Arithmetic and Algebra I
First to stand up can claim √10000 points
Flip a coin:
Heads for +100
Tails for -100
1 + 2 + 3 + 4 + ... = 94
What was the last term?
14
At the grocery store, Alexander Garry Joseph buys 5-kg of apples, 12-kg of potatoes, 7 bananas (at 1.5-kg a piece), 2-litres of water, 2-kg of onions, 34.67-kg of ground beef, five 50-gram bags of crisps, three fillets of salmon (each 0.45-kg), 7 and a half tomatoes (where 1 tomato is 56-grams), a 1-litre can of water, a 5-litre bucket of water, a 3.5-litre box of water, and a sponge soaked with 2.45-litres of water.
If 1-mL of water equals 1-gram of water, what is 1+1?
2
What does the permille function (‰) represent?
Division by 1000
Evalute the expression: 00
Explain.
Undefined
Evaluate the following expression:
174 - 237 + 5√(174 + 237) + e23 + 2∞ - 417 + 723
Infinity
Any expression + ∞ = ∞
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 = 20
On a dial pad, letters are grouped into 3, except for PQRS and WXYZ. Each group of letters corresponds to a digit from 2 through 9. The digits 1 and 0 are not tied to any letters.
For example: A, B, or C are given by dialling the number 2.
What is the sequence of numbers pressed to dial "mathematics?" Ignore repeated digits.
6, 2, 8, 4, 3, 6, 2, 8, 4, 2, 7
Which symbol is used to represent exponentiation in text?
Caret (^)
What is the following numeral system called?
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
Bonus question: From where does it originate?
Arabic numeral system
Bonus: India
Determine all possible solutions:
1 ± 2 ± 3 ± 4
± creates more solutions by suggesting addition or subtraction.
-8, -4, -2, 0, 2, 4, 6, 10
Let i = √(-1)
Simplify the following in terms of i.
-4i + i [ √(-16) + 2i ] - i5
-5i - 6
(remainder from Jeopardy V)
Andrew roll a fair die 5 times in succession and records his results: (6, 6, 6, 6, 6)
Tristan rolls the same die 5 more times and records his results: (1, 3, 1, 4, 6)
Which result is more likely to occur? Explain.
Both are equally likely to occur.
Rolling any number on a fair die has the same probability. Each roll is an independent event.
Name the following Greek symbols:
(a) Used to represent the change in a quantity
(b) The ratio of a circle's circumference to its diameter
(c) Commonly used to represent an unknown angle
(a) Delta (∆)
(b) Pi (π)
(c) Theta (θ)
Express the numbers 4 and 9 in Roman Numerals. Provide two variations for each.
Using both additive and subtractive notation,
4: IV, IIII
9: IX, VIIII
Without the use of the first root, convert the following into a single radical, without anything outside the radical:
[√(2x)] ⋅ [0.5√(2/x)] ⋅ [3√64] ⋅ [√(y)]
[√(2x)] ⋅ [0.5√(2/x)] ⋅ [3√64] ⋅ [√(y)]
[√(2x)] ⋅ [√(y)] ⋅ [(2/x)2] ⋅ [3√64]
[√(2xy)] ⋅ [4x-2] ⋅[4]
[√(2xy)] ⋅ [√(16x-4] ⋅[√16]
√(512yx-3)
A = B2 , B = C2 , C = D2 , ... , Y = Z2
Express A in terms of Z.
A = Z2^25
A = B2 = B2^1
A = (C2)2 = C4 = C2^2
A = (D2)4 = D8 = D2^3
A = (E2)8 = E16 = E2^4...
(remainder from Jeopardy IV)
Jesse has 10 chromosomes;
a potato has N chromosomes;
and a fly has M chromosomes.
If the product of their chromosome counts is 400, what are the chromosome counts of the potato and fly that will result in the lowest sum of total chromosomes?
5 and 8, respectively
What symbol is commonly used to denote a function?
Bonus question:
Historically, many European nations used this symbol for what purpose?
Florin (ƒ)
Bonus: as currency
Is zeroth root of a number (0√n) possible? Explain.
0√n = n1/0
Division by zero is undefined.
A triangular prism lies in a three-dimensional space. The coordinates of five of its vertices are given:
(2, 0, 1), (2, 0, -3), (-2, 5, -1), (-3, 1, 1), (-3, 1, -3)
What are the coordinates of the last vertex?
(3, 4, -1)
A regular hexagon is inscribed within a circle. If the area of the hexagon is 24cm2, what is the area of the circle? Answer to the nearest cm2.
An answer in exact value rewards 200 bonus points.
16π/√3 cm2
or
29cm2
(remainder from Jeopardy IV)
A circle and a square have the same area. If the diagonal in the square is k meters long, what is the radius of the circle in terms of k?
A = 1/2 k2
1/2 k2 = πr2
r2 = 1/2π k2
r = k/√(2π) or r = k√(2π)/2π
What mathematical symbol was previously written out as a phrase?
Bonus question:
What was the phrase?
Equal sign (=)
Bonus: "is equal to"
What set of numbers is this?
{x | x+3/2 ∈ I}
Odd numbers