Arithmetic I
Name a number that is both a perfect square and a perfect cube. (1 and zero do not count.)
64, 729, 4096
Evaluate the series:
1 + 2 + 3 + ... + 99 + 100
5050
Mean = 50.5
50.5 x 100 = 5050
If a picture is worth a thousand words, and you can type 50 words per minute, then, assuming units follow dimensional logic, how many pictures can you draw in an hour?
3 pictures:
1 hour = 60 minutes
(60 minutes)×(50 words/1 minute) = 3000 words
(3000 words)×(1 picture/1000 words) = 3 pictures
Ryuga buys a dozen eggs, a score of apples, and a ream of napkins.
How much of each object did he buy?
12 eggs, 20 apples, and 500 napkins.
What is the only even prime number?
2
Arrange the following fractions in ascending order:
17/40, 1/2, 5/12, 7/17, 5/11
7/17, 5/12, 17/40, 5/11, 1/2
Convert 1/15 into a repeating decimal.
0.066666...
Deus Tecta ties a rope around the 'equator' of the Sun. If he wants to raise the rope 1 meter off the Sun's surface in all directions, how much more rope would he need?
The circumference of a circle with found with:
C = 2πr
C = 2π(r + 1)
C = 2πr + 2π
Thus, an additional 2π meters of rope is needed.
(approximately 6.28 meters)
Besson comes up with a new mathematical equation that relates the energy of a particle to the square of a triangle's hypotenuse:
Energy of a particle: E = mc2
Pythagorean Theorem: c2 = a2 + b2
E = m(a2 + b2)
What, if anything, is wrong with Besson's equation?
Besson's equation is nonsense.
The 'c' variable present in both equations represents two completely unrelated quantities.
What are the characteristics of a regular polygon?
All sides are of equal length.
Interior angles are all congruent.
Please write your answer in scientific notation.
Estimate:
279954 x 4029774 - 19653198
1.13 x 1012
Find the next term in the following sequence:
1, 2, 4, 8, 16, ?
Where term n = (1/24)(n4 - 6n3 + 23n2 - 18n + 24)
31
(1/24)[64 - 6(6)3 + 23(6)2 - 18(6) + 24] =31
Church bells ring N times when the time is N:00.
Aldyn arrives at the church as the bells are ringing, stays for 6.7 hours, then leaves.
If the bells rang a total of 33 times during his stay, at what times did he arrive and leave?
3:00 to 8:00 (either AM or PM).
The total number of rings, 33, is the sum of 6 sequential natural numbers.
By guess and check:
3+4+5+6+7+8 = 33
King Louis MMMDCXXIX has a piece of paper that is 0.02 cm thick. Assuming he is strong enough to do so, how many times does he have to fold his paper to make it 1 cm thick?
6 times
0.02 x 2 = 0.04
0.04 x 2 = 0.08 ... 0.16, 0.32, 0.64, 1.28
Why is it possible to create a digon (two-sided polygon) in a 3-dimensional space, but not on a 2-dimensional plane?
Bonus question: name a digon.
On a 2D plane, two lines can only intersect never, once, or at every point. However, in a 3D space, there is another axis on which the two lines can curve to produce a closed shape.
Bonus: a lune is the most common digon; it is essentially two longitudes on a globe.
What is the 20th term of the Fibonacci sequence? (First two terms are 0, 1)
4181
a + a = b
b - 1 = a
b2 - a = c
d/2 - 5 = c
d = ?
d = 16
Most digital clocks display digits using a seven segment system.
Is it mathematically possible to create a display system with 4 segments? How about 3 segments?
A four-segment display is possible, since there are enough ways to display all 10 digits uniquely:
24 = 16, 16 > 10
However, a three-segment display is not possible:
23 = 8, 8 < 10
Tyrone is trying to visualize a tesseract, which is the 4-dimensional extension of a cube.
Since the 4th dimension is time, Tyrone argues that a tesseract is merely a cube moving through time.
What, if anything, is wrong with Tyrone's claim?
There are two versions of the fourth dimension: temporal and spacial. A tesseract has strictly 4 spacial dimensions.
What improper fraction was commonly used as an approximation of pi around 4000 years ago?
22/7
What is the largest prime number below 4000?
3989
3991=13x307
3997=7x571
How many composite numbers are between 61 and 100? (Inclusive)
32 composite numbers
(8 prime numbers are 61, 67, 71, 73, 79, 83, 89, 97)
Wolfgang spends 390 minutes and 48 seconds at school each day. During this time, how many degrees will the hour hand on a 12-hour analog clock have moved?
97.7o
The hour hand moves 360˚ every 1440 minutes (24 hours). Therefore, in 1 minute, the hour hand moves 0.25˚.
390 min 48 sec = 390.8 min
390.8 x 0.25˚ = 97.7˚
Jada wants to find out how many spherical marbles could fit in an Earth-sized balloon.
The volume of a marble is 2 cm3. The volume of the Earth is 1.083×1027 cm3.
By dividing the volume of the Earth by the volume of a marble, Jada determines that 5.415×1026 marbles can fit inside the big balloon.
Is Jada's conclusion flawed? Explain.
Yes, Jada's conclusion is flawed.
Since marbles are spherical solids, placing them next to each other will always leave unoccupied space.
So, for a closer estimate, Jada would need to consider the system's packing density.
Without using decimals or fractions/dividing, create an expression that results in an irrational value that is between 5 and 5.1.
Answers may vary.
Example: √26