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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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Subjects
:
clep
,
math
Instructions:
Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can
study here
.
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. 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.
magnitude and direction
The numbers are conventionally plotted using the real part
Algebraic number theory
Numerals
2. 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.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Commutative Law of Addition
variable
The multiplication of two complex numbers is defined by the following formula:
3. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Downward
Complex numbers
Third Axiom of Equality
4. Product
multiplication
base-ten number
Composite Number
repeated elements
5. 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
addition
Algebraic number theory
an equation in two variables defines
In Diophantine geometry
6. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Factor of the given number
Place Value Concept
order of operations
constructing a parallelogram
7. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
Natural Numbers
upward
Algebraic number theory
8. A number that has no factors except itself and 1 is a
rectangular coordinates
Even Number
Prime Number
16(5+R)
9. Sixteen less than number Q
Q-16
Inversive geometry
Definition of genus
Associative Law of Addition
10. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th
Definition of genus
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Positional notation (place value)
constant
11. LAWS FOR COMBINING NUMBERS
complex number
Analytic number theory
rectangular coordinates
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
12. 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:
solutions
Odd Number
Associative Law of Multiplication
13. The real and imaginary parts of a complex number can be extracted using the conjugate:
variable
The real number a of the complex number z = a + bi
a complex number is real if and only if it equals its conjugate.
upward
14. A number is divisible by 5 if its
righthand digit is 0 or 5
(x-12)/40
Analytic number theory
Place Value Concept
15. The objects in a set have at least
Second Axiom of Equality
Complex numbers
Factor of the given number
one characteristic in common such as similarity of appearance or purpose
16. A number is divisible by 9 if
the sum of its digits is divisible by 9
Number fields
upward
Positional notation (place value)
17. Any number that is not a multiple of 2 is an
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Odd Number
repeated elements
Complex numbers
18. Number X decreased by 12 divided by forty
(x-12)/40
Set
Downward
Digits
19. More than one term (5x+4 contains two)
polynomial
Algebraic number theory
the number formed by the three right-hand digits is divisible by 8
magnitude
20. 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.
In Diophantine geometry
Commutative Law of Addition
Complex numbers
Associative Law of Addition
21. 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
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
In Diophantine geometry
C or
Associative Law of Addition
22. Increased by
Odd Number
counterclockwise through 90
The multiplication of two complex numbers is defined by the following formula:
addition
23. 2 -3 -4 -5 -6
consecutive whole numbers
multiplication
addition
Associative Law of Multiplication
24. Sum
Associative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Q-16
addition
25. A number is divisible by 8 if
T+9
Composite Number
magnitude
the number formed by the three right-hand digits is divisible by 8
26. Any number that la a multiple of 2 is an
an equation in two variables defines
Even Number
expression
coefficient
27. Remainder
subtraction
a curve - a surface or some other such object in n-dimensional space
variable
Analytic number theory
28. The place value which corresponds to a given position in a number is determined by the
an equation in two variables defines
Commutative Law of Multiplication
Second Axiom of Equality
Base of the number system
29. A number is divisible by 3 if
upward
polynomial
its the sum of its digits is divisible by 3
repeated elements
30. Plus
addition
Third Axiom of Equality
a curve - a surface or some other such object in n-dimensional space
C or
31. 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.)
Associative Law of Addition
monomial
Commutative Law of Multiplication
Number fields
32. 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.
Associative Law of Multiplication
Factor of the given number
multiplication
The real number a of the complex number z = a + bi
33. 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.
Second Axiom of Equality
constant
The multiplication of two complex numbers is defined by the following formula:
magnitude
34. 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.
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
negative
K+6 - K+5 - K+4 K+3.........answer is K+3
35. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
quadratic field
expression
rectangular coordinates
Forth Axiom of Equality
36. 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.
Associative Law of Addition
Third Axiom of Equality
magnitude and direction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
37. 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 Addition
the number formed by the two right-hand digits is divisible by 4
Equal
Commutative Law of Addition
38. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Multiple of the given number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The numbers are conventionally plotted using the real part
39. Does not have an equal sign (3x+5) (2a+9b)
expression
Odd Number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Commutative Law of Multiplication
40. Implies a collection or grouping of similar - objects or symbols.
Analytic number theory
Set
coefficient
The numbers are conventionally plotted using the real part
41. The objects or symbols in a set are called Numerals - Lines - or Points
its the sum of its digits is divisible by 3
Members of Elements of the Set
Equal
variable
42. 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.
Associative Law of Addition
expression
Odd Number
Set
43. Are used to indicate sets
Braces
one characteristic in common such as similarity of appearance or purpose
Associative Law of Multiplication
addition
44. As shown earlier - c - di is the complex conjugate of the denominator c + di.
addition
positive
the number formed by the two right-hand digits is divisible by 4
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
45. The Arabic numerals from 0 through 9 are called
Digits
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
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).
Analytic number theory
46. The set of all complex numbers is denoted by
its the sum of its digits is divisible by 3
addition
magnitude and direction
C or
47. A letter tat represents a number that is unknown (usually X or Y)
The numbers are conventionally plotted using the real part
Q-16
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
variable
48. The greatest of 3 consecutive whole numbers - the smallest of which is F
righthand digit is 0 or 5
the genus of the curve
F - F+1 - F+2.......answer is F+2
base-ten number
49. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
Definition of genus
positive
a complex number is real if and only if it equals its conjugate.
50. Product of 16 and the sum of 5 and number R
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Commutative Law of Addition
base-ten number
16(5+R)