(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,
Ingrid starts with
For what value of
It is now 1:00 a.m. What time will it be
A group of eight students have lockers that are arranged as shown, in two rows of four lockers with one row directly on top of the other. The students are allowed to paint their lockers either blue or red according to two rules. The first rule is that there must be two blue lockers and two red lockers in each row. The second rule is that lockers in the same column must have different colours. How many ways are there for the students to paint their lockers according to the rules?
In trapezoid
A train is traveling from City A to City B. If the train travels
at a speed of 80 km/h, it will arrive
In
A Tim number is a five-digit positive
integer with the property that it is a multiple of
The real numbers
For every positive integer
For example, the subsets of
What is the smallest even positive integer
A square garden has an area of
Let
In the diagram, square
What is the total area of the shaded parts of the square?
Let
If
How many integers
Let
A water tank initially contains
Let
Point
Three of the positive divisors of
Let
The numbers
Let
The parabola with equation
(45 minutes)
Calculating devices are not permitted.
Express answers as simplified exact numbers except where otherwise
indicated. For example,
A fish and chips truck sells three kinds of fish: cod, haddock,
and halibut. During a music festival, the truck sold
If
Point
What is the integer equal to
If
How many ordered triples
The distinct prime factors of
Using the diagram below, a seven digit integer can be created as follows: trace a path that uses each line segment exactly once and use the labels on the line segments as digits.
For example, the path that goes from
Alheri has three hoses. Water flows out of each hose at the same constant rate. Using all three hoses, she starts to fill a swimming pool at 6:00 a.m. and calculates that the pool will be full at exactly 6:00 p.m. on the same day. At 11:00 a.m., one of the hoses unexpectedly stops working. Assuming water still flows out of the other two hoses at the same rate as before, at what time will the pool be full?
The lines with the two equations below intersect at the point
What is the integer equal to
For how many integers
A positive integer is called mystical if it
has at least two digits and every pair of two consecutive digits, read
from left to right, forms a perfect square. For example,
In a
Kasun wants to place an integer from
In how many ways can Kasun place integers in the grid so that they satisfy the condition?
There are exactly three real numbers
In
Square
Let
Jolene and Tia are playing a two-player game at a carnival. In
one bin, there are five red balls numbered
Jolene and Tia win if the number on the ball chosen by Tia is a
multiple of
The positive integer
Square
What is the ratio of the area of
The sequence
In
The real numbers
Let