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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. 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.
multiplication
one characteristic in common such as similarity of appearance or purpose
Second Axiom of Equality
upward
2. As shown earlier - c - di is the complex conjugate of the denominator c + di.
equation
quadratic field
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Forth Axiom of Equality
3. Number symbols
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}
Prime Factor
Numerals
4. Total
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 multiplication of two complex numbers is defined by the following formula:
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
5. 2 -3 -4 -5 -6
polynomial
Second Axiom of Equality
base-ten number
consecutive whole numbers
6. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
coefficient
solutions
magnitude and direction
rectangular coordinates
7. Are used to indicate sets
order of operations
the number formed by the three right-hand digits is divisible by 8
Braces
subtraction
8. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
9. A number that has factors other than itself and 1 is a
subtraction
the genus of the curve
Composite Number
Associative Law of Addition
10. Subtraction
Associative Law of Addition
solutions
difference
addition
11. Has an equal sign (3x+5 = 14)
equation
Number fields
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.
Associative Law of Addition
12. A number is divisible by 9 if
In Diophantine geometry
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
the sum of its digits is divisible by 9
Associative Law of Multiplication
13. Does not have an equal sign (3x+5) (2a+9b)
Factor of the given number
magnitude and direction
Natural Numbers
expression
14. 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 number formed by the three right-hand digits is divisible by 8
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Inversive geometry
15. A number is divisible by 8 if
Numerals
the number formed by the three right-hand digits is divisible by 8
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).
a curve - a surface or some other such object in n-dimensional space
16. 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.
upward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
the sum of its digits is divisible by 9
Braces
17. 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.
order of operations
The numbers are conventionally plotted using the real part
Associative Law of Addition
the genus of the curve
18. 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.
Downward
quadratic field
Inversive geometry
base-ten number
19. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Braces
negative
Members of Elements of the Set
addition
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.
a complex number is real if and only if it equals its conjugate.
Multiple of the given number
Commutative Law of Multiplication
Associative Law of Addition
21. If a factor of a number is prime - it is called a
counterclockwise through 90
Prime Factor
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Braces
22. 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
Absolute value and argument
Equal
equation
upward
23. 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
To separate a number into prime factors
Algebraic number theory
Distributive Law
even and the sum of its digits is divisible by 3
24. A letter tat represents a number that is unknown (usually X or Y)
variable
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude and direction
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 defining characteristic of a position vector is that it has
magnitude and direction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
upward
solutions
26. 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
Multiple of the given number
algebraic number
C or
Associative Law of Addition
27. 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
Factor of the given number
rectangular coordinates
28. 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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29. 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.
Commutative Law of Addition
magnitude
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Commutative Law of Multiplication
30. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
equation
Factor of the given number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
31. A number that has no factors except itself and 1 is a
rectangular coordinates
Prime Number
order of operations
a curve - a surface or some other such object in n-dimensional space
32. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
C or
rectangular coordinates
Associative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
33. 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
Complex numbers
Definition of genus
The real number a of the complex number z = a + bi
a curve - a surface or some other such object in n-dimensional space
34. No short method has been found for determining whether a number is divisible by
consecutive whole numbers
magnitude
7
C or
35. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
subtraction
Commutative Law of Addition
right-hand digit is even
upward
36. Implies a collection or grouping of similar - objects or symbols.
Place Value Concept
Natural Numbers
Set
Members of Elements of the Set
37. First axiom of equality
addition
a curve - a surface or some other such object in n-dimensional space
consecutive whole 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.
38. The number without a variable (5m+2). In this case - 2
Set
order of operations
constant
The multiplication of two complex numbers is defined by the following formula:
39. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
negative
To separate a number into prime factors
positive
Multiple of the given number
40. A curve in the plane
Associative Law of Multiplication
Prime Factor
Numerals
an equation in two variables defines
41. The number touching the variable (in the case of 5x - would be 5)
coefficient
Downward
Algebraic number theory
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
42. The place value which corresponds to a given position in a number is determined by the
Braces
Definition of genus
subtraction
Base of the number system
43. A number is divisible by 5 if its
righthand digit is 0 or 5
Third Axiom of Equality
Odd Number
magnitude
44. 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.
(x-12)/40
consecutive whole numbers
Analytic number theory
Associative Law of Addition
45. Quotient
algebraic number
magnitude
division
Place Value Concept
46. A number is divisible by 3 if
constructing a parallelogram
division
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
its the sum of its digits is divisible by 3
47. The finiteness or not of the number of rational or integer points on an algebraic curve
addition
Positional notation (place value)
algebraic number
the genus of the curve
48. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
righthand digit is 0 or 5
Numerals
solutions
49. Less than
expression
Algebraic number theory
quadratic field
subtraction
50. Sum
Analytic number theory
addition
a complex number is real if and only if it equals its conjugate.
Definition of genus
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