SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
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. Has an equal sign (3x+5 = 14)
Number fields
Analytic number theory
16(5+R)
equation
2. A curve in the plane
the genus of the curve
equation
an equation in two variables defines
Q-16
3. A number is divisible by 3 if
multiplication
expression
K+6 - K+5 - K+4 K+3.........answer is K+3
its the sum of its digits is divisible by 3
4. Sixteen less than number Q
Number fields
Q-16
equation
In Diophantine geometry
5. Number X decreased by 12 divided by forty
addition
Prime Number
(x-12)/40
division
6. A number is divisible by 6 if it is
one characteristic in common such as similarity of appearance or purpose
Algebraic number theory
even and the sum of its digits is divisible by 3
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7. Implies a collection or grouping of similar - objects or symbols.
Set
T+9
In Diophantine geometry
Complex numbers
8. 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.
an equation in two variables defines
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The numbers are conventionally plotted using the real part
7
9. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Odd Number
expression
upward
10. Product of 16 and the sum of 5 and number R
(x-12)/40
16(5+R)
Commutative Law of Addition
addition
11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Multiple of the given number
Associative Law of Multiplication
12. 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.
solutions
Place Value Concept
Forth Axiom of Equality
right-hand digit is even
13. 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.)
multiplication
consecutive whole numbers
Inversive geometry
Number fields
14. This law states that the product of three or more factors is the same regardless of the manner in which they are grouped. Negative signs require no special treatment in the application of this law.
rectangular coordinates
Associative Law of Multiplication
F - F+1 - F+2.......answer is F+2
addition
15. 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
Natural Numbers
C or
righthand digit is 0 or 5
16. A number that has factors other than itself and 1 is a
Composite Number
addition
Complex numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
17. Any number that can be divided lnto a given number without a remainder is a
polynomial
Forth Axiom of Equality
Analytic number theory
Factor of the given number
18. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Positional notation (place value)
The real number a of the complex number z = a + bi
Digits
Inversive geometry
19. A number is divisible by 8 if
constructing a parallelogram
addition
a curve - a surface or some other such object in n-dimensional space
the number formed by the three right-hand digits is divisible by 8
20. 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.
subtraction
Associative Law of Addition
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
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
righthand digit is 0 or 5
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
variable
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.
16(5+R)
Third Axiom of Equality
addition
upward
23. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Analytic number theory
F - F+1 - F+2.......answer is F+2
rectangular coordinates
Absolute value and argument
24. More than
counterclockwise through 90
addition
even and the sum of its digits is divisible by 3
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.
25. 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
To separate a number into prime factors
constant
polynomial
base-ten number
26. LAWS FOR COMBINING NUMBERS
equation
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.
a curve - a surface or some other such object in n-dimensional space
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
27. A number is divisible by 4 if
Commutative Law of Addition
the number formed by the two right-hand digits is divisible by 4
16(5+R)
Multiple of the given number
28. Any number that is not a multiple of 2 is an
Digits
Members of Elements of the Set
Odd Number
Analytic number theory
29. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
magnitude and direction
addition
Prime Number
30. Are used to indicate sets
Braces
Q-16
Odd Number
quadratic field
31. The Arabic numerals from 0 through 9 are called
subtraction
the sum of its digits is divisible by 9
repeated elements
Digits
32. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
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.
Natural Numbers
Positional notation (place value)
33. 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.
counterclockwise through 90
Commutative Law of Addition
consecutive whole numbers
the genus of the curve
34. 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
magnitude
Second Axiom of Equality
Base of the number system
35. Sum
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
Numerals
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).
36. A number that has no factors except itself and 1 is a
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
counterclockwise through 90
Prime Number
Q-16
37. Integers greater than zero and less than 5 form a set - as follows:
negative
C or
Number fields
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
38. Quotient
Members of Elements of the Set
Downward
division
Analytic number theory
39. Addition of two complex numbers can be done geometrically by
In Diophantine geometry
Q-16
constructing a parallelogram
subtraction
40. The central problem of Diophantine geometry is to determine when a Diophantine equation has
algebraic number
addition
Second Axiom of Equality
solutions
41. 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
7
In Diophantine geometry
the number formed by the three right-hand digits is divisible by 8
42. A number is divisible by 2 if
multiplication
Natural Numbers
right-hand digit is even
division
43. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
rectangular coordinates
Braces
In Diophantine geometry
negative
44. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
To separate a number into prime factors
addition
Algebraic number theory
45. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
repeated elements
Commutative Law of Addition
Associative Law of Multiplication
46. Product
multiplication
positive
subtraction
base-ten number
47. Less than
Factor of the given number
Numerals
subtraction
Absolute value and argument
48. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
addition
In Diophantine geometry
addition
49. Number T increased by 9
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula:
Prime Number
T+9
50. 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:
counterclockwise through 90
7
magnitude
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).