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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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1. LAWS FOR COMBINING NUMBERS
expression
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Even Number

2. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.
The numbers are conventionally plotted using the real part
even and the sum of its digits is divisible by 3
Commutative Law of Multiplication
addition

3. Implies a collection or grouping of similar - objects or symbols.
(x-12)/40
Factor of the given number
Set
base-ten number

4. 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.
an equation in two variables defines
Analytic number theory
coefficient
Commutative Law of Addition

5. If a factor of a number is prime - it is called a
16(5+R)
counterclockwise through 90
addition
Prime Factor

6. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.
base-ten number
a complex number is real if and only if it equals its conjugate.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Commutative Law of Addition

7. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
equation
(x-12)/40
Associative Law of Addition

8. The objects or symbols in a set are called Numerals - Lines - or Points
The real number a of the complex number z = a + bi
Members of Elements of the Set
Forth Axiom of Equality
Second Axiom of Equality

9. 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.
the genus of the curve
Absolute value and argument
Numerals
Associative Law of Addition

10. 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
To separate a number into prime factors
Braces
subtraction
subtraction

11. Sum
addition
Commutative Law of Addition
Associative Law of Addition
variable

12. Has an equal sign (3x+5 = 14)
division
the genus of the curve
equation
Commutative Law of Addition

13. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
the number formed by the two right-hand digits is divisible by 4
Inversive geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

14. The square roots of a + bi (with b ? 0) are - where and where sgn is the signum function. This can be seen by squaring to obtain a + bi.
Prime Number
constant
the number formed by the two right-hand digits is divisible by 4
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

15. 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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16. 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).
Natural Numbers
positive
Associative Law of Addition

17. Number X decreased by 12 divided by forty
Composite Number
Associative Law of Addition
Definition of genus
(x-12)/40

18. No short method has been found for determining whether a number is divisible by
7
Digits
In Diophantine geometry
a curve - a surface or some other such object in n-dimensional space

19. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Odd Number
constant
Positional notation (place value)

20. Quotient
variable
consecutive whole numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
division

21. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
addition
Braces
Set

22. The Arabic numerals from 0 through 9 are called
addition
magnitude and direction
a complex number is real if and only if it equals its conjugate.
Digits

23. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Absolute value and argument
the number formed by the three right-hand digits is divisible by 8
rectangular coordinates
the sum of its digits is divisible by 9

24. Any number that can be divided lnto a given number without a remainder is a
expression
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Factor of the given number
the number formed by the two right-hand digits is divisible by 4

25. Less than
Associative Law of Addition
subtraction
In Diophantine geometry
monomial

26. Increased by
7
variable
magnitude
addition

27. A form of coding in which the value of each digit of a number depends upon its position in relation to the other digits of the number. The convention used in our number system is that each digit has a higher place value than those digits to the right
Distributive Law
Downward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Positional notation (place value)

28. Total
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Factor of the given number
algebraic number

29. 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.
Algebraic number theory
the genus of the curve
Associative Law of Multiplication
upward

30. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
addition
coefficient
F - F+1 - F+2.......answer is F+2
upward

31. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Prime Number
negative

32. Number symbols
Numerals
one characteristic in common such as similarity of appearance or purpose
Factor of the given number
Inversive geometry

33. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
variable
subtraction
constructing a parallelogram

34. A number is divisible by 4 if
Third Axiom of Equality
monomial
the number formed by the two right-hand digits is divisible by 4
Base of the number system

35. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f
algebraic number
Prime Factor
subtraction
rectangular coordinates

36. A letter tat represents a number that is unknown (usually X or Y)
variable
one characteristic in common such as similarity of appearance or purpose
difference
Commutative Law of Addition

37. The number touching the variable (in the case of 5x - would be 5)
coefficient
base-ten number
complex number
repeated elements

38. 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.
constructing a parallelogram
rectangular coordinates
Commutative Law of Addition
Third Axiom of Equality

39. The greatest of 3 consecutive whole numbers - the smallest of which is F
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.
Number fields
even and the sum of its digits is divisible by 3
F - F+1 - F+2.......answer is F+2

40. A number is divisible by 2 if
right-hand digit is even
the genus of the curve
even and the sum of its digits is divisible by 3
Commutative Law of Multiplication

41. Are used to indicate sets
Braces
Q-16
constructing a parallelogram
addition

42. The defining characteristic of a position vector is that it has
the genus of the curve
polynomial
magnitude and direction
solutions

43. Any number that is not a multiple of 2 is an
Odd Number
upward
complex number
Analytic number theory

44. 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 -
subtraction
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Third Axiom of Equality
even and the sum of its digits is divisible by 3

45. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
order of operations
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Factor of the given number

46. Does not have an equal sign (3x+5) (2a+9b)
the genus of the curve
Composite Number
expression
The real number a of the complex number z = a + bi

47. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
a complex number is real if and only if it equals its conjugate.
magnitude and direction
T+9

48. Number T increased by 9
even and the sum of its digits is divisible by 3
T+9
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.
The numbers are conventionally plotted using the real part

49. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Absolute value and argument
Digits
positive
Associative Law of Addition

50. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
F - F+1 - F+2.......answer is F+2
right-hand digit is even
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.