Wednesday, February 24, 2016
(in North America and South America)
Thursday, February 25, 2016
(outside of North American and South America)
©2015 University of Waterloo
Time: 60 minutes
Calculating devices are allowed, provided that they do not have any of the following features: (i) internet access, (ii) the ability to communicate with other devices, (iii) information previously stored by students (such as formulas, programs, notes, etc.), (iv) a computer algebra system, (v) dynamic geometry software.
Consider the following addition problem.
The result of the addition is
Which of the following has the largest value?
In the diagram, the
In the diagram, each of the five squares is
What percentage of the total area of the five squares is shaded?
Numbers
The value of
Which of the following is equal to 2 m plus 3 cm plus 5 mm?
If
A soccer team played three games. Each game ended in a win, loss, or tie. (If a game finishes with both teams having scored the same number of goals, the game ends in a tie.) In total, the team scored more goals than were scored against them. Which of the following combinations of outcomes is not possible for this team?
Exactly three faces of a
What fraction of the total surface area of the cube is shaded?
An oblong number is the number of dots in a rectangular grid with one more row than column. The first four oblong numbers are 2, 6, 12, and 20, and are represented below:
What is the 7th oblong number?
In the diagram, the area of square
What is the perimeter of rectangle
Multiplying
In the diagram,
If
When two positive integers
An integer from 10 to 99 inclusive is randomly chosen so that each such integer is equally likely to be chosen. The probability that at least one digit of the chosen integer is a 6 is
What is the tens digit of the smallest six-digit positive integer that is divisible by each of 10, 11, 12, 13, 14, and 15?
Each integer from 1 to 12 is to be placed around the outside of a circle so that the positive difference between any two integers next to each other is at most
What is the value of
Chris received a mark of
In the diagram, points
If
Grid lines are drawn on three faces of a rectangular prism, as shown.
A squirrel walks from
There are
In the diagram,
The area of
Ten very small rubber balls begin equally spaced inside a 55 m long tube. They instantly begin to roll inside the tube at a constant velocity of 1 m/s. When a ball reaches an end of the tube, it falls out of the tube. When two balls bump into each other, they both instantly reverse directions but continue to roll at 1 m/s. Five configurations giving the initial direction of movement of each ball are shown. All gaps indicated in the diagram are the same length and are equal in length to the distance from the ends of the tube to the nearest ball. For which configuration will it take the least time for more than half of the balls to fall out of the tube?
A 0 or 1 is to be placed in each of the nine
The number of ways in which this can be done is
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