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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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Subjects
:
clep
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math
Instructions:
Answer 50 questions in 15 minutes.
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.
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. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
The numbers are conventionally plotted using the real part
Prime Number
Inversive geometry
2. An equation - or system of equations - in two or more variables defines
coefficient
order of operations
a curve - a surface or some other such object in n-dimensional space
Distributive Law
3. One term (5x or 4)
monomial
In Diophantine geometry
Prime Number
16(5+R)
4. 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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5. Any number that is exactly divisible by a given number is a
In Diophantine geometry
Multiple of the given number
solutions
positive
6. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
even and the sum of its digits is divisible by 3
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
division
Commutative Law of Multiplication
7. A number that has factors other than itself and 1 is a
Composite Number
an equation in two variables defines
T+9
Third Axiom of Equality
8. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
equation
Positional notation (place value)
consecutive whole numbers
9. 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.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
subtraction
Distributive Law
Associative Law of Multiplication
10. A number is divisible by 2 if
right-hand digit is even
the genus of the curve
coefficient
division
11. 2 -3 -4 -5 -6
polynomial
Equal
the number formed by the three right-hand digits is divisible by 8
consecutive whole numbers
12. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Inversive geometry
solutions
The numbers are conventionally plotted using the real part
13. First axiom of equality
upward
Q-16
Natural Numbers
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.
14. 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
Multiple of the given number
Downward
Distributive Law
15. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.
addition
Braces
Inversive geometry
Commutative Law of Addition
16. 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:
Equal
Positional notation (place value)
Definition of genus
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).
17. Sum
subtraction
addition
Digits
constant
18. 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
addition
Absolute value and argument
In Diophantine geometry
variable
19. Sixteen less than number Q
Q-16
complex number
the number formed by the two right-hand digits is divisible by 4
Positional notation (place value)
20. Subtraction
consecutive whole numbers
difference
The multiplication of two complex numbers is defined by the following formula:
the sum of its digits is divisible by 9
21. Number T increased by 9
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).
addition
T+9
Commutative Law of Multiplication
22. The finiteness or not of the number of rational or integer points on an algebraic curve
order of operations
Base of the number system
the genus of the curve
Complex numbers
23. More than
Commutative Law of Addition
Third Axiom of Equality
addition
negative
24. The objects in a set have at least
variable
addition
one characteristic in common such as similarity of appearance or purpose
solutions
25. 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
Composite Number
magnitude
Place Value Concept
In Diophantine geometry
26. 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
addition
upward
variable
27. 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.
Definition of genus
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Factor of the given number
Commutative Law of Addition
28. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
(x-12)/40
righthand digit is 0 or 5
Distributive Law
order of operations
29. 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 theory
algebraic number
counterclockwise through 90
7
30. 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
Downward
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Algebraic number theory
algebraic number
31. Any number that la a multiple of 2 is an
Commutative Law of Multiplication
Set
an equation in two variables defines
Even Number
32. Quotient
division
negative
Numerals
Analytic number theory
33. A number that has no factors except itself and 1 is a
Commutative Law of Addition
C or
Inversive geometry
Prime Number
34. The numbers which are used for counting in our number system are sometimes called
its the sum of its digits is divisible by 3
Natural Numbers
Second Axiom of Equality
Positional notation (place value)
35. The defining characteristic of a position vector is that it has
magnitude and direction
the number formed by the three right-hand digits is divisible by 8
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: .
36. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Third Axiom of Equality
Q-16
Members of Elements of the Set
Inversive geometry
37. 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.)
order of operations
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Number fields
right-hand digit is even
38. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
the genus of the curve
order of operations
positive
39. 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.
7
Associative Law of Addition
monomial
To separate a number into prime factors
40. 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
Even Number
base-ten number
The real number a of the complex number z = a + bi
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
41. The greatest of 3 consecutive whole numbers - the smallest of which is F
Definition of genus
F - F+1 - F+2.......answer is F+2
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
42. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
constant
The real number a of the complex number z = a + bi
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Composite Number
43. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
counterclockwise through 90
upward
one characteristic in common such as similarity of appearance or purpose
a complex number is real if and only if it equals its conjugate.
44. Does not have an equal sign (3x+5) (2a+9b)
right-hand digit is even
expression
rectangular coordinates
addition
45. Number symbols
Distributive Law
Numerals
Positional notation (place value)
The multiplication of two complex numbers is defined by the following formula:
46. The set of all complex numbers is denoted by
Even Number
C or
rectangular coordinates
a curve - a surface or some other such object in n-dimensional space
47. Plus
addition
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).
Composite Number
quadratic field
48. 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
right-hand digit is even
Numerals
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula:
49. A number is divisible by 4 if
an equation in two variables defines
the number formed by the two right-hand digits is divisible by 4
consecutive whole numbers
righthand digit is 0 or 5
50. The Arabic numerals from 0 through 9 are called
upward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
rectangular coordinates
Digits
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