Wednesday, May 18, 2022
(in North America and South America)
Thursday, May 19, 2022
(outside of North American and South America)
©2022 University of Waterloo
Time: 1 hour
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 regular pentagon shown has a side length of 2 cm.
The perimeter of the pentagon is
The faces of a cube are labelled with 1, 2, 3, 4, 5, and 6 dots. Three of the faces are shown.
What is the total number of dots on the other three faces?
The equation that best represents "a number increased by five equals 15" is
The line graph shows the number of bobbleheads sold at a store each year.
The sale of bobbleheads increased the most between
Starting at 72, Aryana counts down by 11s:
In the diagram,
The value of
Which of the following values is closest to zero?
A jar contains 267 quarters. One quarter is worth $0.25. How many quarters must be added to the jar so that the total value of the quarters is $100.00?
A package of 8 greeting cards comes with 10 envelopes. Kirra has 7 cards but no envelopes. What is the smallest number of packages that Kirra needs to buy to have more envelopes than cards?
For the points in the diagram, which statement is true?
The 26 letters of the English alphabet are listed in an infinite,
repeating loop:
What is the 258th letter in this sequence?
A public holiday is always celebrated on the third Wednesday of a certain month. In that month, the holiday cannot occur on which of the following days?
A circular spinner is divided into three sections. An arrow is
attached to the centre of the spinner. The arrow is spun once. The
probability that the arrow stops on the largest section is
A positive number is divisible by both 3 and 4. The tens digit is greater than the ones digit. How many positive two-digit numbers have this property?
A rectangular pool measures 20 m by 8 m. There is a 1 m wide walkway around the outside of the pool, as shown by the shaded region.
The area of the walkway is
The results of asking 50 students if they participate in music or sports are shown in the Venn diagram.
What percentage of the 50 students do not participate in music and do not participate in sports?
There are
In the sequence shown, Figure 1 is formed using 7 squares. Each figure after Figure 1 has 5 more squares than the previous figure.
What figure has 2022 squares?
Mateo’s 300 km trip from Edmonton to Calgary passed through Red Deer. Mateo started in Edmonton at 7 a.m. and drove until stopping for a 40 minute break in Red Deer. Mateo arrived in Calgary at 11 a.m. Not including the break, what was his average speed for the trip?
Equilateral triangle
The positive factors of 6 are 1, 2, 3, and 6. There are two perfect squares less than 100 that have exactly five positive factors. What is the sum of these two perfect squares?
In the list
The net shown is folded to form a cube.
An ant walks from face to face on the cube, visiting each face
exactly once. For example,
The number 385 is an example of a three-digit number for which one of the digits is the sum of the other two digits. How many numbers between 100 and 999 have this property?
Student A, Student B, and Student C have been hired to help scientists develop a new flavour of juice. There are 4200 samples to test. Each sample either contains blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90% of the samples containing blueberry and reports correctly on exactly 88% of the samples that do not contain blueberry. The results for all three students are shown below.
Student A | Student B | Student C | |
---|---|---|---|
Percentage correct on samples containing blueberry |
90% | 98% | |
Percentage correct on samples not containing blueberry |
88% | 86% |
Student B reports 315 more samples as containing blueberry than
Student A. For some positive integers