Final Question

1
Mathemania for Teachers!
Problem Solving
Sets and Functions
Numeration Systems
Number Theory
Fractions
5
5
5
5
5
10
10
10
10
10
25
25
25
25
25
50
50
50
50
50
100
100
100
100
100
Final Question
2
Problem Solving
3
Problem Solving 5 Points
True or False Problem Solving for some may be
an exercise for others .
True
4
Problem Solving 10 Points
Find a pattern in the following sequence and
write the next term 3, 5, 11, 21, 35
53
5
Problem Solving 25 Points
What is the fifth number in the set of triangular
numbers?
15
6
Problem Solving 50 Points
There are 78 people around a table. Each person
shakes hands with the person to his or her
immediate right and left. How many handshakes
take place? Write an algebraic expression for the
number of handshakes.
78 handshakes and n handshakes.
7
Problem Solving 100 Points
Two men and two boys want to cross a river, using
a small canoe. The canoe can carry two boys or
one man. What is the least number of times the
canoe must cross the river to get everyone to the
other side?
9 crossings
8
Sets and Functions
9
Sets and Functions 5 Points
Given the universal set U 0, 1, 2, 3, 4, 5,
6, and sets A 2, 4, 6 and B 1, 2, 3, 4
determine the set A ? B and A? B.
A ? B 1,2,3,4,6 and A ? B 2, 4
10
Sets and Functions 10 Points
Sketch a Venn diagram to illustrate the following
set A?? B?
11
Sets and Functions 25 Points
Consider the function that relates the length x
of each line segment to f(x), which is half of
the length of the segment. Determine the range
value f(x) for each of the following domain
values 1, 2, 3, 4, and 5.
For the domain values 1, 2, 3, 4, 5, the
corresponding range values are .5, 1, 1.5, 2, and
2.5.
12
Sets and Functions 50 Points
In a certain town there live 150 men. 85 are
married, 70 have a telephone, 75 own a car, 55
are married and have a telephone, 35 have a
telephone and a car, 40 are married and have a
car, and 30 are married, have a car, and have a
telephone. How many men are single and do not
have either a car or a telephone?
20 men
13
Sets and Functions 100 Points
Which of the following sets of numbers is closed
under division? Natural (counting) numbers,
Whole numbers, Fractions, Even numbers, Odd
numbers or all multiples of 5.
Just the set of all Fractions.
14
Numeration Systems
15
Numeration Systems 5 Points
Round 6,281,497 to the nearest hundred thousand.
6,300,000
16
Numeration Systems 10 Points
Use equal products to find a replacement for
each number that is more convenient for mental
calculation. Show the new numbers and determine
the answer for 25 x 28.
25 x 4 x 7 100 x 7 700
17
Numeration Systems 25 Points
True or False The set of whole numbers is
closed for subtraction.
False
18
Numeration Systems 50 Points
Calculate 4325 x 225
21,1045
19
Numeration Systems 100 Points
If the number 652 is expanded and written in
positional numeration, what is the digit in the
units place?
6 is the digit in the units place.
20
Number Theory
21
Number Theory 5 Points
Determine if the following is true or
false 3?48,025
False
22
Number Theory 10 Points
Is 371 a prime number?
No-it is a composite number.
23
Number Theory 25 Points
Find the GCF (280, 165) and the LCM(12, 210) .
GCF is 5 and LCM is 420
24
Number Theory 50 Points
Shane has 72 inches of copper wire and 42 inches
of steel wire. He wants to cut them into pieces,
but wants all the pieces to be the same length.
What is the largest length he can cut these wires
into so that each piece is the same length? How
many pieces of wire will he have?
6 inches and he will have 19 pieces of wire (12
copper and 7 steel).
25
Number Theory 100 Points
Suppose that Douglas the Decimal Dictator changed
our calendar so that there were now ten days in a
week (Onesday, Twosday, Threesday, Foursday,
etc.) Also, since Douglas was born on February
29th, he declares that every year is a leap year.
Furthermore, suppose that January 1st was a
Onesday. How many years will it take for January
1st to land on a Onesday again? Assume that
there are 366 days in a year. ?
5 years, or 183 weeks or 1830 days
26
Integers/Fractions
27
Integers/Fractions 5 Points
True or False? The set of fractions is closed for
multiplication?
True
28
Integers/Fractions 10 Points
Use equal quotients to calculate the answer to
800 ? 16.
800 ? 16 200 ? 4 100 ? 2 50
29
Integers/Fractions 25 Points
Use Fraction Bars to illustrate 2/3 X 1/5 .
2/15
30
Integers/Fractions 50 Points
A schools new pump can fill the swimming pool in
5 hours, the old pump takes 10 hours. How long
will it take to fill the pool if both pumps are
used together?
3 1/3 hours
31
Integers/Fractions 100 Points
Paula removed 4/5 of the disks from a new box of
computer disks, and Sam removed 7/10 of the disks
that remained in the box. If Sam removed 28
disks from the box, how many disks did Paula
remove?
160 disks not that anyone uses computer disks
anymore
32
Final Question
What are Polyas 4 steps to problem solving?

• Understand the problem
• Devise a plan
• Carry out the plan
• Look back