(45 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) previously stored information such as formulas, programs, notes, etc., (iv) a computer algebra system, (v) dynamic geometry software.
Express answers as simplified exact numbers except where otherwise
indicated. For example,
In the diagram, points
Philippe uses a ruler to connect each pair of these points with a line segment. How many line segments does he draw?
What is the smallest positive integer
At 7:00 a.m. yesterday, Sherry correctly determined what time it had been 100 hours before. What was her answer? (Be sure to include “a.m.” or “p.m.” in your answer.)
A standard die with six faces is tossed onto a table. Itai counts the total number of dots on the five faces that are not lying on the table. What is the probability that this total is at least 19?
Suppose that
When the line with equation
Suppose that
Yasmine makes her own chocolate beverage by mixing volumes of milk and
syrup in the ratio
Suppose that
For example, if
In the diagram,
If
If
Let
At the start of 2018, the Canadian Excellent Mathematics Corporation had
Let
Kolapo lists the four-digit positive integers that can be made using the
digits 2, 4, 5, and 9, each once. Kolapo lists these integers in
increasing order. What is the
In the diagram,
What is the value of
Let
The sum of the even integers from 2 to
Let
Suppose that
How many perfect squares are there between 2 and 150?
Let
The line with equation
Let
The triangle in the first quadrant formed by the
(45 minutes)
Calculating devices are not permitted.
Express answers as simplified exact numbers except where otherwise
indicated. For example,
For what value of
What is the value of
Ada is younger than Darwyn. Max is younger than Greta. James is older than Darwyn. Max and James are the same age. Which of the five people is the oldest?
Determine the average (mean) of
Suppose that
How many four-digit palindromes
Adia writes a list in increasing order of the integers between 1 and 100, inclusive, that cannot be written as the product of two consecutive positive integers. What is the 40th integer in her list?
For how many ordered pairs of positive integers
Shelly-Ann normally runs along the Laurel Trail at a constant speed of 8 m/s. One day, one-third of the trail is covered in mud, through which Shelly-Ann can only run one-quarter of her normal speed, and it takes her 12 s to run the entire length of the trail. How long is the trail, in metres?
Determine the value of
Ezekiel has a rectangular piece of paper with an area of
What is the perimeter of the original rectangle?
What is the value of
Determine the value of
The integers
Suppose that
Suppose that
In the diagram, pentagon
Also,
The height of Cylinder A is equal to its diameter. The height and diameter of Cylinder B are each twice those of Cylinder A. The height of Cylinder C is equal to its diameter. The volume of Cylinder C is the sum of the volumes of Cylinders A and B. What is the ratio of the diameter of Cylinder C to the diameter of Cylinder A?
Suppose that
The integers from 1 to
The real numbers
Suppose that
The numbers
Suppose that
In the diagram,
If