Counting
How many permutations of {1, 2, 3, 4} are there such that 1 comes before 2?
12
The area of an equilateral triangle, in square inches, is the same as its perimeter, in inches. What is its perimeter?
12 * sqrt(3) inches
What is the product of the roots of the equation 2x² + 3x + 14 = 0?
7
What is the last digit of 3 to the power 2026?
How many ways can the letters "FLUFFY" be arranged such that the three 'F's are not all consecutive?
96
What is the area of a triangle whose sides measure 13 ft, 14 ft, and 15 ft?
84 ft2
What should you add to both sides of the equation 4x² + 7x = 10 in order to complete the square?
49/16
What reduced fraction has the decimal expansion 0.1232323..., where after the initial 1, the pattern 23 repeats forever?
61/495
How many paths from (0, 0) to (5, 5), taking steps of one unit in the positive x or y direction at a time, do not pass through the points (2, 3) or (3, 2)?
52
A rectangle is inscribed in a circle. There is a central angle of 120° between the two vertices of one of the rectangle's sides, which has length 8 ft. What is the area of the circle?
64pi/3 ft²
For how many distinct integer values of k does the equation 5x²+k²x+18 = 0 have no real solutions?
9
How many zeros are at the end of 50!?
(That's a factorial, but I am also very excited.)
12
The sides of a square are to each be painted with one of 5 colors. In how many ways can this be done, if two colorings which differ only by rotating the square count as the same?
165
Triangle ABC has lengths AB = 7, BC = 8, and an area of 21 square units. If x is the measure of angle B, then find tan(x)².
9/7
For x > 0, simplify -ln(2/x) + ln(4/x) - ln(8/x)..... - ln(512/x) + ln(1024/x).
ln(32) or 5 ln(2)
In base ten, the integer 40909 is a multiple of 11. In which other base b is 40909_b a multiple of 11_b?
21