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CLEP General Mathematics: Number Systems And Sets
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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. 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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
7
Associative Law of Addition
addition
2. Less than
counterclockwise through 90
Algebraic number theory
In Diophantine geometry
subtraction
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
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
In Diophantine geometry
Forth Axiom of Equality
4. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
even and the sum of its digits is divisible by 3
multiplication
Prime Number
counterclockwise through 90
5. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Place Value Concept
Prime Factor
rectangular coordinates
K+6 - K+5 - K+4 K+3.........answer is K+3
6. Plus
Braces
addition
solutions
Associative Law of Addition
7. An equation - or system of equations - in two or more variables defines
Commutative Law of Addition
a curve - a surface or some other such object in n-dimensional space
7
Equal
8. One term (5x or 4)
monomial
solutions
the sum of its digits is divisible by 9
C or
9. 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
righthand digit is 0 or 5
base-ten number
Downward
C or
10. The place value which corresponds to a given position in a number is determined by the
T+9
Base of the number system
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).
Members of Elements of the Set
11. 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
Third Axiom of Equality
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Q-16
12. The greatest of 3 consecutive whole numbers - the smallest of which is F
difference
F - F+1 - F+2.......answer is F+2
even and the sum of its digits is divisible by 3
an equation in two variables defines
13. More than
addition
subtraction
Definition of genus
Complex numbers
14. A curve in the plane
complex number
addition
an equation in two variables defines
consecutive whole numbers
15. 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.
Natural Numbers
Associative Law of Addition
the sum of its digits is divisible by 9
16(5+R)
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:
rectangular coordinates
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
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).
F - F+1 - F+2.......answer is F+2
17. 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.)
Third Axiom of Equality
Number fields
positive
polynomial
18. Implies a collection or grouping of similar - objects or symbols.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Set
Equal
equation
19. 2 -3 -4 -5 -6
Third Axiom of Equality
Natural Numbers
consecutive whole numbers
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
20. 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
difference
rectangular coordinates
Algebraic number theory
monomial
21. Any number that la a multiple of 2 is an
Even Number
multiplication
an equation in two variables defines
polynomial
22. Number T increased by 9
the number formed by the three right-hand digits is divisible by 8
T+9
Set
repeated elements
23. The central problem of Diophantine geometry is to determine when a Diophantine equation has
expression
Digits
solutions
Composite Number
24. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
Base of the number system
upward
16(5+R)
25. A number that has factors other than itself and 1 is a
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
consecutive whole numbers
equation
Composite Number
26. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
7
Factor of the given number
Odd Number
repeated elements
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
Complex numbers
an equation in two variables defines
positive
28. 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.
Commutative Law of Addition
Equal
the sum of its digits is divisible by 9
subtraction
29. Integers greater than zero and less than 5 form a set - as follows:
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The real number a of the complex number z = a + bi
addition
30. Subtraction
T+9
addition
difference
base-ten number
31. Any number that is not a multiple of 2 is an
T+9
Odd Number
Prime Factor
Positional notation (place value)
32. A number that has no factors except itself and 1 is a
rectangular coordinates
Inversive geometry
addition
Prime Number
33. Are used to indicate sets
Braces
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
multiplication
positive
34. The relative greatness of positive and negative numbers
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).
Downward
Forth Axiom of Equality
magnitude
35. The Arabic numerals from 0 through 9 are called
Forth Axiom of Equality
division
Digits
subtraction
36. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
a curve - a surface or some other such object in n-dimensional space
In Diophantine geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Downward
37. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
division
negative
In Diophantine geometry
Definition of genus
38. 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
complex number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Natural Numbers
39. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
Forth Axiom of Equality
Complex numbers
Third Axiom of Equality
40. 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
Definition of genus
complex number
The numbers are conventionally plotted using the real part
magnitude
41. A number is divisible by 8 if
In Diophantine geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
magnitude
the number formed by the three right-hand digits is divisible by 8
42. Sixteen less than number Q
repeated elements
equation
Inversive geometry
Q-16
43. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Q-16
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
subtraction
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
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).
Commutative Law of Addition
45. A letter tat represents a number that is unknown (usually X or Y)
repeated elements
solutions
Odd Number
variable
46. 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.
even and the sum of its digits is divisible by 3
Third Axiom of Equality
addition
In Diophantine geometry
47. 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.
addition
Forth Axiom of Equality
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
48. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Set
Factor of the given number
variable
Inversive geometry
49. Does not have an equal sign (3x+5) (2a+9b)
expression
a curve - a surface or some other such object in n-dimensional space
(x-12)/40
difference
50. The objects in a set have at least
Second Axiom of Equality
addition
one characteristic in common such as similarity of appearance or purpose
even and the sum of its digits is divisible by 3
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