1
Elizabeth noticed a candy
machine in a store with this sign:
“One penny per turn.” Elizabeth
had 5 pennies in her pocket. She
put 1 penny into the machine, and
out popped 1 gumball. She put in a
2nd penny; 4 gum balls popped out.
With the 3rd penny, 7 gumballs
came out. With her 4th penny, 10
gumballs fell out. With her last
penny, Elizabeth received 13
gumballs. If she had 3 more
pennies, how many gumballs
would she have received with her
6th, 7th, and 8th pennies? If the
pattern continued, how many
gumballs would she have after
using 16 pennies?
2
Elizabeth’s sister, Cheryl, had 5
pennies in her pocket. She put 1 penny
into the candy machine, and out popped
1 gumball. She put in a 2nd penny, and 4
gumballs popped out. With the 3rd
penny, 10 gumballs came out. Her 4th
penny resulted in 19 gumballs. With her
last penny, Cheryl received 31 gumballs.
If she had 3 more pennies, how many
gumballs would her 6th, 7th, and 8th
pennies have garnered.
3 The
pattern
ABBCCCDDDDEEEEE . . .
continuously repeats such
that after the final Z, the
letters ABBCCCDDDDEEEEE . . .
begin again. What will be the
3000th letter in the pattern?
4 Find
1/3, 1, 3, 9, 27, 81, 243,
____, ____
7 Here
are three Sierpinski
triangles. Draw the next two
triangles in the sequence.
the next three
numbers in the special
sequence of numbers.
3, 1, 4, 1, 5, 9, 2, 6, 5,
___, ___, ___
5 If
the consecutive odd
counting numbers are arranged
as shown, what will be the
middle (center) number in the
11th row?
6 Determine
the next two
values in the following
sequence:
8 For
each triangle in the
sequence in the previous
problem, identify the
smallest triangle and count
the number of these triangles
that occur. Look for a
pattern. How many of the
smallest-sized triangles
would you need for the sixth
triangle in the sequence? The
tenth triangle?
9
If the heart pattern
continues, how many hearts
will be found on day 12? How
many hearts will be found on
day n? Explain your
reasoning.
10 A
total of 84 quarters
are lined up side by side on
a table.
You replace every second
quarter with a dime. After
you have completed this task,
you replace every third coin
with a nickel.
Once this is completed, you
replace every fourth coin
with a penny. What is the
total value of the final 84
coins on the table?
11
How many multiples of 4
from 1 through 1000 do not
contain any of the digits 6,
7, 8, 9, or 0?
12
Bohdan and Marie are
staining their deck. The deck
is 22'×11' and requires two
coats of stain. If a gallon
of stain covers 400 square
feet, how many gallons will
they need? The stain costs
$19.99 a gallon, two large
brushes cost $7.99 each, two
trim brushes cost $4.39 each,
two pairs of gloves cost
$2.29 each, and paint thinner
is $3.09. How much will the
project cost altogether?
drinks are served per year in
Seattle?
15
What is the greatest
prime number that can be
represented as both the sum
of 2 prime numbers and as the
difference of 2 prime
numbers?
13
At Patrick's Diner, the
appetizer special is a basket
of fried mushrooms, onion
rings, and mozzarella sticks.
The cook has fried 24
mozzarella sticks, 30 onion
rings, and 42 mushrooms to
exactly fill several orders.
What is the largest number of
orders of appetizer baskets
that the cook can prepare?
Each basket must contain the
same number of each
individual kind of appetizer.
14
Seattle has many coffee
drinkers. Recently, the city
council proposed a 10¢ tax on
each fancy coffee drink
served in the city, and
estimated that the tax would
raise $7 million per year.
About how many fancy coffee
16
Susie is locked out of
her house and can only
remember a few numbers of the
combination to the hidden
lockbox containing a key. She
knows that it follows a
certain mathematical pattern.
There are 7 numbers in the
code, and she knows that the
first 4 numbers are 2, 5, 11,
and 23. She can also remember
the last number, which is
191. Find the missing
numbers, and explain the rule
you found.
17
The year credit cards
were first used was 10 years
before President Kennedy took
office. The sum of the digits
in the year is 16 and their
product is 45. What year was
it?
