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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. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
Natural Numbers
multiplication
Composite Number

2. A curve in the plane
Factor of the given number
addition
an equation in two variables defines
Forth Axiom of Equality

3. Any number that can be divided lnto a given number without a remainder is a
subtraction
Place Value Concept
counterclockwise through 90
Factor of the given number

4. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
complex number
addition
The real number a of the complex number z = a + bi

5. Plus
Digits
addition
Natural Numbers
K+6 - K+5 - K+4 K+3.........answer is K+3

6. Quotient
division
Composite Number
The real number a of the complex number z = a + bi
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.

7. Product
the sum of its digits is divisible by 9
multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
monomial

8. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
In Diophantine geometry
repeated elements
order of operations

9. 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.)
Definition of genus
negative
expression
Number fields

10. 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.
addition
addition
Third Axiom of Equality
expression

11. The number touching the variable (in the case of 5x - would be 5)
one characteristic in common such as similarity of appearance or purpose
Absolute value and argument
the number formed by the two right-hand digits is divisible by 4
coefficient

12. Decreased by
the number formed by the three right-hand digits is divisible by 8
subtraction
quadratic field
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

13. The Arabic numerals from 0 through 9 are called
Digits
monomial
The multiplication of two complex numbers is defined by the following formula:
expression

14. 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
T+9
the sum of its digits is divisible by 9
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Algebraic number theory

15. A number is divisible by 6 if it is
magnitude
variable
righthand digit is 0 or 5
even and the sum of its digits is divisible by 3

16. 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.
Associative Law of Multiplication
Base of the number system
Commutative Law of Addition
Number fields

17. The relative greatness of positive and negative numbers
counterclockwise through 90
magnitude
negative
one characteristic in common such as similarity of appearance or purpose

18. Number T increased by 9
Number fields
rectangular coordinates
coefficient
T+9

19. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag
monomial
Set
order of operations
complex number

20. The finiteness or not of the number of rational or integer points on an algebraic curve
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 genus of the curve
Composite Number
subtraction

21. As shown earlier - c - di is the complex conjugate of the denominator c + di.
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Composite Number
Positional notation (place value)

22. Subtraction
difference
Algebraic number theory
constructing a parallelogram
monomial

23. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Composite Number
Inversive geometry
counterclockwise through 90
7

24. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
addition
The real number a of the complex number z = a + bi
upward
order of operations

25. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
polynomial
repeated elements
subtraction
Downward

26. Total
right-hand digit is even
coefficient
addition
variable

27. A number is divisible by 5 if its
The real number a of the complex number z = a + bi
righthand digit is 0 or 5
division
Base of the number system

28. A letter tat represents a number that is unknown (usually X or Y)
consecutive whole numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
variable

29. A number that has no factors except itself and 1 is a
Associative Law of Addition
a curve - a surface or some other such object in n-dimensional space
Prime Number
Second Axiom of Equality

30. One term (5x or 4)
7
Place Value Concept
monomial
repeated elements

31. 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.
Commutative Law of Addition
The numbers are conventionally plotted using the real part
Prime Factor
The real number a of the complex number z = a + bi

32. The objects or symbols in a set are called Numerals - Lines - or Points
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Multiplication
Commutative Law of Addition
Members of Elements of the Set

33. 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
Distributive Law
counterclockwise through 90
C or
To separate a number into prime factors

34. A number is divisible by 8 if
monomial
Even Number
To separate a number into prime factors
the number formed by the three right-hand digits is divisible by 8

35. 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:
(x-12)/40
addition
To separate a number into prime factors

36. The number without a variable (5m+2). In this case - 2
Distributive Law
Complex numbers
constant
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

37. A number is divisible by 4 if
division
algebraic number
the number formed by the two right-hand digits is divisible by 4
addition

38. 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
a complex number is real if and only if it equals its conjugate.
The numbers are conventionally plotted using the real part
In Diophantine geometry
Base of the number system

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.
quadratic field
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
its the sum of its digits is divisible by 3

40. 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
Even Number
polynomial
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

41. 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.
Forth Axiom of Equality
Associative Law of Addition
coefficient
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

42. Any number that is exactly divisible by a given number is a
Multiple of the given number
order of operations
16(5+R)
the number formed by the two right-hand digits is divisible by 4

43. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
addition
rectangular coordinates
Complex numbers
Distributive Law

44. More than one term (5x+4 contains two)
even and the sum of its digits is divisible by 3
subtraction
polynomial
solutions

45. Has an equal sign (3x+5 = 14)
Q-16
In Diophantine geometry
equation
F - F+1 - F+2.......answer is F+2

46. Sixteen less than number Q
the number formed by the two right-hand digits is divisible by 4
Associative Law of Addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Q-16

47. The central problem of Diophantine geometry is to determine when a Diophantine equation has
an equation in two variables defines
quadratic field
Third Axiom of Equality
solutions

48. 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.
Complex numbers
Analytic number theory
coefficient
its the sum of its digits is divisible by 3

49. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Associative Law of Multiplication
algebraic number
polynomial

50. 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 -
In Diophantine geometry
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Multiplication
Definition of genus