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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. 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.)
even and the sum of its digits is divisible by 3
Number fields
multiplication
Commutative Law of Addition
2. No short method has been found for determining whether a number is divisible by
7
C or
In Diophantine geometry
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).
3. Does not have an equal sign (3x+5) (2a+9b)
polynomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
subtraction
expression
4. The real and imaginary parts of a complex number can be extracted using the conjugate:
Inversive geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
Place Value Concept
a complex number is real if and only if it equals its conjugate.
5. 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.
(x-12)/40
In Diophantine geometry
subtraction
Forth Axiom of Equality
6. 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
Equal
Prime Number
Digits
The numbers are conventionally plotted using the real part
7. 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.
a complex number is real if and only if it equals its conjugate.
Complex numbers
subtraction
Even Number
8. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Commutative Law of Addition
Multiple of the given number
Number fields
9. More than one term (5x+4 contains two)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
polynomial
solutions
a complex number is real if and only if it equals its conjugate.
10. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
repeated elements
Members of Elements of the Set
Even Number
11. One term (5x or 4)
an equation in two variables defines
monomial
Number fields
Prime Number
12. The central problem of Diophantine geometry is to determine when a Diophantine equation has
upward
solutions
(x-12)/40
Even Number
13. Number T increased by 9
addition
T+9
Definition of genus
Equal
14. 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
negative
the number formed by the three right-hand digits is divisible by 8
To separate a number into prime factors
The multiplication of two complex numbers is defined by the following formula:
15. The number without a variable (5m+2). In this case - 2
Complex numbers
Members of Elements of the Set
variable
constant
16. 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 -
addition
right-hand digit is even
Composite Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
17. 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.
Complex numbers
consecutive whole numbers
magnitude
Commutative Law of Addition
18. A number is divisible by 8 if
magnitude
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
the number formed by the three right-hand digits is divisible by 8
19. Product of 16 and the sum of 5 and number R
subtraction
Associative Law of Addition
even and the sum of its digits is divisible by 3
16(5+R)
20. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
order of operations
Algebraic number theory
Complex numbers
21. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
positive
In Diophantine geometry
Even Number
22. 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
Algebraic number theory
complex number
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.
right-hand digit is even
23. Plus
its the sum of its digits is divisible by 3
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).
Algebraic number theory
addition
24. Any number that can be divided lnto a given number without a remainder is a
Commutative Law of Addition
Factor of the given number
Inversive geometry
the number formed by the three right-hand digits is divisible by 8
25. 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:
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
negative
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
26. Remainder
The multiplication of two complex numbers is defined by the following formula:
subtraction
Members of Elements of the Set
division
27. 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
In Diophantine geometry
7
subtraction
Prime Factor
28. 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.
Number fields
F - F+1 - F+2.......answer is F+2
T+9
Commutative Law of Addition
29. The Arabic numerals from 0 through 9 are called
Digits
In Diophantine geometry
rectangular coordinates
monomial
30. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the
Place Value Concept
Prime Number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Factor of the given number
31. 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.
Equal
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Braces
Associative Law of Addition
32. 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
solutions
The real number a of the complex number z = a + bi
algebraic number
Base of the number system
33. An equation - or system of equations - in two or more variables defines
16(5+R)
Associative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space
Second Axiom of Equality
34. 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.
even and the sum of its digits is divisible by 3
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).
Q-16
The numbers are conventionally plotted using the real part
35. The numbers which are used for counting in our number system are sometimes called
Associative Law of Addition
a complex number is real if and only if it equals its conjugate.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Natural Numbers
36. Product
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Definition of genus
Associative Law of Multiplication
multiplication
37. 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.
The numbers are conventionally plotted using the real part
Numerals
38. A number is divisible by 6 if it is
counterclockwise through 90
even and the sum of its digits is divisible by 3
upward
a curve - a surface or some other such object in n-dimensional space
39. Sum
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Equal
addition
rectangular coordinates
40. Are used to indicate sets
division
quadratic field
Braces
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).
41. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Third Axiom of Equality
Even Number
repeated elements
42. 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
a curve - a surface or some other such object in n-dimensional space
magnitude and direction
base-ten number
The numbers are conventionally plotted using the real part
43. More than
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
C or
addition
Digits
44. 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
complex number
magnitude
Braces
even and the sum of its digits is divisible by 3
45. A number is divisible by 2 if
polynomial
magnitude
right-hand digit is even
Odd Number
46. Any number that la a multiple of 2 is an
expression
7
Natural Numbers
Even Number
47. Number symbols
Numerals
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the sum of its digits is divisible by 9
The multiplication of two complex numbers is defined by the following formula:
48. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
The multiplication of two complex numbers is defined by the following formula:
repeated elements
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
algebraic number
49. The objects in a set have at least
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).
an equation in two variables defines
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
one characteristic in common such as similarity of appearance or purpose
50. 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.
Place Value Concept
16(5+R)
Associative Law of Addition
the number formed by the two right-hand digits is divisible by 4