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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
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.
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. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Algebraic number theory
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
upward
Inversive geometry
2. Does not have an equal sign (3x+5) (2a+9b)
expression
coefficient
Commutative Law of Addition
repeated elements
3. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
magnitude and direction
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
positive
subtraction
4. 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
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).
its the sum of its digits is divisible by 3
5. The set of all complex numbers is denoted by
division
even and the sum of its digits is divisible by 3
Composite Number
C or
6. Any number that can be divided lnto a given number without a remainder is a
Associative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Factor of the given number
Associative Law of Multiplication
7. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
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8. Less than
7
subtraction
order of operations
constant
9. 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
equation
To separate a number into prime factors
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
10. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Associative Law of 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.
subtraction
11. 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.
its the sum of its digits is divisible by 3
Third Axiom of Equality
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.
rectangular coordinates
12. A curve in the plane
Inversive geometry
division
counterclockwise through 90
an equation in two variables defines
13. Remainder
polynomial
positive
subtraction
Analytic number theory
14. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Definition of genus
solutions
Commutative Law of Addition
15. LAWS FOR COMBINING NUMBERS
Absolute value and argument
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
In Diophantine geometry
16. 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.
Commutative Law of Multiplication
Associative Law of Addition
Definition of genus
addition
17. Product of 16 and the sum of 5 and number R
Definition of genus
Composite Number
16(5+R)
constructing a parallelogram
18. 2 -3 -4 -5 -6
Second Axiom of Equality
7
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
consecutive whole numbers
19. 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
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).
a curve - a surface or some other such object in n-dimensional space
The multiplication of two complex numbers is defined by the following formula:
base-ten number
20. A number is divisible by 8 if
To separate a number into prime factors
the number formed by the three right-hand digits is divisible by 8
a curve - a surface or some other such object in n-dimensional space
coefficient
21. The objects or symbols in a set are called Numerals - Lines - or Points
consecutive whole numbers
Members of Elements of the Set
the number formed by the three right-hand digits is divisible by 8
addition
22. The finiteness or not of the number of rational or integer points on an algebraic curve
expression
Digits
the genus of the curve
Natural Numbers
23. Plus
To separate a number into prime factors
addition
subtraction
Analytic number theory
24. The number touching the variable (in the case of 5x - would be 5)
coefficient
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
addition
Multiple of the given number
25. Any number that la a multiple of 2 is an
repeated elements
counterclockwise through 90
Even Number
To separate a number into prime factors
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
Second Axiom of Equality
In Diophantine geometry
Positional notation (place value)
rectangular coordinates
27. 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
consecutive whole numbers
monomial
counterclockwise through 90
28. 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
monomial
right-hand digit is even
To separate a number into prime factors
Odd Number
29. Number X decreased by 12 divided by forty
Positional notation (place value)
Odd Number
Numerals
(x-12)/40
30. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
righthand digit is 0 or 5
upward
order of operations
Positional notation (place value)
31. Decreased by
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Positional notation (place value)
subtraction
magnitude and direction
32. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Third Axiom of Equality
The real number a of the complex number z = a + bi
Prime Number
negative
33. Implies a collection or grouping of similar - objects or symbols.
Numerals
magnitude and direction
expression
Set
34. Sum
Absolute value and argument
7
addition
C or
35. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Even Number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
righthand digit is 0 or 5
Numerals
36. Total
In Diophantine geometry
righthand digit is 0 or 5
Members of Elements of the Set
addition
37. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
Commutative Law of Addition
Forth Axiom of Equality
constructing a parallelogram
38. A number is divisible by 9 if
the sum of its digits is divisible by 9
Odd Number
its the sum of its digits is divisible by 3
an equation in two variables defines
39. 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.
monomial
polynomial
algebraic number
Associative Law of Addition
40. 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.
Positional notation (place value)
rectangular coordinates
quadratic field
magnitude
41. First axiom of equality
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.
quadratic field
coefficient
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).
42. One term (5x or 4)
monomial
Associative Law of Addition
algebraic number
Factor of the given number
43. More than one term (5x+4 contains two)
polynomial
division
constant
addition
44. The numbers which are used for counting in our number system are sometimes called
Positional notation (place value)
negative
(x-12)/40
Natural Numbers
45. 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
Place Value Concept
Equal
its the sum of its digits is divisible by 3
variable
46. The greatest of 3 consecutive whole numbers - the smallest of which is F
Second Axiom of Equality
7
(x-12)/40
F - F+1 - F+2.......answer is F+2
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
Equal
Base of the number system
In Diophantine geometry
even and the sum of its digits is divisible by 3
48. 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.
In Diophantine geometry
Positional notation (place value)
Second Axiom of Equality
Multiple of the given number
49. A number is divisible by 2 if
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Second Axiom of Equality
Multiple of the given number
right-hand digit is even
50. Any number that is exactly divisible by a given number is a
Third Axiom of Equality
Multiple of the given number
variable
Commutative Law of Multiplication
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