Tuesday, February 28, 2017
(in North America and South America)
Wednesday, March 1, 2017
(outside of North American and South America)
©2017 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.
The expression
The value of
A snowman is built by stacking three spheres with their centres aligned vertically. The spheres have radii of 10 cm, 20 cm and 30 cm.
How tall is the snowman?
Which of the following fractions has the greatest value?
The graph shows the volume of water in a 300 L tank as it is being drained at a constant rate.
At what rate is the water leaving the tank, in litres per hour?
Penelope folds a piece of paper in half, creating two layers of paper. She folds the paper in half again, creating a total of four layers of paper. If she continues to fold the paper in half, which of the following is a possible number of layers that could be obtained?
The operation
Each of three cards is labelled with three numbers. Which of the following groups of three cards has the properties that the first and second cards have exactly one number in common, the first and third cards have exactly one number in common, and the second and third cards have exactly one number in common?
A restaurant bill, including 13% tax but not including a tip, is $226. The server is paid a tip of 15% based on the bill before tax. How much is the tip that the server is paid?
In the diagram,
Also,
What is the measure of
If
The figure shown is made up of 10 identical squares.
If the area of the figure is 160
The mean (average) of the three integers
The mean of the two integers
The mean of the five integers
In the addition shown, each of
What is the value of
Igor is shorter than Jie. Faye is taller than Goa. Jie is taller than Faye. Han is shorter than Goa. Who is the tallest?
A bag contains red, blue and purple marbles, and does not contain any other marbles. The ratio of the number of red marbles to the number of blue marbles is
If
The positive integers
The number of integers
Two lines with slopes
Car X and Car Y are travelling in the same direction in two different lanes on a long straight highway. Car X is travelling at a constant speed of 90 km/h and has a length of 5 m. Car Y is travelling at a constant speed of 91 km/h and has a length of 6 m. Car Y starts behind Car X and eventually passes Car X. The length of time between the instant when the front of Car Y is lined up with the back of Car X and the instant when the back of Car Y is lined up with the front of Car X is
The integers 1 to 6 are to be inserted into the grid shown.
No two integers that differ by 1 may be in squares that
share an edge. If the 1 is inserted as shown, how many
different integers can be placed in the box labelled
In the diagram, square
If each of these four rectangles has the same perimeter, what is the area of the shaded rectangle?
The triangle with side lengths 6, 8 and 10 is right-angled, while the triangle with side lengths 6, 8 and 9 is an acute triangle and the triangle with side lengths 6, 8 and 11 is an obtuse triangle. An obtuse triangle with positive area has side lengths 10, 17 and
Three coins are placed in the first three of six squares, as shown.
A move consists of moving one coin one space to the right, assuming that this space is empty. (No coin can jump over another coin, so the order of the coins will never change.) How many different sequences of moves can be used to move the three coins from the first three squares to the last three squares?
A positive integer
For example,
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