18
The number 1961 has
rotational symmetry, because
the number looks the same
when rotated 180 degrees.
Find the next greatest number
that also has this unique
feature.
20
Chris and his
friends are going to a
concert 176 miles from
home. Chris departs at
4:00 p.m. and travels at
an average speed of 55
mph. His friends depart
at 4:30 p.m. and drive an
average rate of 64 mph.
Who will arrive at the
concert first? At what
time will each car
arrive?
19
A mathematics teacher
collects old books. One day,
a student asked him how many
old math books he has. He
replied, “If I divide the
books into two unequal whole
numbers, then 64 times the
difference between the two
numbers equals the difference
between the squares of the
two numbers.” How many old
math books does the teacher
have?
21
John is planning a
trip to a theme park for
his birthday. His
parents have asked him to
consider cost when making
his choice. The first
park, Adventure World,
charges $15.00 admission
plus an additional $1.50
for every roller-coaster
ride. The second park,
Grand Amazon, charges
$5.00 admission plus an
additional $2.25 for
every roller coaster
ride. If John plans to
ride the roller coaster
16 times, which park will
be less expensive? How
many times will John need
to ride the roller
coaster for the other
theme park to be less
expensive?
22
If two U.S.
pennies have the same
weight as one U.S.
quarter, and 4 pounds of
quarters are worth $100,
then how much is 4 pounds
of pennies worth?
23
The Math Team in
Quaker Valley traveled to
Harrisburg for a math
competition. The bus
averaged 40 mph on the
drive from Sewickley to
Harrisburg but averaged
60 mph during the return
trip. What was the
average speed of the bus
the entire trip?
24
Brick masons are
building a decorative
stone wall at your
school. The stone blocks
will be stacked on top of
one another. The stones
are placed so that each
row of stones has 1 fewer
stone than the row below
it. If the masons are
going to use 105 stones
and want only 1 stone
block on top of the wall,
how many stones will need
to be in the bottom row?
25
Sam can run 50
meters in 8 seconds.
Lacey can run 20 meters
in 5 seconds If they
keep up this pace, how
much longer (in seconds)
would it take Lacey to
run 2 kilometers compared
with Sam? Provide your
solution in seconds.
26
Using this pattern of circles,
draw stage 4. How many circles
will be in stage 10? How many
circles will be in stage 20?
markers, how many total markers
are in Greg’s bag? If Greg has
another bag with 28 red markers,
how many yellow markers are in
his bag?
29 Rick’s box of cereal contains
27 Justine has a bag at school
with only green, yellow, and red
markers. She has 2 green, 7 yellow,
and 4 red markers Marcie brings a
bag to school containing 117
markers in these same colors. If
Marcie’s bag contains the same
proportion of green to yellow to
red markers as Justine’s bag, how
many of each color are in her bag?
28
Sean has a bag at school
with 2 green, 7 yellow, and 4 red
markers. Greg also brings a bag to
school that contains markers in
these colors. If Greg’s bag contains
the same proportion of green to
yellow to red markers as Sean’s
bag, and Greg’s bag has 16 green
blue and purple marshmallows. He
pours some cereal and sees 10 blue
and 8 purple marshmallows in his
bowl. The next morning, he pours
himself a much larger bowl of
cereal. If the new bowl has 108
marshmallows that are in the same
ratio of blue to purple, how many
blue and how many purple
marshmallows are in the larger
bowl?
30 Newton Middle School’s sixth
grade has 175 students. One-fifth
of the sixth graders will receive
free tickets to a Detroit Piston’s
basketball game. Euler Middle
School has 585 sixth graders and
will receive the exact same number
of tickets as Newton Middle School.
How many tickets will be given
away to Euler’s sixth grade? How
many tickets should be given out at
Euler Middle School for the lottery
to be fair?
31 Ryan and Ashley are math
tutors. Ryan charges $20 for the
initial tutoring consultation to
assess the learner and $8 per hour
for tutoring. Ashley does not
charge for the initial consultation
but charges $10 per hour for
tutoring. Mrs. Hernandez is looking
for a math tutor for 4 weeks at 2
hours per week for her son. Which
tutor will be less expensive? Who
will be less expensive if she asks
for tutoring for 4 hours per week
for 4 weeks?