Cluborama
Sequences
Number Systems
Geometry
Polynomials
100
What’s the next number in this series? 2,6,12,20,30, _
42
100
3, 7, 11, 15, 19, 23, _
27
100
What is the decimal equivalent of the binary number 1101?
13
100
If all the side lengths are integers, what is the maximum possible value of AB?
18
100
Given the quadratic equation 123x^2 - 456x + 789 = 0, find the sum and product of its roots.
Sum = 152/41
Product = 263/41
200
Using only 8, 8’s how can you get the number 1000?
888 + 88 + 8 + 8 + 8 = 1000
200
2, 6, 18, 54, _
162
200
Convert the decimal number 42 to binary.
101010
200
What is x?
60/7
200
Given that ab = 2, a^2 + b^2 = 4, and that a + b > 0, find a and b.
a = b = sqrt(2)
300
How many 3-digit positive integers (that is, integers between 1000 and 9999, inclusive) having only odd digits are divisible by 5?
25
300
1, 1, 2, 3, 5, 8, 13, _
21
300
What is the base 5 representation of the decimal number 50?
200
300
Two sides of an isosceles triangle are 22 and 61. Compute the area of the triangle.
660
300
If one root of the quadratic equation x^2 - 4x + k is 2, find k.
k = 4
400
Let "#" be a special operation. If 5 # 1 = 46, 9 # 1 = 810, and 6 # 3 = 39, then what is 5 # 3?
313
400
1, 2, 4, 6, 10, 12, 16, _
18
400
What’s the decimal equivalent of the base-12 number 3C?
48
400
Each side of a rectangular box is an integer greater than 1. The sum of the areas of two adjacent faces is 25. Compute the area of the face that is adjacent to these two.
6
400
Factor x^3 - 2x^2 - 2x - 3
(x-3)(x^2+x+1)
500
Two girls on bicycles, 20 km apart, began racing directly toward each other. The instant they started, a fly on the handlebar of one bicycle started flying straight toward the other cyclist. As soon as it reached the other handlebar it turned and started back. The fly flew back and forth in this way, from handlebar to handlebar until the two bicycles met. If each bicycle had a constant speed of 10 km/h and the fly flew at a speed of 15 km/h, how far did the fly fly?
15 km
500
A, E, F, H, I, K, L, M, _
N
500
Convert the octal number 57 to its binary representation.
101111
500
7/29
500
Factor a(b-c)^3+b(c-a)^3+c(a-b)^3
(a-b)(b-c)(c-a)(a+b+c)