Wednesday, February 22, 2023
(in North America and South America)
Thursday, February 23, 2023
(outside of North American and South America)
©2022 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.
Which of the following integers has the greatest value?
In the diagram, 30 identical small squares are shown.
How many of these 30 squares are shaded?
The value of
If
The expression
If
Jurgen is travelling to Waterloo by bus. He packs for 25 minutes. He then walks to the bus station, which takes 35 minutes. He arrives 60 minutes before his bus leaves. His bus leaves at 6:45 p.m. At what time did he start packing?
A sign has 31 spaces on a single line.
The word RHOMBUS is written from left to right in 7 consecutive
spaces.
There is an equal number of empty spaces on each side of the word.
Counting from the left, in what space number should the letter R be
put?
The decimal representation of
Another way to write this decimal representation is
Similarly,
The decimal representation of
In the decimal representation of
In the diagram, points
An ant walks directly from
A rectangular prism has a volume of
Morgan uses a spreadsheet to create a table of values. In the
first column, she lists the positive integers from 1 to 400. She then
puts integers in the second column in the following way: if the integer
in the first column of a given row is
On February 1, it was 16.2℃ outside Jacinta’s house at 3:00 p.m. On February 2, it was -3.6℃ outside Jacinta’s house at 2:00 a.m. If the temperature changed at a constant rate between these times, the rate at which the temperature decreased was
Each of four doors is randomly either open or closed. What is the probability that exactly two of the four doors are open?
Nasim buys trading cards in packages of 5 cards and in packages
of 8 cards. He can purchase exactly 18 cards by buying two 5-packs and
one 8-pack, but he cannot purchase exactly 12 cards with any combination
of packages. For how many of the integers
At the start of this month, Mathilde and Salah each had 100 coins. For Mathilde, this was 25% more coins than she had at the start of last month. For Salah, this was 20% fewer coins than he had at the start of last month. The total number of coins that they had at the start of last month was
In a survey, 100 students were asked if they like lentils and were also asked if they like chickpeas. A total of 68 students like lentils. A total of 53 like chickpeas. A total of 6 like neither lentils nor chickpeas. How many of the 100 students like both lentils and chickpeas?
In the diagram,
What is the value of
Ellie’s drawer of hair clips contains 4 red clips, 5 blue clips,
and 7 green clips. Each morning, she randomly chooses one hair clip to
wear for the day. She returns this clip to the drawer each evening. One
morning, Kyne removes
Four larger circles with radius 5 are arranged so that their centres are the vertices of a square. Each of the larger circles is tangent to (that is, just touches) two of the other circles, as shown.
A smaller circle with radius
Each correct answer is an integer from 0 to 99, inclusive.
Starting with a positive integer
For example, starting with
Alicia starts a sequence with
The integers 1, 2, 4, 5, 6, 9, 10, 11, 13 are to be placed in the circles and squares below with one number in each shape.
Each integer must be used exactly once and the integer in each circle
must be equal to the sum of the integers in the two neighbouring
squares. If the integer
Dewa writes down a list of four integers. He calculates the average of each group of three of the four integers. These averages are 32, 39, 40, 44. What is the largest of the four integers?
Cube
For how many integers
Consider positive integers
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