Basic Math by the Definition

15 Points Per Correct Answer - No time limit  

1. If a and b are positive integers, then there exists a positive integer d which satisfies the following properties: 1. a is divisible by d and b is divisible by d 2. Suppose D is another positive integer having the property a is divisible by D and b is divisible by D. Then d is divisible by D. What is d known as? The least common multiple of a and b The quotient of a and b The product of a and b The greatest common divisor of a and b

2. If a and b are positive integers, then there exists a positive integer m which satisfies the following properties: 1. m is divisible by a and m is divisible by b 2. Suppose M is another positive integer having the property M is divisible by a and M is divisible by b. Then M is divisible by m. What is m known as? The quotient of a and b The greatest common divisor of a and b The least common multiple of a and b The product of a and b

3. Let Q be the set of all numbers of the form a/b where a and b are both integers and b cannot be 0. What is the set Q called? The set of rational numbers The set of complex numbers The set of real numbers The set of natural numbers

4. Let a and b be positive integers. Then there exist integers q and r which satisfy a = b*q + r with r greater than or equal to 0 and less than b. What is r called? The quotient The remainder The dividend The divisor

5. Suppose a and b are real numbers (b positive) which satisfy a^2 = b. What is a called? The square of b The exponent of b The base 2 logarithm of b A square root of b

6. Let a be a real number. Then there exists a real number b which satisfies: a + b = 0. Furthermore, if c is another real number which satisfies a + c = 0, then c = b. What is this number b called? The reciprocal of a The additive inverse of a The square of a The square root of a

7. This is a type of sequence of numbers in which the difference between successive terms is constant. Harmonic series Geometric progression Arithmetic progression Geometric series

8. Which function f has the following definition for a real number x? If x is greater than or equal to 0, then f(x) = x, otherwise f(x) = -x. f(x) = -x f(x) = the square root of x f(x) = x^2 f(x) = the absolute value of x

9. A positive integer can be written uniquely (up to order of the factors) as a product of powers of distinct primes. What is this theorem called? The Fundamental Theorem of Algebra The Fundamental Theorem of Galois Theory The Fundamental Theorem of Calculus The Fundamental Theorem of Arithmetic

10. What is the figure that is defined to be the set of all points in the plane that are equidistant from a single point? A square A parabola A line A circle