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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Plus
Multiple of the given number
counterclockwise through 90
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

2. Decreased by
expression
subtraction
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
F - F+1 - F+2.......answer is F+2

3. Are used to indicate sets
righthand digit is 0 or 5
Numerals
Braces
Odd Number

4. Has an equal sign (3x+5 = 14)
one characteristic in common such as similarity of appearance or purpose
the genus of the curve
equation
polynomial

5. Implies a collection or grouping of similar - objects or symbols.
Set
Commutative Law of Multiplication
Associative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space

6. The set of all complex numbers is denoted by
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
C or
Algebraic number theory

7. 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.
rectangular coordinates
Composite Number
Third Axiom of Equality
its the sum of its digits is divisible by 3

8. Number X decreased by 12 divided by forty
counterclockwise through 90
repeated elements
(x-12)/40
base-ten number

9. Less than
T+9
complex number
expression
subtraction

10. A curve in the plane
subtraction
an equation in two variables defines
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The numbers are conventionally plotted using the real part

11. 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
Base of the number system
The multiplication of two complex numbers is defined by the following formula:
To separate a number into prime factors
Commutative Law of Addition

12. No short method has been found for determining whether a number is divisible by
K+6 - K+5 - K+4 K+3.........answer is K+3
7
Forth Axiom of Equality
Composite Number

13. More than one term (5x+4 contains two)
quadratic field
subtraction
polynomial
Associative Law of Multiplication

14. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Third Axiom of Equality
Downward
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.
counterclockwise through 90

15. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
difference
Inversive geometry
Definition of genus
subtraction

16. 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.
Absolute value and argument
Commutative Law of Multiplication
Multiple of the given number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

17. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
solutions
In Diophantine geometry
magnitude and direction

18. 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
16(5+R)
Place Value Concept
Numerals
even and the sum of its digits is divisible by 3

19. 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.
addition
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
Associative Law of Multiplication

20. As shown earlier - c - di is the complex conjugate of the denominator c + di.
quadratic field
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
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.
even and the sum of its digits is divisible by 3

21. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.
7
Associative Law of Addition
Digits
Factor of the given number

22. 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
Prime Number
multiplication
Definition of genus
In Diophantine geometry

23. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
Factor of the given number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

24. The number touching the variable (in the case of 5x - would be 5)
Numerals
coefficient
counterclockwise through 90
The multiplication of two complex numbers is defined by the following formula:

25. More than
upward
addition
algebraic number
magnitude and direction

26. The defining characteristic of a position vector is that it has
Inversive geometry
Commutative Law of Addition
righthand digit is 0 or 5
magnitude and direction

27. Quotient
To separate a number into prime factors
polynomial
division
consecutive whole numbers

28. The place value which corresponds to a given position in a number is determined by the
Base of the number system
repeated elements
the number formed by the two right-hand digits is divisible by 4
complex number

29. The finiteness or not of the number of rational or integer points on an algebraic curve
expression
the genus of the curve
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
base-ten number

30. The objects in a set have at least
The real number a of the complex number z = a + bi
one characteristic in common such as similarity of appearance or purpose
negative
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

31. 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
difference
constructing a parallelogram
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

32. A letter tat represents a number that is unknown (usually X or Y)
order of operations
Analytic number theory
variable
addition

33. Any number that can be divided lnto a given number without a remainder is a
Odd Number
coefficient
Factor of the given number
the genus of the curve

34. Total
Distributive Law
addition
16(5+R)
Even Number

35. 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.
Commutative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
order of operations

36. 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:
right-hand digit is even
monomial
Associative Law of Addition

37. 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.
Complex numbers
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Associative Law of Addition
algebraic number

38. Increased by
Braces
addition
Members of Elements of the Set
a curve - a surface or some other such object in n-dimensional space

39. A number is divisible by 3 if
its the sum of its digits is divisible by 3
Complex numbers
Even Number
F - F+1 - F+2.......answer is F+2

40. Addition of two complex numbers can be done geometrically by
right-hand digit is even
magnitude and direction
complex number
constructing a parallelogram

41. 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
base-ten number
Equal
Definition of genus
In Diophantine geometry

42. 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:
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).
In Diophantine geometry
Multiple of the given number
constructing a parallelogram

43. Does not have an equal sign (3x+5) (2a+9b)
Place Value Concept
counterclockwise through 90
F - F+1 - F+2.......answer is F+2
expression

44. The greatest of 3 consecutive whole numbers - the smallest of which is F
Distributive Law
Definition of genus
constant
F - F+1 - F+2.......answer is F+2

45. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.
Second Axiom of Equality
To separate a number into prime factors
subtraction
Commutative Law of Addition

46. A number is divisible by 8 if
Complex numbers
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
T+9
the number formed by the three right-hand digits is divisible by 8

47. Any number that is exactly divisible by a given number is a
Multiple of the given number
magnitude
righthand digit is 0 or 5
right-hand digit is even

48. 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
repeated elements
The multiplication of two complex numbers is defined by the following formula:
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Natural Numbers

49. Any number that la a multiple of 2 is an
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Base of the number system
variable
Even Number

50. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
right-hand digit is even
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
righthand digit is 0 or 5