Algebra
2 - x > 3
Determine the range of values for x.
x < -1
A square has an area of 81 cm2. What is its perimeter?
The perimeter of the square is 36 cm
How many ways are there to rearrange 3 books into different orders?
There are 6 different ways to rearrange 3 books.
What is the Greatest Common Factor of 32 and 56?
The Greatest Common Factor is 8.
The floor function, denoted ⌊x⌋ rounds down. For example, ⌊1.99⌋ = 1.
Similarly, the ceiling function, denoted ⌈x⌉ rounds up. For example: ⌈0.01⌉ = 1.
What is ⌈⌊0.98 + 0.12⌋+0.12⌉?
The value of this expression is 2.
x2 - 6x + 9 = 9
Determine the value(s) of x.
x = 0, 6
Alice and Bob race around a circular track with a 99999mm radius and a 2m thickness. Alice runs on the inside, and Bob runs on the outside. After 2 laps, how much more distance has Bob travelled than Alice?
Bob has travelled 8π meters further than Alice.
Adam rolls 2 dice simultaneously. What is the probability that the sum of the results is greater than 6?
Adam has a 7/12 chance of rolling higher than 6.
Determine which of the following numbers are divisible by 11: 3267, 2512, 374, 10101. Do not use a calculator.
The numbers 3267 and 374 are divisible by 11.
Let a binary number be defined such that each position is a power of 2.
For example: 1102 = 1 * 22 + 1 * 21 + 0 * 20 = 6.
What is 1012 * 1112? Express your answer in binary.
The value of this expression is 1000112.
The graph 2(x-3)4 + 1 intersects the x-axis how many times?
0, It does not intersect the x-axis.
A sphere has a radius of 5 metres. What is the exact value of the sphere's volume?
Hint: The volume of a sphere is 4πr3/3
The volume of the sphere is 500π/3 m3
Bob walks into a room and flips 3 coins. He then comes out and tells you at least one coin is heads. What is the chance that exactly 2 coins are heads?
There is a 3/7 chance that exactly 2 coins are heads.
What are the last 2 digits of 7^2026 + 5^2026?
The last 2 digits of this sum is 74.
Let i be defined such that i^2 = -1.
What is the value of 1/i in the form a + bi?
The value of 1/i is -i.
What are all real solutions to the equation x2/3 + 5x1/3 = 6. Recall fractional powers are the same as roots, for example, x1/2 = √x.
x = 1, -216
Define T1 as an isosceles right triangle with side lengths 1, 1, √2 . T2 is drawn such that it is an isosceles right triangle with its short side drawn on the hypotenuse of T1. This process is repeated n times for Tn, where Tn’s short side is drawn on Tn-1's hypotenuse. What is the area of T5?
The area of T5 is 8.
How many 4-digit numbers have exactly 2 different repeating digits? (for example, 9988 and 9898 both follow this criteria, but 9999, 0011 and 9989 do not.)
243 4-digit numbers have exactly 2 different repeating digits.
Call a number that is 3 digits, has a 5 in it, and is divisible by 25 cool. How many cool numbers are there? (Three-digit numbers do not start with zero.)
There are 28 cool numbers.
What is the sum of the series 3 + 1 + ⅓ + 1/9… to infinity?
Let x and y be 2 even integers such that
y = x(x+1)2 - x/2 and x is between 0 and 2026 (inclusive).
How many possible pairs (x, y) are there that satisfy these conditions?
There are 507 possible pairs (x, y) that satisfy these conditions.
A dog is leashed to the corner of a 2m by 3m shed by a 3m long rope. What is the total area the dog can roam in?
The dog can roam in an area of 7πm2
What is the number of axis-aligned rectangles you can form in a 3 by 4 rectangle grid using only intersection points?
There are 60 different axis-aligned rectangles.
How many numbers between 1 and 2026 share a factor with 2025 that is not 1?
There are 945 numbers between 1 and 2026 that share at least 1 factor with 2025 that is not 1.
Logarithms, denoted logb(x), undo exponentiation. For example, log10(100) = 2, as 102 = 100.
What is the value of log3(5) x log5(7) x log7(9) … log727(729)?
Hint: Logs can be converted by the change-of-base rule, which is: logba = logna / lognb, where n is any base.
The value of this expression is 6.