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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 shown earlier - c - di is the complex conjugate of the denominator c + di.
Algebraic number theory
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Analytic number theory
2. A number is divisible by 8 if
Multiple of the given number
the number formed by the three right-hand digits is divisible by 8
Even Number
magnitude
3. The defining characteristic of a position vector is that it has
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
magnitude and direction
Downward
4. 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
consecutive whole numbers
algebraic number
a complex number is real if and only if it equals its conjugate.
addition
5. Increased by
The numbers are conventionally plotted using the real part
addition
T+9
algebraic number
6. Number symbols
Numerals
constructing a parallelogram
the genus of the curve
Multiple of the given number
7. Number T increased by 9
repeated elements
Set
the number formed by the two right-hand digits is divisible by 4
T+9
8. Remainder
the genus of the curve
Inversive geometry
order of operations
subtraction
9. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
magnitude and direction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
addition
even and the sum of its digits is divisible by 3
10. The greatest of 3 consecutive whole numbers - the smallest of which is F
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Number fields
F - F+1 - F+2.......answer is F+2
11. Any number that la a multiple of 2 is an
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.
Even Number
Composite Number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
12. 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
addition
C or
The multiplication of two complex numbers is defined by the following formula:
Number fields
13. 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
Downward
multiplication
C or
14. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
polynomial
In Diophantine geometry
counterclockwise through 90
15. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
polynomial
Analytic number theory
Inversive geometry
Third Axiom of Equality
16. A number that has factors other than itself and 1 is a
The multiplication of two complex numbers is defined by the following formula:
division
Composite Number
Inversive geometry
17. First axiom of equality
addition
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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
order of operations
18. Decreased by
upward
Natural Numbers
subtraction
Number fields
19. Does not have an equal sign (3x+5) (2a+9b)
expression
addition
The real number a of the complex number z = a + bi
the sum of its digits is divisible by 9
20. 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:
Inversive geometry
complex number
Members of Elements of the Set
21. Product
Distributive Law
algebraic number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
multiplication
22. 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:
Associative Law of Addition
Downward
rectangular coordinates
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).
23. 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.)
addition
Number fields
base-ten number
Associative Law of Multiplication
24. A letter tat represents a number that is unknown (usually X or Y)
Members of Elements of the Set
variable
monomial
subtraction
25. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.
base-ten number
division
quadratic field
upward
26. A number is divisible by 3 if
Composite Number
C or
its the sum of its digits is divisible by 3
an equation in two variables defines
27. 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.
Base of the number system
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Braces
difference
28. One term (5x or 4)
monomial
repeated elements
Inversive geometry
Set
29. 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
The multiplication of two complex numbers is defined by the following formula:
difference
the number formed by the three right-hand digits is divisible by 8
30. Less than
equation
an equation in two variables defines
coefficient
subtraction
31. 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.
the sum of its digits is divisible by 9
C or
Analytic number theory
constant
32. A number is divisible by 9 if
constant
Algebraic number theory
Associative Law of Addition
the sum of its digits is divisible by 9
33. 2 -3 -4 -5 -6
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
C or
Factor of the given number
consecutive whole numbers
34. Has an equal sign (3x+5 = 14)
Equal
equation
Members of Elements of the Set
Numerals
35. Any number that is not a multiple of 2 is an
The multiplication of two complex numbers is defined by the following formula:
The numbers are conventionally plotted using the real part
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Odd Number
36. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
base-ten number
Set
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
37. The objects or symbols in a set are called Numerals - Lines - or Points
Factor of the given number
base-ten number
Members of Elements of the Set
Algebraic number theory
38. More than
subtraction
counterclockwise through 90
Numerals
addition
39. The relative greatness of positive and negative numbers
16(5+R)
magnitude
Factor of the given number
To separate a number into prime factors
40. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
division
order of operations
rectangular coordinates
one characteristic in common such as similarity of appearance or purpose
41. Sum
monomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
difference
addition
42. The Arabic numerals from 0 through 9 are called
Positional notation (place value)
Digits
one characteristic in common such as similarity of appearance or purpose
magnitude and direction
43. Any number that can be divided lnto a given number without a remainder is a
Associative Law of Multiplication
The real number a of the complex number z = a + bi
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).
Factor of the given number
44. Are used to indicate sets
its the sum of its digits is divisible by 3
solutions
Braces
Associative Law of Addition
45. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
C or
upward
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Second Axiom of Equality
46. 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 multiplication of two complex numbers is defined by the following formula:
Commutative Law of Multiplication
In Diophantine geometry
Downward
47. The real and imaginary parts of a complex number can be extracted using the conjugate:
The numbers are conventionally plotted using the real part
upward
Commutative Law of Addition
a complex number is real if and only if it equals its conjugate.
48. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Commutative Law of Multiplication
coefficient
Place Value Concept
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.
multiplication
Odd Number
Associative Law of Multiplication
coefficient
50. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
even and the sum of its digits is divisible by 3
a curve - a surface or some other such object in n-dimensional space
Associative Law of Multiplication
repeated elements