 5 cookies and Mum ate 2 how many do i have now?)
The Missing addend approach (I have 4 dollars but need 9 dollars to buy a sandwich how much more do i need?)

Question 25

Repeated addition approach (x)

Answer 25

axb=b+b+b+……b+b (a amount of times)

Question 26

Rectangular Array Approach (x)

Answer 26

axb is the number of elements in an array having a as rows and b as collums

Question 27

Cartesian Product Approach (x)

Answer 27

if a=n(A) and b=n(B) then axb=n(AxB) (tree diagram)

Question 28

3 Multiplication Approaches:

Answer 28

• Repeated addition approach
• Rectangular array approach
• Cartesian product approach

Question 29

Closure Property (x)

Answer 29

the product of two whole numbers is a whole number

Question 30

Commutative property (x)

Answer 30

ab = ba

Question 31

Associative property (x)

Answer 31

(ab)c = a(bc)

Question 32

Identity Property (x)

Answer 32

The number 1 is a unique whole number, 1xa = ax1 = a

Question 33

Distributive property of multiplication over addition

Answer 33

a(b+c) = ab + ac

Question 34

Property Zero (x)

Answer 34

ax0 = 0xa = 0

Question 35

Distributive property of multiplication over subtraction

Answer 35

a(b-c) = ab - ac

Question 36

7 Properties of Multiplication

Answer 36

1. Closure
2. Commutative
3. Associative
4. Identity
5. Distributive multiplication over addition
6. Distributive multiplication over subtraction
7. Zero

Question 37

Sharing Division

Answer 37

make a specified number of groups and share items between them. Ex. 20 kids, 4 teams, how many in each group?

Question 38

Measurement Division

Answer 38

make groups of a specified size and see how many groups you get. ex. 20 kids, 4 per team, how many groups?

Question 39

Division missing factor approach

Answer 39

if a and b are whole numbers and b does not = 0, then a divided by b =c if and only if a = b x c

Question 40

Dividend

Answer 40

a (being divided)

Question 41

Divisor

Answer 41

b (doing the dividing)

Question 42

quotient/missing factor

Answer 42

c

Question 43

Property of Zero (division)

Answer 43

if a does not = 0, then 0 divided by a = 0

Question 44

The division algorithm

Answer 44

if a and b are any whole numbers with b not = 0, then there exist unique whole numbers q (quotient) and r (remainder) such that a = bxq + r, where 0 is < or = to r which is < b

Question 45

Division Repeated-substraction approach

Answer 45

keep repeating the division number how ever many times possible until you’re left with a remainder

Question 46

Transitive Property of less than

Answer 46

if a<b></b>

Question 47

Addition property of less than

Answer 47

if a<b></b>

Question 48

Multiplication property of less than

Answer 48

if a<b></b>

Question 49

3 properties of less than

Answer 49

Addition, Multiplication, Transitive

Question 50

Compatible (friendly) numbers

Answer 50

can reorder, look for numbers that add together to make ‘easy’ numbers (10’s)

Question 51

Additive compensation

Answer 51

borrow from one number to give to another to make the addition easier

Question 52

equal additions method

Answer 52

increase each number by the same amount to make subtraction easier

Question 53

multiplicative compensation

Answer 53

regroup the multiplication to get easier numbers