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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. 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.)
7
Number fields
Positional notation (place value)
addition
2. 2 -3 -4 -5 -6
rectangular coordinates
consecutive whole numbers
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
positive
3. A number is divisible by 4 if
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).
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.
Commutative Law of Multiplication
4. Number X decreased by 12 divided by forty
a curve - a surface or some other such object in n-dimensional space
(x-12)/40
a complex number is real if and only if it equals its conjugate.
Definition of genus
5. Addition of two complex numbers can be done geometrically by
Associative Law of Addition
constructing a parallelogram
Number fields
Set
6. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
To separate a number into prime factors
In Diophantine geometry
positive
Definition of genus
7. If a factor of a number is prime - it is called a
Natural Numbers
Absolute value and argument
Prime Factor
Factor of the given number
8. More than one term (5x+4 contains two)
The numbers are conventionally plotted using the real part
Base of the number system
even and the sum of its digits is divisible by 3
polynomial
9. The numbers which are used for counting in our number system are sometimes called
counterclockwise through 90
Natural Numbers
Definition of genus
subtraction
10. One term (5x or 4)
rectangular coordinates
Set
Members of Elements of the Set
monomial
11. A number is divisible by 2 if
Analytic number theory
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Third Axiom of Equality
right-hand digit is even
12. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
complex number
magnitude and direction
righthand digit is 0 or 5
negative
13. The place value which corresponds to a given position in a number is determined by the
In Diophantine geometry
Base of the number system
T+9
Positional notation (place value)
14. The square roots of a + bi (with b ? 0) are - where and where sgn is the signum function. This can be seen by squaring to obtain a + bi.
C or
F - F+1 - F+2.......answer is F+2
Downward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
15. 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.
Algebraic number theory
T+9
a curve - a surface or some other such object in n-dimensional space
16. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Numerals
polynomial
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Downward
17. Does not have an equal sign (3x+5) (2a+9b)
expression
Even Number
magnitude and direction
Forth Axiom of Equality
18. 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
base-ten number
Numerals
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
To separate a number into prime factors
19. A number is divisible by 5 if its
righthand digit is 0 or 5
Associative Law of Addition
T+9
Third Axiom of Equality
20. Has an equal sign (3x+5 = 14)
equation
In Diophantine geometry
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
21. Less than
variable
magnitude and direction
subtraction
magnitude
22. 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
an equation in two variables defines
Braces
C or
The real number a of the complex number z = a + bi
23. Any number that can be divided lnto a given number without a remainder is a
To separate a number into prime factors
monomial
Factor of the given number
F - F+1 - F+2.......answer is F+2
24. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
expression
complex number
Downward
25. Plus
Positional notation (place value)
subtraction
addition
Members of Elements of the Set
26. 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
difference
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
In Diophantine geometry
Commutative Law of Multiplication
27. 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
subtraction
To separate a number into prime factors
addition
the number formed by the two right-hand digits is divisible by 4
28. Increased by
polynomial
addition
positive
Even Number
29. The real and imaginary parts of a complex number can be extracted using the conjugate:
even and the sum of its digits is divisible by 3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Downward
a complex number is real if and only if it equals its conjugate.
30. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Third Axiom of Equality
one characteristic in common such as similarity of appearance or purpose
upward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
31. As shown earlier - c - di is the complex conjugate of the denominator c + di.
a complex number is real if and only if it equals its conjugate.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
one characteristic in common such as similarity of appearance or purpose
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
32. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Prime Factor
order of operations
Odd Number
Inversive geometry
33. 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
the number formed by the two right-hand digits is divisible by 4
Number fields
right-hand digit is even
algebraic number
34. 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 -
Absolute value and argument
Base of the number system
Composite Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
35. A curve in the plane
an equation in two variables defines
subtraction
counterclockwise through 90
Base of the number system
36. 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.
Positional notation (place value)
Complex numbers
Commutative Law of Addition
repeated elements
37. 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
Factor of the given number
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
38. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
constant
order of operations
Base of the number system
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.
39. Any number that la a multiple of 2 is an
positive
difference
Even Number
magnitude and direction
40. Subtraction
(x-12)/40
the sum of its digits is divisible by 9
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
difference
41. 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.
The numbers are conventionally plotted using the real part
variable
Associative Law of Addition
Braces
42. 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
even and the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The real number a of the complex number z = a + bi
43. The number touching the variable (in the case of 5x - would be 5)
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).
quadratic field
righthand digit is 0 or 5
coefficient
44. Remainder
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Multiplication
constant
subtraction
45. The Arabic numerals from 0 through 9 are called
Second Axiom of Equality
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Digits
rectangular coordinates
46. A number is divisible by 9 if
negative
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
counterclockwise through 90
the sum of its digits is divisible by 9
47. 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.
Positional notation (place value)
Natural Numbers
The numbers are conventionally plotted using the real part
the sum of its digits is divisible by 9
48. 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.
base-ten number
Third Axiom of Equality
Factor of the given number
complex number
49. The defining characteristic of a position vector is that it has
addition
magnitude and direction
base-ten number
Odd Number
50. 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.
Second Axiom of Equality
To separate a number into prime factors
Commutative Law of Addition
addition