1999 CEMC Gauss (Grade 7) Problems
Contents
[hide]Part A: Each correct answer is worth 5 points
Problem 1
equals
Problem 2
The integer is exactly divisible by
Problem 3
Susan wants to place kg of sugar in small bags. If each bag holds
kg, how many bags are needed?
Problem 4
is equal to
Problem 5
Which one of the following gives an odd integer?
Problem 6
In ,
. What is the sum, in degrees, of the other two angles?
Problem 7
If the numbers, ,
, and
are arranged from smallest to largest, the correct order is
Problem 8
The average of ,
,
,
, and
is
7
Problem 9
André is hiking on the paths shown in the map. He is planning to visit sites A to M in alphabetical order. He can never retrace his steps and he must proceed directly from one site to the next. What is the largest number of labelled points he can visit before going out of alphabetical order?
Problem 10
In the diagram, line segments meet at as shown. If the short line segments are each
cm long, what is the area of the shape?
Part B: Each correct answer is worth 6 points
Problem 11
The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles wide. The number of tiles that touch the walls of the room is
Problem 12
Five students named Fred, Gail, Henry, Iggy, and Joan are seated around a circular table in that order. To decide who goes first in a game, they play "countdown". Henry starts by saying "34", with Iggy saying "33". If they continue to count down in their circular order, who will eventually say "1"?
Problem 13
In the diagram, the percent of small squares that are shaded is
Problem 14
Which of the following is an odd integer, contains the digit , is divisible by
, and lies between
and
?
Problem 15
A box contains pink,
blue,
green,
red, and
purple cubes that are identical in size. If a cube is selected at random, what is the probability that it is green?
Problem 16
The graph shown at the right indicates the time taken by five people to travel various distances. On average, which person travelled the fastest?
Problem 17
In a "Fibonacci" sequence of numbers, each term beginning with the third, is the sum of the previous two terms. The first number in such a sequence is , and the third term is
. What is the eighth term in the sequence?
Problem 18
The results of the hair colour of people are shown in this circle graph. How many people have blonde hair?
Problem 19
What is the area, in , of the shaded part of the rectangle?
Problem 20
The first 9 positive odd integers are placed in the magic square so that the sum of the numbers in each row, column and diagonal are equal. Find the value of A + E.
Part C: Each correct answer is worth 8 points
Problem 21
A game is played on the board. In this game, the player can move three places in any direction (up, down, right or left) and then can move two places in a direction perpendicular to the first move. If a player starts on S, which position on the board (P, Q, R, T, or W) cannot be reached through any sequence of moves?
Problem 22
Forty-two cubes with cm edges are glued together to form a solid rectangular block. If the perimeter of the base of the block is
cm, then the height, in cm, is
Problem 23
is a square. Points P and Q are outside the square such that triangles JMP and MLQ are equilateral. The size, in degrees, of angle
is
Problem 24
Five holes of increasing size are cut along the edge of one face of a box as shown. The number of points scored when a marble is rolled through that hole is the number above the hole. There are three sizes of marbles: small, medium and large. The small marbles fit through any of the holes, the medium fit only through holes 3, 4, and 5, and the large fit only through hole 5. You may choose up to 10 marbles of each size to roll and each rolled marble goes through a hole. For a score of 23, what is the maximum number of marbles that could have been rolled?
Problem 25
In a softball league, after each team has played every other team 4 times, the total accumulated points are: Lions 22, Tigers 19, Mounties 14, and Royals 12. If each team received 3 points for a win, 1 point for a tie and no points for a loss, how many games ended in a tie?
See also
1999 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
Preceded by 1998 CEMC Gauss (Grade 7) |
Followed by 2000 CEMC Gauss (Grade 7) | |
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CEMC Gauss (Grade 7) |