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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. Subtraction
difference
the sum of its digits is divisible by 9
right-hand digit is even
solutions

2. 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
K+6 - K+5 - K+4 K+3.........answer is K+3
base-ten number
Place Value Concept
constructing a parallelogram

3. 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
In Diophantine geometry
Natural Numbers
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

4. Plus
Commutative Law of Addition
addition
Positional notation (place value)
expression

5. A number is divisible by 5 if its
counterclockwise through 90
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
righthand digit is 0 or 5

6. The set of all complex numbers is denoted by
C or
order of operations
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.

7. A number is divisible by 2 if
right-hand digit is even
T+9
subtraction
counterclockwise through 90

8. 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.
right-hand digit is even
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
polynomial
a curve - a surface or some other such object in n-dimensional space

9. 2 -3 -4 -5 -6
Number fields
Commutative Law of Multiplication
consecutive whole numbers
Associative Law of Multiplication

10. The objects or symbols in a set are called Numerals - Lines - or Points
the number formed by the two right-hand digits is divisible by 4
variable
Members of Elements of the Set
solutions

11. Product of 16 and the sum of 5 and number R
Complex numbers
16(5+R)
Braces
equation

12. 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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Prime Factor
variable
Place Value Concept

13. 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.
repeated elements
Complex numbers
Inversive geometry
Q-16

14. Does not have an equal sign (3x+5) (2a+9b)
Prime Factor
expression
K+6 - K+5 - K+4 K+3.........answer is K+3
C or

15. A number that has factors other than itself and 1 is a
The numbers are conventionally plotted using the real part
Composite Number
magnitude and direction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

16. The greatest of 3 consecutive whole numbers - the smallest of which is F
coefficient
Q-16
righthand digit is 0 or 5
F - F+1 - F+2.......answer is F+2

17. Addition of two complex numbers can be done geometrically by
Composite Number
constructing a parallelogram
counterclockwise through 90
expression

18. 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.
Members of Elements of the Set
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
algebraic number
Commutative Law of Addition

19. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th
The real number a of the complex number z = a + bi
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
subtraction
right-hand digit is even

20. Has an equal sign (3x+5 = 14)
Algebraic number theory
equation
the number formed by the three right-hand digits is divisible by 8
coefficient

21. 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
Third Axiom of Equality
Even Number
Positional notation (place value)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

22. No short method has been found for determining whether a number is divisible by
F - F+1 - F+2.......answer is F+2
The multiplication of two complex numbers is defined by the following formula:
Braces
7

23. The numbers which are used for counting in our number system are sometimes called
The multiplication of two complex numbers is defined by the following formula:
subtraction
Associative Law of Addition
Natural Numbers

24. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Positional notation (place value)
Numerals

25. Any number that is exactly divisible by a given number is a
Associative Law of Multiplication
Braces
C or
Multiple of the given number

26. 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.
Number fields
Commutative Law of Addition
subtraction
magnitude and direction

27. 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
Even Number
7
Commutative Law of Addition

28. 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.
Odd Number
magnitude and direction
a curve - a surface or some other such object in n-dimensional space
Forth Axiom of Equality

29. Any number that is not a multiple of 2 is an
Odd Number
The numbers are conventionally plotted using the real part
a curve - a surface or some other such object in n-dimensional space
Composite Number

30. The finiteness or not of the number of rational or integer points on an algebraic curve
Commutative Law of Multiplication
the genus of the curve
Q-16
magnitude

31. 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:
Digits
The real number a of the complex number z = a + bi
Number fields

32. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
expression

33. 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:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
To separate a number into prime factors
In Diophantine geometry

34. A number is divisible by 9 if
the sum of its digits is divisible by 9
Digits
the number formed by the two right-hand digits is divisible by 4
(x-12)/40

35. 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.
even and the sum of its digits is divisible by 3
difference
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

36. A number that has no factors except itself and 1 is a
Prime Number
solutions
positive
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

37. If the same quantity is subtracted from each of two equal quantities - the resulting quantities are equal. If equals are subtracted from equals - the results are equal.
counterclockwise through 90
Second Axiom of Equality
In Diophantine geometry
constant

38. Product
solutions
division
multiplication
addition

39. 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.
Associative Law of Addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the sum of its digits is divisible by 9

40. First axiom of equality
Place Value Concept
Positional notation (place value)
the number formed by the two right-hand digits is divisible by 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.

41. Any number that la a multiple of 2 is an
difference
To separate a number into prime factors
Complex numbers
Even Number

42. Any number that can be divided lnto a given number without a remainder is a
multiplication
Factor of the given number
a complex number is real if and only if it equals its conjugate.
Downward

43. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
multiplication
Braces
7
K+6 - K+5 - K+4 K+3.........answer is K+3

44. The defining characteristic of a position vector is that it has
magnitude and direction
(x-12)/40
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition

45. A number is divisible by 4 if
Set
the number formed by the two right-hand digits is divisible by 4
its the sum of its digits is divisible by 3
division

46. A letter tat represents a number that is unknown (usually X or Y)
Set
Definition of genus
Place Value Concept
variable

47. 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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48. The number without a variable (5m+2). In this case - 2
constant
To separate a number into prime factors
a complex number is real if and only if it equals its conjugate.
addition

49. 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
a curve - a surface or some other such object in n-dimensional space
Equal
Multiple of the given number
Numerals

50. 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
Multiple of the given number
addition
an equation in two variables defines
To separate a number into prime factors