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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
Start Test
Study First
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. Any number that can be divided lnto a given number without a remainder is a
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.
Factor of the given number
Natural Numbers
equation
2. 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.
complex number
its the sum of its digits is divisible by 3
base-ten number
3. 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.
solutions
Associative Law of Addition
addition
subtraction
4. A number is divisible by 6 if it is
order of operations
even and the sum of its digits is divisible by 3
quadratic field
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).
5. 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
Digits
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
division
6. A number that has factors other than itself and 1 is a
Associative Law of Multiplication
Composite Number
7
Second Axiom of Equality
7. More than one term (5x+4 contains two)
The multiplication of two complex numbers is defined by the following formula:
difference
polynomial
consecutive whole numbers
8. A number is divisible by 3 if
In Diophantine geometry
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
its the sum of its digits is divisible by 3
9. The set of all complex numbers is denoted by
coefficient
Q-16
Second Axiom of Equality
C or
10. 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
To separate a number into prime factors
Natural Numbers
Algebraic number theory
11. Are used to indicate sets
Third Axiom of Equality
T+9
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).
Braces
12. The relative greatness of positive and negative numbers
addition
Base of the number system
magnitude
T+9
13. Another way of encoding points in the complex plane other than using the x- and y-coordinates is to use the distance of a point P to O - the point whose coordinates are (0 - 0) (the origin) - and the angle of the line through P and O. This idea leads
positive
Members of Elements of the Set
Absolute value and argument
Positional notation (place value)
14. Number X decreased by 12 divided by forty
Absolute value and argument
Prime Factor
multiplication
(x-12)/40
15. 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
division
Members of Elements of the Set
Equal
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.
16. Less than
subtraction
expression
difference
Members of Elements of the Set
17. 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
Second Axiom of Equality
The multiplication of two complex numbers is defined by the following formula:
counterclockwise through 90
18. 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:
order of operations
expression
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
19. The greatest of 3 consecutive whole numbers - the smallest of which is F
Associative Law of Multiplication
C or
a curve - a surface or some other such object in n-dimensional space
F - F+1 - F+2.......answer is F+2
20. 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
quadratic field
Multiple of the given number
multiplication
21. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Base of the number system
Downward
Algebraic number theory
Associative Law of Multiplication
22. 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.
solutions
Factor of the given number
Third Axiom of Equality
variable
23. A number that has no factors except itself and 1 is a
The numbers are conventionally plotted using the real part
Distributive Law
Commutative Law of Multiplication
Prime Number
24. 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
the genus of the curve
addition
base-ten number
subtraction
25. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
upward
Third Axiom of Equality
its the sum of its digits is divisible by 3
26. 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
upward
Associative Law of Addition
Positional notation (place value)
The numbers are conventionally plotted using the real part
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.
one characteristic in common such as similarity of appearance or purpose
repeated elements
Analytic number theory
Number fields
28. As shown earlier - c - di is the complex conjugate of the denominator c + di.
repeated elements
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
coefficient
Associative Law of Multiplication
29. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Second Axiom of Equality
Multiple of the given number
repeated elements
Definition of genus
30. 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.)
the sum of its digits is divisible by 9
Number fields
addition
The multiplication of two complex numbers is defined by the following formula:
31. 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:
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
a curve - a surface or some other such object in n-dimensional space
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).
32. A curve in the plane
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Commutative Law of Addition
an equation in two variables defines
C or
33. The defining characteristic of a position vector is that it has
Positional notation (place value)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
magnitude and direction
expression
34. Plus
Prime Factor
Associative Law of Addition
Complex numbers
addition
35. Product
multiplication
Absolute value and argument
Odd Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
36. Any number that is not a multiple of 2 is an
Odd Number
upward
rectangular coordinates
Prime Factor
37. Does not have an equal sign (3x+5) (2a+9b)
a complex number is real if and only if it equals its conjugate.
coefficient
expression
Q-16
38. Has an equal sign (3x+5 = 14)
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.
constant
equation
negative
39. 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.
subtraction
Composite Number
equation
Second Axiom of Equality
40. One term (5x or 4)
order of operations
polynomial
K+6 - K+5 - K+4 K+3.........answer is K+3
monomial
41. Number symbols
subtraction
Numerals
In Diophantine geometry
Second Axiom of Equality
42. Number T increased by 9
Braces
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
polynomial
T+9
43. Product of 16 and the sum of 5 and number R
The real number a of the complex number z = a + bi
Commutative Law of Addition
16(5+R)
magnitude and direction
44. A number is divisible by 8 if
one characteristic in common such as similarity of appearance or purpose
solutions
the number formed by the three right-hand digits is divisible by 8
division
45. An equation - or system of equations - in two or more variables defines
Positional notation (place value)
a curve - a surface or some other such object in n-dimensional space
addition
Distributive Law
46. 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.
Complex numbers
The numbers are conventionally plotted using the real part
right-hand digit is even
The multiplication of two complex numbers is defined by the following formula:
47. 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
Associative Law of Multiplication
F - F+1 - F+2.......answer is F+2
In Diophantine geometry
addition
48. Addition of two complex numbers can be done geometrically by
Absolute value and argument
Natural Numbers
constructing a parallelogram
In Diophantine geometry
49. 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
Braces
addition
Definition of genus
difference
50. Quotient
Associative Law of Multiplication
rectangular coordinates
Place Value Concept
division