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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 that has no factors except itself and 1 is a
equation
Prime Number
complex number
constructing a parallelogram

2. 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.
constructing a parallelogram
The multiplication of two complex numbers is defined by the following formula:
addition
Complex numbers

3. Less than
The real number a of the complex number z = a + bi
solutions
subtraction
Factor of the given number

4. Are often studied as extensions of smaller number fields: a field L is said to be an extension of a field K if L contains K. (For example - the complex numbers C are an extension of the reals R - and the reals R are an extension of the rationals Q.)
Number fields
Analytic number theory
Absolute value and argument
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

5. 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.
division
the number formed by the two right-hand digits is divisible by 4
Commutative Law of Multiplication
Multiple of the given number

6. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Number fields
Natural Numbers
counterclockwise through 90
the sum of its digits is divisible by 9

7. A curve in the plane
righthand digit is 0 or 5
an equation in two variables defines
Digits
Positional notation (place value)

8. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
polynomial
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7
one characteristic in common such as similarity of appearance or purpose

9. Number symbols
Numerals
addition
polynomial
The numbers are conventionally plotted using the real part

10. Plus
even and the sum of its digits is divisible by 3
Associative Law of Addition
Natural Numbers
addition

11. Product
its the sum of its digits is divisible by 3
multiplication
constructing a parallelogram
constant

12. LAWS FOR COMBINING NUMBERS
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the sum of its digits is divisible by 9
16(5+R)

13. Are used to indicate sets
Q-16
Downward
Braces
magnitude and direction

14. Any number that is not a multiple of 2 is an
Base of the number system
16(5+R)
(x-12)/40
Odd Number

15. Subtraction
Prime Factor
Odd Number
difference
coefficient

16. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
equation
coefficient
its the sum of its digits is divisible by 3

17. A number that has factors other than itself and 1 is a
T+9
Analytic number theory
Composite Number
monomial

18. First axiom of equality
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Addition
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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

19. A number is divisible by 5 if its
one characteristic in common such as similarity of appearance or purpose
multiplication
righthand digit is 0 or 5
Even Number

20. 2 -3 -4 -5 -6
subtraction
consecutive whole numbers
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Set

21. Implies a collection or grouping of similar - objects or symbols.
quadratic field
Composite Number
Multiple of the given number
Set

22. Does not have an equal sign (3x+5) (2a+9b)
Digits
the number formed by the two right-hand digits is divisible by 4
expression
addition

23. Product of 16 and the sum of 5 and number R
16(5+R)
F - F+1 - F+2.......answer is F+2
Equal
expression

24. An equation - or system of equations - in two or more variables defines
righthand digit is 0 or 5
Number fields
Commutative Law of Addition
a curve - a surface or some other such object in n-dimensional space

25. Any number that la a multiple of 2 is an
Even Number
constant
The multiplication of two complex numbers is defined by the following formula:
difference

26. A number is divisible by 4 if
monomial
counterclockwise through 90
Natural Numbers
the number formed by the two right-hand digits is divisible by 4

27. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the

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28. This law states that the product of three or more factors is the same regardless of the manner in which they are grouped. Negative signs require no special treatment in the application of this law.
counterclockwise through 90
negative
addition
Associative Law of Multiplication

29. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.
solutions
addition
Third Axiom of Equality
Analytic number theory

30. The greatest of 3 consecutive whole numbers - the smallest of which is F
addition
Associative Law of Addition
F - F+1 - F+2.......answer is F+2
solutions

31. 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
Inversive geometry
its the sum of its digits is divisible by 3
K+6 - K+5 - K+4 K+3.........answer is K+3
In Diophantine geometry

32. Number X decreased by 12 divided by forty
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
(x-12)/40
the number formed by the two right-hand digits is divisible by 4
K+6 - K+5 - K+4 K+3.........answer is K+3

33. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
7
Definition of genus
Composite Number

34. A number is divisible by 9 if
constant
the sum of its digits is divisible by 9
K+6 - K+5 - K+4 K+3.........answer is K+3
Base of the number system

35. 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.
In Diophantine geometry
Odd Number
Analytic number theory
monomial

36. No short method has been found for determining whether a number is divisible by
C or
repeated elements
In Diophantine geometry
7

37. The base which is most commonly used is ten - and the system with ten as a base is called the decimal system (decem is the Latin word for ten). Any number is assumed - unless indicated - to be a
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).
base-ten number
Absolute value and argument
solutions

38. 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
Algebraic number theory
Prime Factor
Commutative Law of Multiplication
Forth Axiom of Equality

39. Any number that is exactly divisible by a given number is a
Distributive Law
Multiple of the given number
order of operations
Absolute value and argument

40. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Forth Axiom of Equality
Downward
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
solutions

41. Increased by
addition
The real number a of the complex number z = a + bi
Composite Number
constant

42. Total
Composite Number
addition
Downward
Q-16

43. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:
Downward
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).
Definition of genus
base-ten number

44. In particular - the square of the imaginary unit is -1: The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed - if i is treated as a number so that di mean
The multiplication of two complex numbers is defined by the following formula:
addition
T+9
Place Value Concept

45. A number is divisible by 3 if
Definition of genus
its the sum of its digits is divisible by 3
negative
the number formed by the three right-hand digits is divisible by 8

46. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the
The numbers are conventionally plotted using the real part
T+9
Complex numbers
Place Value Concept

47. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Number fields
Multiple of the given number
Base of the number system

48. Sixteen less than number Q
Q-16
variable
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
right-hand digit is even

49. The Arabic numerals from 0 through 9 are called
the number formed by the three right-hand digits is divisible by 8
subtraction
Digits
monomial

50. Has an equal sign (3x+5 = 14)
Members of Elements of the Set
The real number a of the complex number z = a + bi
righthand digit is 0 or 5
equation