Grade Eight Problems
Be a math detective!
1)
The Adams family was going to buy a car for $5800. The car dealer
offered the Adams family two options for buying the car. They could pay
the full amount in cash, or they could pay $1000.00 down and $230.00 a
month for 24 months on the installment plan. How much more would they pay
for the car on the installment plan?
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2)
Lisa Lilly was the best runner in the eighth grade. One day she
ran 100m in 40 seconds, 200m in 1 minute and 10 seconds, and 200m over
low hurdles in one and a half minutes. How many more seconds did it take
her to run the 200m over low hurdles then it did to run the 200m dash?
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3)
Three students have to write a make up test. Mark scored 24/60 on
his first test and 32/40 on his make up test. Jake scored 35/70 on his
first test and 54/60 on his makeup test. Marilyn scored 27/90 on her first
test and 45/50 on her second test.
A) Which student improved the most and by what percentage?
B) If the teacher gives each student a final grade using 70%
of the makeup test mark and 30% of the first test mark, what mark would
each student receive? Who did the best overall?
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4)
George, Sam, Andrew and Brandon each had four dates to four different
Parish Center Dances with four different girls, named Cher, Connie, Melissa
and Kendra. On the second date, George dated Connie and Brandan dated Kendra.
On the third date Andrew went out with Melissa and Sam went out with Connie.
Melissa went out with George and Cher went out with Sam on the fourth date.
What couples went out together on the first date if no pairs went out more
than once?
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5)
A large piece of construction paper is .01mm thick. It is cut in
half and one piece is placed on the other to make a pile. These are cut
in half and all four pieces are placed in a pile. These four are cut in
half and placed in a pile, and the process is continued. After the pieces
have been cut and piled for the tenth time, what is the height of the pile
in cm.
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6)
What is the sum of all the digits in the sequence 1, 2, 3, 4, 5,
6, 7,...99, 100?
NOTE: (Sum of the digits, not the numbers!)
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7)
Silver's Cleaners decided to raise the price of dry cleaning a sports
coat from $4.00 to $5.00. The same percentage increase was applied to dry
cleaning a jacket. The old cost of dry cleaning a jacket was $10.00. What
is the new cost of dry cleaning a jacket?
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8)
A Christmas gift is tied
with ribbon as shown. The bow requires 47cm of ribbon. What is the total
length of the ribbon in metres?
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9)
Four strips of paneling 40 cm long and 4cm wide are arranged to
form a square. What is the area of the inner square in cm^{2}?
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10)
In the following diagram of the front view of
the Great Pyramid, the measure of the angle PRQ is 120 degrees, and the
measure of the angle PST is 110 degrees. What is the measure of the angle
RPS in degrees?
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11)
Mr. MacDonald recorded the test marks for his eighth grade class
of 25 students. He used the marks recorded to calculate the average to
be 72. Sandra's mark of 86 was incorrectly marked as 36. What was the correct
average for the test?
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12)
Chip said to Dale "If you give me one acorn, then we will have an
equal number of acorns." Dale replied with delight "If you give me one
acorn, then I will have double the number you have!" What was the total
number of acorns they had in their tree? How many did Chip have and how
