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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. 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
Digits
an equation in two variables defines
algebraic number
polynomial
2. Number X decreased by 12 divided by forty
(x-12)/40
Commutative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Prime Number
3. The relative greatness of positive and negative numbers
expression
even and the sum of its digits is divisible by 3
magnitude
Analytic number theory
4. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Algebraic number theory
multiplication
order of operations
Prime Factor
5. A number is divisible by 9 if
solutions
The numbers are conventionally plotted using the real part
Members of Elements of the Set
the sum of its digits is divisible by 9
6. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
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.
The multiplication of two complex numbers is defined by the following formula:
Downward
7. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
In Diophantine geometry
coefficient
(x-12)/40
upward
8. 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 -
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
subtraction
Q-16
9. Sixteen less than number Q
(x-12)/40
Even Number
Q-16
Absolute value and argument
10. Implies a collection or grouping of similar - objects or symbols.
Number fields
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Members of Elements of the Set
Set
11. The number without a variable (5m+2). In this case - 2
Composite Number
constant
Even Number
a complex number is real if and only if it equals its conjugate.
12. 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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13. The central problem of Diophantine geometry is to determine when a Diophantine equation has
complex number
difference
addition
solutions
14. Total
addition
Composite Number
F - F+1 - F+2.......answer is F+2
Analytic number theory
15. Any number that la a multiple of 2 is an
negative
Members of Elements of the Set
Associative Law of Multiplication
Even Number
16. 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
base-ten number
Algebraic number theory
solutions
Commutative Law of Addition
17. 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.
Forth Axiom of Equality
multiplication
The numbers are conventionally plotted using the real part
Q-16
18. Has an equal sign (3x+5 = 14)
equation
counterclockwise through 90
division
T+9
19. The finiteness or not of the number of rational or integer points on an algebraic curve
solutions
the genus of the curve
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
algebraic number
20. The defining characteristic of a position vector is that it has
Place Value Concept
order of operations
Complex numbers
magnitude and direction
21. 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
The numbers are conventionally plotted using the real part
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
equation
22. Sum
the genus of the curve
Braces
addition
counterclockwise through 90
23. The objects or symbols in a set are called Numerals - Lines - or Points
Base of the number system
Complex numbers
addition
Members of Elements of the Set
24. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Even Number
Multiple of the given number
variable
25. Any number that is not a multiple of 2 is an
Number fields
variable
The real number a of the complex number z = a + bi
Odd Number
26. The real and imaginary parts of a complex number can be extracted using the conjugate:
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
a complex number is real if and only if it equals its conjugate.
monomial
In Diophantine geometry
27. 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
Q-16
Equal
constant
Commutative Law of Multiplication
28. Number symbols
Members of Elements of the Set
an equation in two variables defines
Associative Law of Multiplication
Numerals
29. Are used to indicate sets
The numbers are conventionally plotted using the real part
Braces
division
algebraic number
30. 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:
Distributive Law
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
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
31. Decreased by
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
Base of the number system
magnitude
32. The Arabic numerals from 0 through 9 are called
Even Number
magnitude
Digits
C or
33. 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
monomial
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
In Diophantine geometry
Prime Factor
34. 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.
quadratic field
To separate a number into prime factors
Equal
an equation in two variables defines
35. 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 real number a of the complex number z = a + bi
constant
subtraction
addition
36. Product
multiplication
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
upward
Odd Number
37. Less than
Odd Number
Absolute value and argument
addition
subtraction
38. Integers greater than zero and less than 5 form a set - as follows:
positive
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Absolute value and argument
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
39. 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
F - F+1 - F+2.......answer is F+2
subtraction
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula:
40. 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
Prime Number
Algebraic number theory
one characteristic in common such as similarity of appearance or purpose
Positional notation (place value)
41. The place value which corresponds to a given position in a number is determined by the
algebraic number
Absolute value and argument
addition
Base of the number system
42. 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.
Associative Law of Addition
multiplication
a curve - a surface or some other such object in n-dimensional space
an equation in two variables defines
43. More than
subtraction
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
Third Axiom of Equality
44. 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.
Commutative Law of Addition
Associative Law of Addition
Complex numbers
difference
45. A number is divisible by 4 if
subtraction
the number formed by the two right-hand digits is divisible by 4
rectangular coordinates
right-hand digit is even
46. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Definition of genus
Commutative Law of Addition
repeated elements
47. A number that has no factors except itself and 1 is a
the genus of the curve
Set
its the sum of its digits is divisible by 3
Prime Number
48. Any number that is exactly divisible by a given number is a
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Multiple of the given number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
49. The number touching the variable (in the case of 5x - would be 5)
coefficient
upward
the genus of the curve
addition
50. A number is divisible by 3 if
T+9
In Diophantine geometry
complex number
its the sum of its digits is divisible by 3