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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. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
magnitude
division
2. The set of all complex numbers is denoted by
Digits
C or
polynomial
the genus of the curve
3. 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
expression
In Diophantine geometry
rectangular coordinates
addition
4. The defining characteristic of a position vector is that it has
Associative Law of Multiplication
magnitude and direction
Numerals
consecutive whole numbers
5. LAWS FOR COMBINING NUMBERS
Prime Factor
T+9
quadratic field
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
6. A number is divisible by 2 if
right-hand digit is even
algebraic number
Digits
variable
7. Sum
Equal
Commutative Law of Multiplication
The real number a of the complex number z = a + bi
addition
8. 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 Multiplication
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).
Associative Law of Addition
addition
9. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
subtraction
Forth Axiom of Equality
division
repeated elements
10. 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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11. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Second Axiom of Equality
positive
polynomial
rectangular coordinates
12. Any number that is not a multiple of 2 is an
Odd Number
Numerals
Algebraic number theory
T+9
13. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
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).
Base of the number system
order of operations
14. The place value which corresponds to a given position in a number is determined by the
Base of the number system
the sum of its digits is divisible by 9
Commutative Law of Multiplication
addition
15. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Inversive geometry
Natural Numbers
magnitude and direction
16. The number without a variable (5m+2). In this case - 2
Associative Law of Multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
constant
Base of the number system
17. Product of 16 and the sum of 5 and number R
Associative Law of Multiplication
Commutative Law of Multiplication
16(5+R)
a curve - a surface or some other such object in n-dimensional space
18. 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:
Second Axiom of Equality
upward
Natural Numbers
19. The objects in a set have at least
coefficient
Inversive geometry
one characteristic in common such as similarity of appearance or purpose
Associative Law of Addition
20. 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
Factor of the given number
In Diophantine geometry
Digits
Multiple of the given number
21. 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
difference
even and the sum of its digits is divisible by 3
22. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
algebraic number
one characteristic in common such as similarity of appearance or purpose
23. The relative greatness of positive and negative numbers
magnitude
Third Axiom of Equality
subtraction
Complex numbers
24. 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
variable
Braces
25. The finiteness or not of the number of rational or integer points on an algebraic curve
C or
Second Axiom of Equality
Associative Law of Addition
the genus of the curve
26. An equation - or system of equations - in two or more variables defines
Absolute value and argument
a curve - a surface or some other such object in n-dimensional space
Prime Number
Set
27. Has an equal sign (3x+5 = 14)
Commutative Law of Multiplication
equation
To separate a number into prime factors
Odd Number
28. Does not have an equal sign (3x+5) (2a+9b)
subtraction
equation
expression
its the sum of its digits is divisible by 3
29. Number T increased by 9
one characteristic in common such as similarity of appearance or purpose
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
T+9
addition
30. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
addition
right-hand digit is even
31. Number X decreased by 12 divided by forty
rectangular coordinates
(x-12)/40
Positional notation (place value)
the sum of its digits is divisible by 9
32. 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 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).
rectangular coordinates
multiplication
Algebraic number theory
33. 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.
(x-12)/40
even and the sum of its digits is divisible by 3
Place Value Concept
The numbers are conventionally plotted using the real part
34. 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
constructing a parallelogram
base-ten number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
T+9
35. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
constructing a parallelogram
counterclockwise through 90
Inversive geometry
Third Axiom of Equality
36. Are used to indicate sets
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).
variable
Absolute value and argument
Braces
37. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
righthand digit is 0 or 5
constant
subtraction
38. 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 number formed by the two right-hand digits is divisible by 4
Analytic number theory
addition
repeated elements
39. Product
Natural Numbers
upward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
multiplication
40. Less than
Natural Numbers
Commutative Law of Addition
complex number
subtraction
41. More than one term (5x+4 contains two)
polynomial
Braces
Forth Axiom of Equality
F - F+1 - F+2.......answer is F+2
42. If a factor of a number is prime - it is called a
Base of the number system
Associative Law of Addition
Distributive Law
Prime Factor
43. Implies a collection or grouping of similar - objects or symbols.
magnitude and direction
multiplication
Set
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
44. A number is divisible by 5 if its
the number formed by the two right-hand digits is divisible by 4
rectangular coordinates
solutions
righthand digit is 0 or 5
45. Any number that la a multiple of 2 is an
T+9
Even Number
coefficient
Equal
46. 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.
Number fields
Commutative Law of Addition
the sum of its digits is divisible by 9
Definition of genus
47. 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
repeated elements
expression
Odd Number
48. 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.
counterclockwise through 90
Forth Axiom of Equality
negative
The real number a of the complex number z = a + bi
49. First axiom of equality
Place Value Concept
Even Number
the number formed by the two right-hand digits is divisible by 4
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.
50. Increased by
T+9
Equal
addition
counterclockwise through 90