many did Dale have?
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13)
Bart Simpson decided to make a graph of his weekly earning of $120.00
from his paper route. To make the size of each sector proportional to the
amount distributed what does the angle x in degrees have to be?
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14)
Jane was walking the long way home from school. She started walking
East. She walked 3 km East when she met a dog. She ran back to the school
and decided to take the alternative route. So she walked North 4 km to
her home. If she had walked straight home from where she met the dog, how
far would it have been to her home?
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15)
The Gillis's house has a pool with the shape as shown. They want
to make a cover for it for the harsh winter. How much to the nearest cent
are they going to have to spend on material if it costs $5.00/m^{2}.
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16)
Lisa Simpson was in her math class. She was told to make a figure
with four thumbtacks, an elastic band and a piece of wood. She made the
following figure. Her math teacher measured some of the sides of her figure
and told Lisa to find the length of the side LM in mm. Can you help her?
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17)
Batman must solve the following problem to escape the Riddler. The
midpoints of the sides of a square are joined as shown. A fraction of
the original square is shaded. What is the fraction? Can you help him?
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18)
Matthew is at a zoo. He takes a picture of a onemetre snake beside
a brick wall. When he developed his pictures, the onemetre snake is 2cm
long and the wall is 4.5cm high. What was the actual height of the brick
wall in cm.
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19)
Joe's rich uncle gave him a looney on his first birthday. On each
birthday after that he doubled his previous gift. By the day after Joe's
eight birthday, what was the total amount that his uncle had given him?
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20)
Ms. Smith, Ms. Gracia, and Ms. O'Leary all teach at St. Andrew Junior
High School. One of the women is a mathematics teacher, one an art teacher
and one science teacher. The art teacher , an only child, has taught the
least number of years. Ms. Garcia, who married Ms. Smith's brother, has
taught more years than the mathematics teacher. Name the subject each woman
teaches.
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21)
Jim has three times as many comic books as Charles. Charles has
twothirds as many comic books as Bob. Bob has 27 comic books. How many
comic books does Jim have.
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22)
Friendly's Clothing Store bought handkerchiefs, six for $10, and
sold them 4 for $10. They made $60 profit. How many handkerchiefs did they
sell?
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23)
You, in your new red Porsche, decide to make a 160km trip to Carolina
Beach, travelling at 80km/hr. You make the return trip travelling at a
rate of 48km/hr. What was your average speed for the entire trip?
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24)
The Oland Center gym has 2kg and 5kg disks for weight lifting. Due
to their budget this year they only have fourteen disks in all. The total
weight of the 2kg disks is the same as the total weight of the 5kg disks.
What is the total weight of all the disks?
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25)
Bugs Bunny has three carrots of lengths 10cm, 12cm and 15cm. How
can he use these carrots to mark off a length of 17cm?
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26)
Who am I???
The names of my mother, my father, my brother, my sister and me in
no particular order are Sandy, Sharon, Pat, Jennifer and Connie

