Tuesday, February 26, 2019
(in North America and South America)
Wednesday, February 27, 2019
(outside of North American and South America)
©2018 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 perimeter of a square is 28. What is the side length of this square?
In the diagram, some of the hexagons are shaded.
What fraction of all of the hexagons are shaded?
Yesterday, each student at Pascal C.I. was given a snack. Each student received either a muffin, yogurt, fruit, or a granola bar. No student received more than one of these snacks. The percentages of the students who received each snack are shown in the circle graph.
What percentage of students did not receive a muffin?
What is the smallest integer that can be placed in the box so that
If
In the diagram, point
The number line between
What is the sum of the lengths of
The median of the numbers in the list
In the diagram, each partially shaded circle has a radius of 1 cm and has a right angle marked at its centre.
In
Three
The cubes have a total of 11 exposed
In a magic square, the numbers in each row, the numbers in each column, and the numbers on each diagonal have the same sum.
In the magic square shown, the value of
In the diagram,
Also,
The list
Many of the students in M. Gamache’s class brought a skateboard or a bicycle to school yesterday. The ratio of the number of skateboards to the number of bicycles was
Sophie has written three tests. Her marks were 73%, 82% and 85%. She still has two tests to write. All tests are equally weighted. Her goal is an average of 80% or higher. With which of the following pairs of marks on the remaining tests will Sophie not reach her goal?
If
Hagrid has 100 animals. Among these animals,
each is either striped or spotted but not both,
each has either wings or horns but not both,
there are 28 striped animals with wings,
there are 62 spotted animals, and
there are 36 animals with horns.
How many of Hagrid’s spotted animals have horns?
In the diagram, each of
The combined area of the three triangles is 56. If
There are six identical red balls and three identical green balls in a pail. Four of these balls are selected at random and then these four balls are arranged in a line in some order. How many different-looking arrangements are possible?
In the diagram, square
Line segments
What is the units (ones) digit of the integer equal to
The integer 2019 can be formed by placing two consecutive two-digit positive integers, 19 and 20, in decreasing order. What is the sum of all four-digit positive integers greater than 2019 that can be formed in this way?
A path of length 14 m consists of 7 unshaded stripes, each of length 1 m, alternating with 7 shaded stripes, each of length 1 m. A circular wheel of radius 2 m is divided into four quarters which are alternately shaded and unshaded. The wheel rolls at a constant speed along the path from the starting position shown.
The wheel makes exactly 1 complete revolution. The percentage of time during which a shaded section of the wheel is touching a shaded part of the path is closest to
If
In the diagram,
For some real number
the area of
the area of
the area of
the area of
the area of
the area of
The area of
Thank you for writing the Pascal Contest!
Encourage your teacher to register you for the Fryer Contest which will be written in April.
Visit our website cemc.uwaterloo.ca to find
Visit our website cemc.uwaterloo.ca to