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Test your basic knowledge |
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. Any number that is not a multiple of 2 is an
Numerals
one characteristic in common such as similarity of appearance or purpose
In Diophantine geometry
Odd Number
2. 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.
Associative Law of Addition
Odd 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.
algebraic number
3. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f
algebraic number
Distributive Law
even and the sum of its digits is divisible by 3
addition
4. 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
Commutative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
negative
5. Quotient
division
In Diophantine geometry
the number formed by the three right-hand digits is divisible by 8
quadratic field
6. 2 -3 -4 -5 -6
coefficient
Commutative Law of Multiplication
complex number
consecutive whole numbers
7. More than
addition
Downward
repeated elements
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
8. Remainder
expression
Algebraic number theory
subtraction
one characteristic in common such as similarity of appearance or purpose
9. 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
subtraction
Complex numbers
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Positional notation (place value)
10. 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.
solutions
rectangular coordinates
Absolute value and argument
Associative Law of Addition
11. A number is divisible by 5 if its
addition
Associative Law of Addition
righthand digit is 0 or 5
The multiplication of two complex numbers is defined by the following formula:
12. 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.)
K+6 - K+5 - K+4 K+3.........answer is K+3
a curve - a surface or some other such object in n-dimensional space
Number fields
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
13. The central problem of Diophantine geometry is to determine when a Diophantine equation has
T+9
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Inversive geometry
solutions
14. 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 -
In Diophantine geometry
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
upward
multiplication
15. Any number that can be divided lnto a given number without a remainder is a
constant
polynomial
Multiple of the given number
Factor of the given number
16. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
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.
the number formed by the two right-hand digits is divisible by 4
the genus of the curve
17. 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
the genus of the curve
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
The real number a of the complex number z = a + bi
18. Product
multiplication
The real number a of the complex number z = a + bi
the number formed by the two right-hand digits is divisible by 4
Natural Numbers
19. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
the number formed by the two right-hand digits is divisible by 4
Digits
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
solutions
20. Another way of encoding points in the complex plane other than using the x- and y-coordinates is to use the distance of a point P to O - the point whose coordinates are (0 - 0) (the origin) - and the angle of the line through P and O. This idea leads
Associative Law of Addition
magnitude
Numerals
Absolute value and argument
21. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
22. More than one term (5x+4 contains two)
Natural Numbers
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The real number a of the complex number z = a + bi
polynomial
23. An equation - or system of equations - in two or more variables defines
Odd Number
a curve - a surface or some other such object in n-dimensional space
T+9
Factor of the given number
24. 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.
a curve - a surface or some other such object in n-dimensional space
Second Axiom of Equality
Members of Elements of the Set
monomial
25. A number is divisible by 2 if
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Analytic number theory
right-hand digit is even
Positional notation (place value)
26. Sixteen less than number Q
Q-16
consecutive whole numbers
7
difference
27. Number X decreased by 12 divided by forty
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
(x-12)/40
counterclockwise through 90
28. 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.
negative
positive
Forth Axiom of Equality
7
29. The Arabic numerals from 0 through 9 are called
one characteristic in common such as similarity of appearance or purpose
multiplication
Definition of genus
Digits
30. 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
addition
repeated elements
division
31. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
addition
Prime Factor
Odd Number
32. The finiteness or not of the number of rational or integer points on an algebraic curve
coefficient
Complex numbers
the genus of the curve
expression
33. Has an equal sign (3x+5 = 14)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
equation
16(5+R)
constructing a parallelogram
34. Does not have an equal sign (3x+5) (2a+9b)
Prime Number
subtraction
expression
solutions
35. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
Associative Law of Multiplication
division
the number formed by the three right-hand digits is divisible by 8
36. 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
the number formed by the two right-hand digits is divisible by 4
even and the sum of its digits is divisible by 3
division
base-ten number
37. 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:
right-hand digit is even
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).
solutions
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
38. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
polynomial
K+6 - K+5 - K+4 K+3.........answer is K+3
Odd Number
subtraction
39. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
Second Axiom of Equality
righthand digit is 0 or 5
Commutative Law of Addition
40. 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
righthand digit is 0 or 5
a curve - a surface or some other such object in n-dimensional space
difference
To separate a number into prime factors
41. 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
Definition of genus
equation
a curve - a surface or some other such object in n-dimensional space
42. Implies a collection or grouping of similar - objects or symbols.
Equal
the number formed by the three right-hand digits is divisible by 8
Base of the number system
Set
43. The set of all complex numbers is denoted by
complex number
16(5+R)
C or
Braces
44. 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.
Commutative Law of Addition
F - F+1 - F+2.......answer is F+2
even and the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
45. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Braces
Base of the number system
46. The greatest of 3 consecutive whole numbers - the smallest of which is F
upward
Place Value Concept
F - F+1 - F+2.......answer is F+2
The multiplication of two complex numbers is defined by the following formula:
47. A curve in the plane
equation
Commutative Law of Addition
Distributive Law
an equation in two variables defines
48. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Place Value Concept
Algebraic number theory
49. 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.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Forth Axiom of Equality
the genus of the curve
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
50. A number is divisible by 8 if
base-ten number
the number formed by the three right-hand digits is divisible by 8
magnitude
multiplication