Pat is younger than I am.

I am older than Connie.

Sharon is younger than Jennifer.
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27)
28)
Bob is reading a 445 page book. He has already read 157 pages. If
he reads 24 pages a day, how long will it take him to finish the book?
b) Bob read 157 pages of a 445 page book. He finished the rest in
9 days. How many pages did he average each day while completing the book?
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29)
Pioneer Video is giving away a free movie to anyone who can solve
this puzzle. Place the numbers one to nine in the squares so that none
of the rows, columns or diagonals have the same sum.
 
++
 
++
 
Olivia won a free movie, what was her solution?
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30)
Homer Simpson entered a pie eating contest at the country fair.
Homer was determined to win and went into training for 6 days. Each day
he ate 4 more pies than the day before. Homer ate 150 pies while in training.
How many pies did he eat each day?
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31)
Belgium Cheese costs $1.70 for 1/2 kilograms. How much will 2 and
1/2 kilograms of cheese cost?
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32)
The area of one side of the box is 120cm^{2}. The area of
another side of the box is 72 cm^{2}. The area of the top of the
box is 60 cm^{2}. What is the volume of the box?
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33)
Yosemite Sam built a square fence using 48 posts which enclosed
a square field. He placed the posts 5 metres apart. What is the area of
the field bounded by the fence?
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34)
Every positive integer can be expressed as the sum of four or fewer
squared numbers (NOTE: you can use the same integer more than once)
Examples:
5 = 1 * 1 + 2 * 2
101 = 4 * 4 + 6 * 6 + 7 * 7
170 = 2 * 2 + 6 * 6 + 7 * 7 + 9 * 9
Try to write 83 as the sum of three square numbers.
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35)
The Canadian record for the most consecutive situps is 17,000 in
7 hours and 27 minutes.
At a rate of 40 situps per minute, how many hours and minutes would
it take to tie the record. Is this rate better than the Canadian record?
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36)
On an algebra test, I had seven times as many correct answers as
incorrect ones. There were 120 items on the test, how many did I get right?
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37)
If I pile grapefruit in a pyramid with 1 grapefruit in the first
layer, 4 in the second layer (from the top), 9 in the third layer, and
16 in the fourth layer, how many grapefruit will I need to make a pile
with 10 layers?
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38)
BigBird wants to make a picture frame for his picture of Elmo.
He is given the piece of plywood shown. He wants to make it in a shape
(the shaded area). In order to do so, he must connect all the midpoints
of the sides of a rectangle. What is the area of the piece of wood he will
be using for the picture frame? What is the perimeter of the inside of
frame?
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39)
The length of a rectangle is four times as long as its width. The
area of the rectangle is 100 metres squared. What are the dimensions of
the rectangle?
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40)
On a flight from Sydney, Nova Scotia to Saskatoon, Sask. the plane
averaged 760km/hr. On the return trip from Saskatoon to Sydney, the same
plane averaged 904km/hr. The distance from Sydney to Saskatoon is approximately
4112km. How much longer was the trip West than the trip East? How long
was each flight in minutes?
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41)
What's the number I'm thinking of? It is greater than 44 squared
and less than 45 squared. 5 squared is one of its factors, and it is a
multiple of 13.
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42)
There are three circles:

A = the largest

B = the middle sized one

C = the smallest
Circle A has a diameter of 20cm. The smaller circles are drawn so
that the radius of Circle A is the diameter of Circle B, and the radius
of circle B is the diameter of Circle C. What is the area of circle C?
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43)
44)
The Earth is about 1.49*10^{8} kilometres from the sun and
about 3.84*10^{5} km away from the moon. The Distance from the
Earth to the sun is about how many times as great as the distance from
the Earth to the moon?
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45)
Charlotte and Angie went on a vacation to Surrey B.C. together.
They recorded their expenses and decided to share them equally at the end
of the trip. Given the data below, how much does Angie owe Charlotte?
Charlotte Paid: Angie Paid:
_________________________________________________________
Food: $54.77
Gas: $38.25
Lodging: $78.20
Entertainment: $39.50
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46)
My father is four times as old as me. In 20 years, he will be only
twice as old as me. How old is my father and how old am I?
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47)
1/2 + 1/2^{2} = 3/4
1/2 + 1/2^{2} + 1/2^{3} = 7/8
1/2 + 1/2^{2} +1/2^{3} +1/2^{4} = 15/16
a) What is :
1/2 + 1/2^{2} + 1/2^{3} + 1/2^{4} + 1/2^{5} + 1/2^{6} + 1/2^{7} + 1/2^{8} = ???
b) What is the pattern?
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48)
If Brandon walks 2.5km in 12 minutes, how far can he walk in half
an hour (in meters at the same rate)?
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49)
When Malcolm was visiting his Grandpa's farm, he saw that the farm
only raised hens and hogs. Malcolm counted 38 heads and 100 feet in the
barnyard. How many hens and how many hogs did his grandpa have in the barnyard?
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50)
Four men were shipwrecked on an island. Having no food, they went
to work gathering pineapples. After gathering pineapples, they were tired
and all fell asleep. After another while, one of the men awoke and was
very hungry so he ate 1/3 of the pineapples  more than his proper share.
He then went back to sleep. The second man awoke and being hungry, ate
1/3 of the remaining pineapples and went back to sleep. The third man did
the same. When the fourth man awoke, he took only his rightful share of
the remaining pineapples. Then there were 6 pineapples left. How many pineapples
did the men gather?
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51)
Find the average rainfall in Vancouver in the year 1995. Round your
answer to the nearest tenth.
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