Number Sense
Series and Sequences
Logarithms
Math Trivia
Vieta's
100

Evaluate:  290+9+2+492+5+393+3 +0+1+5 

1200

100

What is the sum of all integers  x  for which  -30\leq x\leq 26?

-114

100

If  \log_{25}(x-4)=\frac{1}{2} , find  \frac{1}{\log_x3}.

2

100

What was the number 0 originally called?

Cipher

100

What is the sum of the roots of the polynomial  x^2-17x+2 ?

5000

200

For how many different digits  n is the two-digit number  6n divisible by  n ? (The expression  6n  should be interpreted as a two-digit integer with tens digit  6  and units digit  n , not as  6  times  n .)        

6


200

Asha adds all the odd integers from 1 through 101, inclusive, and then subtracts all the even integers in that same range from her sum. What result does she obtain?     

51

200

How many positive integers b have the property that  \log_b 729 is a positive integer?

4

200

Where did Archimedes hail from?

Syracuse, Greece

200

What is the product of the roots of the polynomial  x^2+3x-15 .

-15

300

How many two-digit prime numbers can be formed by choosing two different digits from the set {2,7,8,9} to be used as the tens digit and units digit?

4

300

To place the first paving stone in a path, Alex starts at the crate of stones, walks three feet, places the stone, and returns to the crate. For each subsequent stone, Alex walks two feet farther each way. Alex will place the first 50 stones in a path. After returning to the crate from placing the  50^{th} stone, what is the total distance Alex walked, in feet?      

5200

300

Evaluate  \log_{\sqrt{5}}125 \sqrt{5}.

7

300

Where were the Arabic numerals invented?

    

India
300

Let  r_1, r_2, r_3 , be the the roots of  x^3-6x^2+21x +a=0. Find all real numbers  a such that the roots  r_1, r_2, r_3 form an arithmetic sequence and are not all real.

-26

400

What is the least four-digit positive integer, with all different digits, that is divisible by each of its digits?

1236

400

The arithmetic mean of an odd number of consecutive odd integers is  y. Find the sum of the smallest and largest of the integers in terms of  y .

2y

400

Rewrite  log_2 4\cdot \log_3 5 \cdot \log_4 6 \cdots \log_{62} 64 as  a\log_b c, where  a,b, and  c are positive integers,  b  is prime, and  c<100. Compute  a+b+c.


72
400

How many sides does an "Enneadecagon" have?

19

400

Suppose that for some  a,b,c we have  a+b+c=6 ,  ab+ac+bc=5 and  abc=-12. What is  a^3+b^3+c^3 ?

90

500

If the least common multiple of A and B is 1575, and the ratio of A to B is 3:7, then what is their greatest common divisor?

75

500

If  x and  y are positive integers for which 3x+2y+xy=115+7x+6y, then what is  x+y?

140

500

Consider the largest solution to the equation  \log_{10x^2} 10+\log_{100x^3}10=-2. Find the value of  \frac{1}{x^{12}}. writing your answer in decimal representation.

10000000

500

What is the only number that is twice the sum of its digits?

18

500

Find the sum of the roots, real and non-real, of the equation  x^{2001}+(12-x)^{2001}=0, given that there are no multiple roots.

500