2005 CEMC Gauss (Grade 7) Problems
Contents
Part A: Each correct answer is worth 5 points
Problem 1
The value of is
Problem 2
The value of is
Problem 3
Contestants on "Gauss Reality TV" are rated by an applause metre. In the diagram, the arrow for one of the contestants is pointing to a rating closest to:
Problem 4
Twelve million added to twelve thousand equals
Problem 5
The largest number in the set {} is
Problem 6
At a class party, each student randomly selects a wrapped prize from a bag. The prizes include books and calculators. There are prizes in the bag. Meghan is the first to choose a prize. If the probability of Meghan choosing a book for her prize is , how many books are in the bag?
Problem 7
Karen has just been chosen the new “Math Idol”. A total of votes were cast and Karen received of them. How many people voted for her?
Problem 8
In the diagram, what is the measure of in degrees?
Problem 9
A movie theatre has eleven rows of seats. The rows are numbered from to . Odd-numbered rows have seats and even-numbered rows have seats. How many seats are there in the theatre?
Problem 10
In relation to Smiths Falls, Ontario, the local time in St. John’s, Newfoundland, is minutes ahead, and the local time in Whitehorse, Yukon, is hours behind. When the local time in St. John’s is 5:36 p.m., the local time in Whitehorse is
1:06 p.m. 2:36 p.m. 4:06 p.m. 12:06 p.m. 10:06 p.m.
Part B: Each correct answer is worth 6 points
Problem 11
The temperature range on a given day is the difference between the daily high and the daily low temperatures. On the graph shown, which day has the greatest temperature range?
Problem 12
A bamboo plant grows at a rate of cm per day. On May 1st at noon it was tall. Approximately how tall, in metres, was it on May 8th at noon?
Problem 13
In the diagram, the length of is twice the length of . What is the area of the triangle ?
Problem 14
The numbers on opposite sides of a die total . What is the sum of the numbers on the unseen faces of the two dice shown?
Problem 15
In the diagram, the area of rectangle is . If , what is the area of quadrilateral ?
Problem 16
Nicholas is counting the sheep in a flock as they cross a road. The sheep begin to cross the road at 2:00 p.m. and cross at a constant rate of three sheep per minute. After counting sheep, Nicholas falls asleep. He wakes up an hour and a half later, at which point exactly half of the total flock has crossed the road since 2:00 p.m. How many sheep are there in the entire flock?
Problem 17
The symbol is evaluated as . If is evaluated as , what is the number that should be placed in the empty space?
Problem 18
A game is said to be fair if your chance of winning is equal to your chance of losing. How many of the following games, involving tossing a regular six-sided die, are fair?
You win if you roll a 2
You win if you roll an even number
You win if you roll a number less than 4
You win if you roll a number divisible by 3.
Problem 19
Chris and Pat are playing catch. Standing apart, Pat first throws the ball to Chris and then Chris throws the ball back to Pat. Next, standing apart, Pat throws to Chris and Chris throws back to Pat. After each pair of throws, Chris moves farther away from Pat. They stop playing when one of them misses the ball. If the game ends when the throw is missed, how far apart are they standing and who misses catching the ball?
Problem 20
While driving at , Sally’s car passes a hydro pole every four seconds. Which of the following is closest to the distance between two neighbouring hydro poles?
Part C: Each correct answer is worth 8 points
Problem 21
Emily was at a garage sale where the price of every item was reduced by of its current price every minutes. At 9:00 a.m., the price of a carpet was dollars. At 9:15 a.m., the price was reduced to dollars. As soon as the price of the carpet fell below dollars, Emily bought it. At what time did Emily buy the carpet?
9:45 a.m. 9:15 a.m. 9:30 a.m. 10:15 a.m. 10:00 a.m.
Problem 22
In a bin at the Gauss Grocery, the ratio of the number of apples to the number of oranges is , and the ratio of the number of oranges to the number of lemons is . What is the ratio of the number of apples to the number of lemons?
Problem 23
Using an equal-armed balance, if balances and balances , which of the following would not balance ?
Problem 24
On a circular track, Alphonse is at point and Beryl is diametrically opposite at point . Alphonse runs counterclockwise and Beryl runs clockwise. They run at constant, but different, speeds. After running for a while they notice that when they pass each other it is always at the same three places on the track. What is the ratio of their speeds?
Problem 25
How many different combinations of pennies, nickels, dimes and quarters use coins to total dollar?
See also
2005 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
Preceded by 2004 CEMC Gauss (Grade 7) |
Followed by 2006 CEMC Gauss (Grade 7) | |
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CEMC Gauss (Grade 7) |