Number Theory
The smallest prime number greater than 50
53
What is the value of x in the equation 3x - 7 = 20
9
The measure of one interior angle of a regular hexagon
120 degrees
The number of different ways to arrange the letters M-A-T-H
24 (4!)
What is 15% of 80
12
The number of positive factors of 36
9 (1,2,3,4,6,9,12,18,36)
What is the 10th term of the arithmetic sequence that starts 4,7,10,13,...
31 (4 + 9x3)
The area of a triangle with base of 12 and height of 5
The probability of rolling a sum of 7 on two fair six-sided dice
1/6
What is the mean of this set (12, 15, 18, 21, 24)
18 (middle term of the arithmetic sequence)
The greatest common divisor of 48 and 72
24
What is the product of the roots of the equation
x^2 - 5x + 6 = 0
6 (product of roots is c/a)
The length of the hypotenuse of a right triangle with legs of 7 and 24
25
The number of unique diagonals of a convex octagon
20 formula is
n*(n-3)/2
Number of seconds in 2.5 hours
9,000 2.5 * 60 * 60
1 (pattern of 3,9,7,1,3,9,7,1,....)
35 ( g(x) = 16; f(16) = 32 + 3 = 35)
Volume of cylinder (in terms of pi) with radius of 3 and height of 10
90pi
The number of ways to choose a committee of 3 students from a group of 10
120 nCr or 10C3 which is 10!/(3!(10-3)!)
A car travels 45 miles per hour. The number of feet it travels in one second. (1 mile = 5,280 feet)
66 (45 x 60 x 60 / 5280)
The sum of all prime factors of 2024
36 (23 x 11 x 23 = 2024 --> 2+11+23 = 36)
What is the sum of the first 50 positive odd integers
2500 (sum of first n positive odd integers is n2)
In a circle the area of a sector with central angle of 60 degrees and radius of 6 (in terms of pi)
6pi
A bag contains 4 red marbles and 6 blue marbles. If two marbles are drawn without replacement, the probability that both are red.
2/15 (4/10 x 3/9 = 12/90 = 2/15)
The value of
sqrt(1+2+3+.....9+10+9+.....+2+1)
10