Give me a problem 1
Kiana has two older twin brothers. The product of their ages is 128. What is the sum of their three ages?
2, 8, 8 -> 18
What number is one third of the way from 1/4 to 3/4?
1/3 x (1/4) + 2/3 x (3/4) = 7/12
This greek mathematician is considered the Father of Geometry.
Who is Euclid?
This theorem relates 3 sides of a right triangle.
What is the Pythagorean Theorem?
What is the total attendance for all Math Team meetings this year (adding number of people at each meeting across all meetings)?
[203, 1010] - 505
Suppose that 2/3 of 10 bananas are worth as much as 8 oranges. How many oranges are worth as much as 1/2 of 5 bananas?
2/3 x 10 bananas = 8 oranges
1 banana = 8 x 3/2 / 10 = 6/5 oranges
5/2 bananas = (5/2) x 6/5 = 3 oranges
What is the volume of a cube whose surface area is twice that of a cube with volume 1?
SA = 12 -> area of one face = 2
-> side length = sqrt(2)
-> volume = 2sqrt(2)
Before calculators as we know them, this analog device was used to perform manual calculations.
What is a slide rule?
This theorem states that an angle bisector of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle
What is the Angle Bisector Theorem?
What is pi to the power of 9?
[14905, 59618] - 29809
A class collects 50 dollars to buy flowers for a classmate who is in the hospital. Roses cost 3 dollars each, and carnations cost 2 dollars each. No other flowers are to be used. How many different bouquets could be purchased for exactly 50 dollars?
Must buy an even number of roses: 0, 2, 4, 6, 8, 10, 12, 14, 16 all possible -> 9
By inserting parentheses, it is possible to give the expression 2 x 3 + 4 x 5 several values. How many different values can be obtained?
(2 x 3) + (4 x 5)
(2 x 3 + 4) x 5
2 x (3 + 4) x 5
2 x (3 + 4) x 5
4
This is the civilization that is believed to have invented the decimal number system.
What is India?
This theorem states that every integer greater than 1 can be represented uniquely as a product of prime numbers
What is the Fundamental Theorem of Arithmetic?
How many people, joining hands, would it take to form a complete circle around the world?
[12000000, 24000000]
Bricklayer Brenda would take 9 hours to build a chimney alone, and bricklayer Brandon would take 10 hours to build it alone. When they work together they talk a lot, and their combined output is decreased by 10 bricks per hour. Working together, they build the chimney in 5 hours. How many bricks are in the chimney?
x bricks total:
(Brenda's rate + Brandon's rate - 10) x 5 hours = x bricks
(x bricks / 9 hours + x bricks / 10 hours - 10 bricks / hour) x 5 hours = x bricks
-> x = 900
For each positive integer n, the mean of the first n terms of a sequence is n. What is the 2008th term of the sequence?
Mean of first 2007 terms is 2007 -> sum of first 2007 terms is 20072
(sum of first 2008 terms)/2008 = 2008
(sum of first 2007 terms) + (2008th term) = 2008 x 2008
2008th term = 20082 - 20072 = 4015
This mathematician is considered the Mother of Computer Science.
Who is Ada Lovelace?
This theorem states states that for any two relatively prime positive integers m,n, the greatest integer that cannot be written in the form am + bn for nonnegative integers a,b is mn - m - n.
What is the Chicken McNugget Theorem?
How many 2x4 Lego bricks would it take to build a to scale Empire State building?
[210, 840] billion
Points A and B lie on a circle centered at O, and angle AOB = 60o. A second circle is internally tangent to the first and tangent to both lines OA and OB. What is the ratio of the area of the smaller circle to that of the larger circle?
If r = radius of the smaller circle, there's a 30,60,90 triangle that implies 3r is the radius of the larger circle so 1/32 = 1/9 is the ratio of the areas.
For how many integer values of k do the graphs of x2 + y2 = k2 and xy = k not intersect?
y=k/x
x4 - k2x2+k2 = 0
If they don't intersect: discriminant < 0
-> k4-4k2<0 -> k = -1, 0, 1
k = 0 -> Intersect at (0,0)
-> 2
This mathematician is credited to have finally proved Euler's Last Theorem in 1995.
Who is Andrew Wiles?
In a simple connected planar graph, (the number of faces) - (the number of edges) + (the number of vertices) = 2.
What is Euler's Formula?
How many lightning strikes are needed to produce the annual power consumption of the US?
(53, 212) billion