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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. A number is divisible by 6 if it is
Prime Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
even and the sum of its digits is divisible by 3
quadratic field

2. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.
Analytic number theory
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude and direction
Prime Factor

3. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
the genus of the curve
upward
order of operations
Commutative Law of Multiplication

4. Remainder
Commutative Law of Addition
order of operations
subtraction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

5. Has an equal sign (3x+5 = 14)
Third Axiom of Equality
equation
T+9
Associative Law of Multiplication

6. Allow for solutions to certain equations that have no real solution: the equation has no real solution - since the square of a real number is 0 or positive.
positive
Prime Number
Complex numbers
magnitude and direction

7. The central problem of Diophantine geometry is to determine when a Diophantine equation has
16(5+R)
complex number
quadratic field
solutions

8. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a
Positional notation (place value)
subtraction
Commutative Law of Addition
Algebraic number theory

9. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.
magnitude and direction
addition
Associative Law of Addition
Forth Axiom of Equality

10. First axiom of equality
the genus of the curve
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.
Composite Number

11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
Odd Number
equation
magnitude and direction

12. The number without a variable (5m+2). In this case - 2
Analytic number theory
constant
Set
monomial

13. More than one term (5x+4 contains two)
polynomial
Distributive Law
Prime Number
F - F+1 - F+2.......answer is F+2

14. Any number that la a multiple of 2 is an
In Diophantine geometry
negative
Even Number
addition

15. The numbers which are used for counting in our number system are sometimes called
Algebraic number theory
consecutive whole numbers
righthand digit is 0 or 5
Natural Numbers

16. Number T increased by 9
addition
Analytic number theory
The real number a of the complex number z = a + bi
T+9

17. The set of all complex numbers is denoted by
C or
Prime Number
Multiple of the given number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

18. One asks whether there are any rational points (points all of whose coordinates are rationals) or integral points (points all of whose coordinates are integers) on the curve or surface. If there are any such points - the next step is to ask how many
F - F+1 - F+2.......answer is F+2
equation
In Diophantine geometry
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.

19. A number that has no factors except itself and 1 is a
Prime Number
Braces
To separate a number into prime factors
Set

20. A number is divisible by 5 if its
T+9
To separate a number into prime factors
Downward
righthand digit is 0 or 5

21. Any number that is exactly divisible by a given number is a
Associative Law of Multiplication
Multiple of the given number
Associative Law of Addition
the sum of its digits is divisible by 9

22. If a factor of a number is prime - it is called a
Absolute value and argument
addition
Prime Factor
coefficient

23. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th
Definition of genus
To separate a number into prime factors
Commutative Law of Addition
In Diophantine geometry

24. Does not have an equal sign (3x+5) (2a+9b)
polynomial
upward
expression
Downward

25. Sixteen less than number Q
equation
a curve - a surface or some other such object in n-dimensional space
Q-16
Braces

26. A number that has factors other than itself and 1 is a
Composite Number
a curve - a surface or some other such object in n-dimensional space
16(5+R)
negative

27. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
the number formed by the two right-hand digits is divisible by 4
a curve - a surface or some other such object in n-dimensional space
Absolute value and argument
order of operations

28. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Complex numbers
subtraction
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
rectangular coordinates

29. The relative greatness of positive and negative numbers
multiplication
magnitude
righthand digit is 0 or 5
Number fields

30. If two equal quantities are divided by the same quantity - the resulting quotients are equal. If equals are divided by equals - the results are equal.
Forth Axiom of Equality
Positional notation (place value)
addition
difference

31. Total
addition
Forth Axiom of Equality
To separate a number into prime factors
In Diophantine geometry

32. Integers greater than zero and less than 5 form a set - as follows:
solutions
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.
Commutative Law of Addition

33. Number symbols
negative
F - F+1 - F+2.......answer is F+2
the genus of the curve
Numerals

34. The finiteness or not of the number of rational or integer points on an algebraic curve
rectangular coordinates
algebraic number
consecutive whole numbers
the genus of the curve

35. Plus
an equation in two variables defines
Number fields
The numbers are conventionally plotted using the real part
addition

36. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
positive
Positional notation (place value)
rectangular coordinates

37. If z is a real number (i.e. - y = 0) - then r = |x|. In general - by Pythagoras' theorem - r is the distance of the point P representing the complex number z to the origin.
counterclockwise through 90
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Odd Number
Members of Elements of the Set

38. The objects or symbols in a set are called Numerals - Lines - or Points
subtraction
right-hand digit is even
If the same quantity is added to each of two equal quantities - the resulting quantities are equal. If equals are added to equals - the results are equal.
Members of Elements of the Set

39. Implies a collection or grouping of similar - objects or symbols.
Set
Multiple of the given number
Natural Numbers
Positional notation (place value)

40. Less than
Associative Law of Addition
positive
addition
subtraction

41. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor
Absolute value and argument
To separate a number into prime factors
expression
Odd Number

42. Sum
Set
equation
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

43. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.
F - F+1 - F+2.......answer is F+2
righthand digit is 0 or 5
Distributive Law
quadratic field

44. One term (5x or 4)
In Diophantine geometry
the number formed by the two right-hand digits is divisible by 4
monomial
Associative Law of Multiplication

45. As shown earlier - c - di is the complex conjugate of the denominator c + di.
In Diophantine geometry
monomial
Algebraic number theory
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

46. Since the elements of the set {2 - 4 - e} are the same as the elements of{4 - 2 - e} - these two sets are said to be
addition corresponds to vector addition while multiplication corresponds to multiplying their magnitudes and adding their arguments (i.e. the angles they make with the x axis).
the number formed by the two right-hand digits is divisible by 4
Equal
addition

47. Are used to indicate sets
upward
T+9
righthand digit is 0 or 5
Braces

48. The objects in a set have at least
the genus of the curve
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
one characteristic in common such as similarity of appearance or purpose

49. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
rectangular coordinates
Algebraic number theory
Number fields
counterclockwise through 90

50. A number is divisible by 8 if
16(5+R)
monomial
addition
the number formed by the three right-hand digits is divisible by 8