Geometry
A right triangle has two perpendicular sides measuring 6 cm and 8 cm.
What is the length of the hypotenuse?
10cm
7C3
35
Expand (x+2)3
x3+6x2+12x+8
Co-inventor of calculus and formulator of the laws of motion, he is widely regarded as one of history's greatest mathematicians.
Sir Isaac Newton
A rectangular box is 8 cm long, 6 cm wide, and 10 cm tall. It is filled halfway with water. A solid cube with side length 4 cm is placed inside and rests on the bottom, completely underwater.
What is the new height of the water?
19/3
A bag contains 3 red balls, 5 blue balls, and 2 green balls. One ball is picked at random. What is the probability that it is not blue?
1/2
The equation x2-18x+k=0 has two distinct real roots. If one root is three times the other, find the value of k.
81
Written by Euclid, this ancient Greek text laid the foundation for geometry.
Euclid’s Elements
Triangle ABC has side lengths AB=7, BC=24, and CA=25
A circle is circumscribed around the triangle, passing through all three vertices.
Find the radius of the circle.
12.5
Alice has some red balls and some black balls in a bag. Altogether, she has 25 balls. Alice picks one ball from the bag. The probability that Alice picks a red ball is x, and the probability that Alice picks a black ball is 4x. Work out how many black balls are in the bag.
20
Find the inverse of f(x)=3x-7
f-1(x) = (x+7)/3
Traced by a point on a rolling circle, this curve famously solves both the brachistochrone and tautochrone problems.
Cycloid
A cone has a base radius of 3 cm and a height of 4 cm. Find its total surface area, including the circular base. Use π ≈ 3.14
75.36cm2
Consider the nine letters in the word MAGNITUDE.
Find the number of ways that the nine letters may be arranged if the four vowels (A, I, U, E) must all be together.
6!*4! = 17280
Solve for x, giving all valid solutions.
log2(x-1)+log(x-1)2 =17/4
x=1+21/4 , x=1+24 = 17
This unsolved Millennium Prize Problem concerns the non-trivial zeros of the zeta function.
Riemann Hypothesis
A rectangular box measures 6 cm × 8 cm × 10 cm. An ant starts at one vertex and crawls along the outside surface to the diagonally opposite vertex. What is the shortest possible distance the ant can travel?
Give an exact answer. The ant may cross faces and edges, but must stay on the surface at all times.
2√72=17.2
A group of 12 people want to go to a concert. They can travel in a small car that takes one driver and one passenger, or two cars, each taking one driver and four passengers. If there are five drivers in the group, in how many different ways can they travel?
5P3 * 9C1 * 8C4 = 60*9*70 = 37800
Sketch the graph of y=x3-3x2-9x+5. Find and label both stationary points, and identify each as a local maximum or local minimum.
Local maximum: (-1,10)
Local minimum: (3,-22)
Who is famous for Königsberg’s bridge.
Leonhard Euler