Arithmetic
1/2 ÷ 1/2 ÷ 1/2 ÷ 1/2 ÷ 1/2 ÷ 1/2
32
2x + 14 - x = 3(4 + x) + 2 - 3x
x = 0
First team to get an error on their calculator (barring syntax errors) and stand up will receive 100 points.
Yay
What is the number n called?
n√a
Index
If Easter in 2024 was March 31st, and Easter this year is April 20th, how much time has elapsed between?
385 days
Evaluate the following expression:
174 - 237 + 5√(174 + 237) + e23 + 2∞ - 417 + 723
Infinity
Any expression + ∞ = ∞
If the sum of two numbers is 150, and one number is 100 greater than the other, then what is the value of the larger number divided by the smaller one?
5
Caecilians are 45-cm long on average. The average height of a Sicilian is 172-cm. To the nearest whole number, what percent of a Sicilian's height is a caecilian's length?
26%
In ancient times, what tool was used to make arithmetic calculations?
Abacus
if H=1, r=1, a=2, y=1/2, p4=36, E=1/4, s=8, and t=3/2, then what is the value of the following:
Happy + (EastEr)!
(1)(2)√(36)(1/2) + [(1/4)(2)(8)(3/2)(1/4)(1)]!
6 + (3)!
6 + 6
12
Evaluate the sum of the series:
(2+2) + (2×2) + (22) + (22) + (2↑↑↑2) + (2↑↑↑↑2)
Pentation: 2↑↑↑2 = 22 = 22 = 4
Hexation: 2↑↑↑↑2 = 2↑↑↑2 = 22 = 22 = 4
4 + 4 + 4 + 4 + 4 + 4 = 24
A + B = 12
B - 2 = A
Ax + By + C = 20
2y + 1 = x
C = ?
C = -2
You just scored 25% on a test, but it's ok, because it was also the median mark in the class.
If there are 11 people in your class, what is the highest possible class average, to the nearest tenth of a percent?
Assume everyone's mark is an integer from 0 to 100 (inclusive).
The data would be:
25, 25, 25, 25, 25, 25, 100, 100, 100, 100, 100
... and the average would be 59.1%.
Express the number 23 in binary.
10111
Since it's almost Easter, order all of the following real numbers from lowest to greatest:
π,√8, e, i
e, √8, π
i is the imaginary unit (not a real number).
Estimate the following expression:
(√2)(√2)
(Write on card provided)
1.6325
If the cube root of a number is x, and the fourth root of that same number is y, what is y as a function of x? What would be the domain?
y = f(x) = x3/4 or 4√x3
Since the index is an even number, x cannot be negative:
Domain: {x| x ≥ 0, x ∈ ℝ}
The probability of selecting a blue marble in a bag of marbles is k/3.
If the probability of selecting a red marble is k/2, and there are only red and blue marbles in the bag, what is the value of k?
k/3 + k/2 = 1
2k + 3k = 6
5k = 6
k = 6/5
What is the greatest number of distinct values that can be assigned to the faces of a fair dodecahedral die?
12
If your perfectly cylindrical friend has a diameter of 16 inches and a height of 72 inches, how many whole eggs would you have to force feed them to double their volume, assuming an egg is 3 cubic inches?
(No calculator, a range of answers will be accepted)
9651 eggs
(Accept 9640 to 9660)
Express as a single radical with a whole-number index:
2√ 4√√ 3√ 3√√ 1√a × 2√ 3√a
288√a × 6√a
a1/288 × a1/6
a1/288 + 1/6
a49/288
288√(a49)
Given the following:
a2 - b2 = a - b
{(a,b)| a>0, b>0; a, b ∈ ℝ}
What values of a and b that satisfy these statements produces the smallest product a × b?
a = b = 1/2
If x = 1/2, what is the value of:
a) (((((x)^x)^x)^x)^x)^x...
b) How does it differ from xxxxxxxxxxxxxxxxxxxxxxx...?
(Explain, calculation not necessary for part b)
a) Taking the square root of a number between 0 and 1 makes its value closer to 1.
Therefore, this expression will approach 1.
b) This is different than the solution of b, as according to order of operations, approaching this expression requires starting from the top of the "power tower", rather than the base, resulting in a value closer to 0.64
Are 1/sin(x) and sin-1(x) equivalent expressions?
Explain.
No.
The surface area of an egg can be approximated with the following formula:
SA = 4π(ab)2/3
... where a is half the minor axis and b is half the major axis.
If the egg is inscribed in a rectangular prism whose lateral surface area is 32 cm2, what is the surface area of the egg?
A lateral = 4ab = 32cm2
ab = 8cm2
4π(ab)2/3 = 4π(8)2/3
= 4π4
= 16π cm2