Wednesday, November 13, 2024
(in North America and South America)
Thursday, November 14, 2024
(outside of North American and South America)
©2024 University of Waterloo
Time: 2 hours
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.
Do not open this booklet until instructed to do so.
There are two parts to this paper. The questions in each part are arranged roughly in order of increasing difficulty. The early problems in Part B are likely easier than the later problems in Part A.
PART A
PART B
For each question in Part A, full marks will be given for a correct answer which is placed in the box. Part marks will be awarded only if relevant work is shown in the space provided in the answer booklet.
A container in the shape of a cube has dimensions
A group of students were asked to choose their favourite of the three colours red, green and blue. Unfortunately, some of the results of the survey were lost. All of the remaining data are expressed in both the pie graph and the bar graph shown below. What is the total number of students that were surveyed?
In the diagram,
The positive integers
Lakshmi creates a table with
Every integer in the first (leftmost) column is
The cells in the second column contain the consecutive integers
from
Every integer in the remaining columns is equal to the sum of the integers in the two cells directly to its left in the same row.
The first three rows of the table are shown below.
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How many different two-digit integers are in exactly
Eight points are equally spaced around the circumference of a
circle and pairs of points are connected by
For each question in Part B, your solution must be well-organized and contain words of explanation or justification. Marks are awarded for completeness, clarity, and style of presentation. A correct solution, poorly presented, will not earn full marks.
Useful Fact for Part B:
The sum of the first
That is,
In the diagram,
In the diagram,
Quadrilateral
Beryl ran
Carol walked
Daryl rode his bicycle for a total of
Errol competed in an endurance competition that took
Given an increasing list of consecutive integers, the 3-sign
sum of the list is the sum of the integers in the list, in order,
except that every third integer is subtracted instead of added. For
example, the 3-sign sum of the list
Determine the 3-sign sum of
For a positive integer
Slice | 3-sign sum |
---|---|
For a positive integer
For each integer
Determine the remainder when