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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.
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. 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
Absolute value and argument
Algebraic number theory
equation
In Diophantine geometry
2. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
a complex number is real if and only if it equals its conjugate.
subtraction
16(5+R)
3. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
The real number a of the complex number z = a + bi
addition
Inversive geometry
Prime Factor
4. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Even Number
Absolute value and argument
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. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Associative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
the number formed by the two right-hand digits is divisible by 4
division
6. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
a curve - a surface or some other such object in n-dimensional space
Q-16
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7
7. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
equation
Commutative Law of Multiplication
multiplication
F - F+1 - F+2.......answer is F+2
8. Any number that is exactly divisible by a given number is a
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
a curve - a surface or some other such object in n-dimensional space
Multiple of the given number
its the sum of its digits is divisible by 3
9. Sixteen less than number Q
Complex numbers
Q-16
rectangular coordinates
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
10. One term (5x or 4)
Positional notation (place value)
the sum of its digits is divisible by 9
monomial
right-hand digit is even
11. 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 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
12. 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
Even Number
addition
The numbers are conventionally plotted using the real part
13. Integers greater than zero and less than 5 form a set - as follows:
Associative Law of Multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Forth Axiom of Equality
Odd Number
14. 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.
(x-12)/40
difference
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
equation
15. Has an equal sign (3x+5 = 14)
Composite Number
Complex numbers
positive
equation
16. First axiom of equality
the sum of its digits is divisible by 9
a complex number is real if and only if it equals its conjugate.
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.
In Diophantine geometry
17. 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
addition
negative
The multiplication of two complex numbers is defined by the following formula:
18. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
C or
Downward
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
an equation in two variables defines
19. A number is divisible by 9 if
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the sum of its digits is divisible by 9
quadratic field
the genus of the curve
20. 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
Odd Number
To separate a number into prime factors
base-ten number
21. 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.
counterclockwise through 90
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Addition
Members of Elements of the Set
22. A number is divisible by 2 if
Inversive geometry
constant
right-hand digit is even
Associative Law of Multiplication
23. 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
The numbers are conventionally plotted using the real part
Multiple of the given number
Equal
In Diophantine geometry
24. The greatest of 3 consecutive whole numbers - the smallest of which is F
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
F - F+1 - F+2.......answer is F+2
Prime Factor
upward
25. 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 -
Braces
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
positive
magnitude and direction
26. If a factor of a number is prime - it is called a
Prime Factor
Commutative Law of Addition
subtraction
the number formed by the two right-hand digits is divisible by 4
27. 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
Complex numbers
a complex number is real if and only if it equals its conjugate.
The real number a of the complex number z = a + bi
expression
28. 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 number formed by the two right-hand digits is divisible by 4
Positional notation (place value)
Analytic number theory
In Diophantine geometry
29. The real and imaginary parts of a complex number can be extracted using the conjugate:
Downward
algebraic number
a complex number is real if and only if it equals its conjugate.
Distributive Law
30. The objects in a set have at least
16(5+R)
one characteristic in common such as similarity of appearance or purpose
Positional notation (place value)
Digits
31. 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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Place Value Concept
order of operations
subtraction
32. 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
Inversive geometry
Numerals
Even Number
base-ten number
33. Number T increased by 9
T+9
division
Braces
Equal
34. LAWS FOR COMBINING NUMBERS
multiplication
Second Axiom of Equality
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
35. Number symbols
Numerals
monomial
an equation in two variables defines
expression
36. More than one term (5x+4 contains two)
Associative Law of Multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Q-16
polynomial
37. Total
addition
Multiple of the given number
repeated elements
Equal
38. The numbers which are used for counting in our number system are sometimes called
polynomial
Factor of the given number
the genus of the curve
Natural Numbers
39. Number X decreased by 12 divided by forty
counterclockwise through 90
righthand digit is 0 or 5
Algebraic number theory
(x-12)/40
40. More than
algebraic number
Definition of genus
addition
Second Axiom of Equality
41. A number that has factors other than itself and 1 is a
subtraction
Composite Number
Distributive Law
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
42. The set of all complex numbers is denoted by
C or
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Absolute value and argument
repeated elements
43. 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.
Absolute value and argument
Third Axiom of Equality
Prime Factor
Forth Axiom of Equality
44. 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.
negative
Associative Law of Addition
(x-12)/40
addition
45. 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.
positive
Second Axiom of Equality
Q-16
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).
46. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
polynomial
Forth Axiom of Equality
counterclockwise through 90
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.
47. No short method has been found for determining whether a number is divisible by
Commutative Law of Addition
positive
7
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
48. Remainder
subtraction
righthand digit is 0 or 5
order of operations
negative
49. A letter tat represents a number that is unknown (usually X or Y)
C or
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
difference
variable
50. Are used to indicate sets
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.
In Diophantine geometry
Braces
(x-12)/40
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