2009 – 2015
Noetic Learning
Mathematics Contest
Grades 2 – 8
Sample Problems
Grade 2 Sample Problems
1) Boys and girls stood in a line. Paige was the 4th from one end and was 8th from the other
end. How many children were standing in the line?
Answer: ____________________ children
2) Dale has a bag of marbles. There are 20 green ones, 35 blues ones, 15 red ones and the
remaining 19 are black. If Dale lets Sally pick one marble out of the bag without looking, which
color marble is she likely to pick: a green one, a blue one, a red one, or a black one?
Answer: ____________________
3) How many letters are in the oval?
Answer: ____________________ letters
4) Each day since Julie arrived at Granny's Orchard, she picked 10 apples, ate 3 of them and
saved the rest. In total, how many apples had Julie saved by the end of the 4th day?
Answer: ____________________ apples
5) According to the scales, which of the following statements is correct?
a) y weighs 20 g
b) y weighs more than 20g
c) y weighs less than 20g
Answer: ____________________
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Grade 3 Sample Problems
1) Bill had 10 goldfish: 6 fantails and 4 pompoms.
Last night, 2 fantails each gave birth to 2
baby fish, and 1 pompom gave birth to 3 baby fish. How many goldfish does Bill have now?
Answer: ____________________ goldfish
2) How much larger is 162 when rounded to the nearest hundred than when rounded to the
nearest 10?
Answer: ____________________
3) How many 3-digit numbers can you make using digits 0, 2 and 9 if you have to use each
digit exactly once in each number?
Answer: ____________________ numbers
4) Jeff left home in March 1999 to tour the world. He returned exactly 40 months later. Which
month of the year did he return home?.
Answer: ____________________
5) How much does one apple weigh if both apples weigh the same and the banana weighs 100
grams?
Answer: ____________________g
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Grade 4 Sample Problems
1) How many 2-digit numbers are even?
Answer: ____________________
2) Daniel has 7 more stamps than Sherry. Together, they have 101 stamps. How many stamps
does Daniel have?
Answer: ____________________ stamps
3) When selecting 2 different numbers from the set {1, 3, 5, 7}, how many different sums are
possible?
Answer: ____________________
4) If today is Thursday October 15, what will be the date of Thanksgiving this year?
Thanksgiving is on the 4th Thursday of November.
Answer: ____________________
5) If the pattern continues, how many dots do we need for figure 4?
Answer: ____________________ dots
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Grade 5 Sample Problems
1) Jim invested $500 in a company’s stock. If his investment doubles in value every year for
each of the next 5 years, how much money will his investment be worth at the end of 5 years?
Answer: $ ____________________
2) Lucas is buying juice bottles for his soccer team. Juice bottles are sold by the carton.
If he
buys 3 cartons of juice bottles, he will be short 3 bottles. If he buys 4 cartons of juice bottles, he
will have 3 bottles extra. How many juice bottles are in each cart
Answer: ____________________ bottles
3) There are 18 students in Mrs. Hargis’s class. Spanish and French are the only two foreign
language classes available, and everyone has to take at least one foreign language class. Nine of
them are taking Spanish and eleven of them are taking French. How many of Mrs. Hargis’s
students are taking both Spanish and French?
Answer: ____________________ students
4) Amy and Vicki went to an orchard to pick apples. Vicki picked two more apples than half
of the apples Amy picked. Together they picked 98 apples. How many apples did Amy pick?
Answer: ____________________ apples
5) Different letters represent different digits. If “A” represents 2, what digit does "E"
represent?
Answer: ____________________
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Grade 6 Sample Problems
1) For any two whole numbers x and y, let x Δ y be defined by x Δ y = 3x – y2.
Therefore, 1 Δ 1 = 2 and 3 Δ 2 = 5. What is the value of (5 Δ 1) Δ 6?
Answer: _________________
2) How many rectangles of any size containing
are there in the following figure?
Answer: _________________ rectangles
3) Sixty-eight college basketball teams battled for the NCAA tournament championship
title in the year 2014. The losing team of each game was eliminated from the tournament.
What was the total number of games played in the 2014 NCAA tournament?
Answer: _________________ games
4) The product of the 3- digit number
and the 1-digit number
different letters represent different digits, what is the value of
is 3663. If
?
Answer: _________________
5) There is a pile of playing cards on the table. Mark takes one-fourth of the cards plus 3 more.
Then Mike takes one-third of the remaining cards plus 2 more. Then Joe takes one-half of the
remaining cards plus 1 more. Finally, Dan takes the remaining 9 cards. How many cards were on
the table at the beginning?
Answer: _________________ cards
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Grade 7 Sample Problems
1) Thirty-one people participated in a company picnic. People sat in groups of either 4 or 5.
How many groups were there?
Answer: __________ groups
2) George has a 10’ × 12’ rectangular garden. If he increases both the length and the width of
the garden by 10%, what is the percentage of increase in area?
Answer: __________ %
3) Mary and Nancy had a total of 42 crayons. After Mary gave 30% of her crayons to Nancy,
Nancy had twice as many as Mary. How many crayons did Mary have originally?
Answer: __________ crayons
4)2 In the following figure, the area of square ABPF is 25 in2 and the area of square PCDE is 144
in . What is the area of hexagon ABCDEF?
Answer: __________ in2
5) Peter received 10 points on a 10-question quiz.
If he received 5 points for each correct
answer and lost 3 points for each wrong or missing answer, how many questions did Peter answer
correctly?
Answer: __________ questions
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Grade 8 Sample Problems
1) The side of square B is 2 inches longer than the side of square A. The area of square B is 64
square feet greater than the area of square A. What is the area of square A?
Answer: __________
2) Four workers can harvest 30 gallons of apples in three hours. If every worker harvests apples
at the same rate, how long will it take five workers to harvest 75 gallons of apples?
Answer: __________ hours
3) Square ABCD has a side of 10 inches. Points E and F are on line segment CD. Point P is on
line segment AB. The area of triangle is PEF is 30% of the area of square ABCD. What is the
length of segment EF? (Note: The following figure is not drawn in scale.)
Answer: __________ inches
4) Daniel rode his bike from home to the library at a speed of 18 miles per hour. He took the
same route to ride back from the library. However, on the way home his speed was only 6 miles
per hour due to the wind. What was the average speed of his round trip?
Answer: __________ miles per hour
5) There are 18 students in Mrs. McLean’s preschool class. Some of them are 4 years old and
the rest are 5 years old. The sum of their ages is a multiple of 17. How many 5-year old students
are in Mrs. McLean’s class?
Answer: __________ students
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