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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. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th
Braces
Definition of genus
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
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.
2. Has an equal sign (3x+5 = 14)
coefficient
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.
equation
the number formed by the three right-hand digits is divisible by 8
3. Implies a collection or grouping of similar - objects or symbols.
(x-12)/40
K+6 - K+5 - K+4 K+3.........answer is K+3
Set
subtraction
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
magnitude
upward
Odd Number
5. A letter tat represents a number that is unknown (usually X or Y)
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).
variable
one characteristic in common such as similarity of appearance or purpose
6. 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.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
counterclockwise through 90
Analytic number theory
division
7. 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.
Associative Law of Multiplication
solutions
Second Axiom of Equality
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
8. The finiteness or not of the number of rational or integer points on an algebraic curve
K+6 - K+5 - K+4 K+3.........answer is K+3
Algebraic number theory
even and the sum of its digits is divisible by 3
the genus of the curve
9. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Base of the number system
expression
10. 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 -
base-ten number
Inversive geometry
the sum of its digits is divisible by 9
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
11. 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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The numbers are conventionally plotted using the real part
Digits
Commutative Law of Multiplication
12. Plus
Commutative Law of Addition
addition
magnitude
T+9
13. 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
T+9
algebraic number
Distributive Law
Multiple of the given number
14. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Positional notation (place value)
Commutative Law of Multiplication
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Inversive geometry
15. The numbers which are used for counting in our number system are sometimes called
consecutive whole numbers
addition
Natural Numbers
Positional notation (place value)
16. The objects in a set have at least
division
F - F+1 - F+2.......answer is F+2
constant
one characteristic in common such as similarity of appearance or purpose
17. Product
Prime Number
multiplication
Prime Factor
Absolute value and argument
18. A number that has factors other than itself and 1 is a
addition
Composite Number
16(5+R)
T+9
19. Quotient
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
K+6 - K+5 - K+4 K+3.........answer is K+3
division
the number formed by the three right-hand digits is divisible by 8
20. Decreased by
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 absolute value (or modulus or magnitude) of a complex number z = x + yi is
subtraction
expression
21. Number X decreased by 12 divided by forty
Commutative Law of Addition
solutions
(x-12)/40
Associative Law of Multiplication
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
Forth Axiom of Equality
The real number a of the complex number z = a + bi
complex number
Third Axiom of Equality
23. Does not have an equal sign (3x+5) (2a+9b)
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
expression
Prime Factor
24. Increased by
addition
counterclockwise through 90
Downward
C or
25. The real and imaginary parts of a complex number can be extracted using the conjugate:
equation
Q-16
Composite Number
a complex number is real if and only if it equals its conjugate.
26. More than one term (5x+4 contains two)
Equal
subtraction
Definition of genus
polynomial
27. The greatest of 3 consecutive whole numbers - the smallest of which is F
16(5+R)
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
equation
F - F+1 - F+2.......answer is F+2
28. Less than
Equal
In Diophantine geometry
subtraction
addition
29. A number is divisible by 2 if
algebraic number
right-hand digit is even
base-ten number
monomial
30. Addition of two complex numbers can be done geometrically by
Distributive Law
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).
constructing a parallelogram
The numbers are conventionally plotted using the real part
31. Number symbols
addition
Factor of the given number
Numerals
Members of Elements of the Set
32. 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
Second Axiom of Equality
base-ten number
the sum of its digits is divisible by 9
Associative Law of Multiplication
33. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Downward
a curve - a surface or some other such object in n-dimensional space
Distributive Law
Set
34. Sum
Third Axiom of Equality
Complex numbers
addition
Composite Number
35. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Associative Law of Addition
repeated elements
even and the sum of its digits is divisible by 3
Multiple of the given number
36. 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
magnitude and direction
counterclockwise through 90
Numerals
Algebraic number theory
37. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
the sum of its digits is divisible by 9
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
division
Commutative Law of Addition
38. A number that has no factors except itself and 1 is a
equation
Prime Number
complex number
its the sum of its digits is divisible by 3
39. Remainder
subtraction
Number fields
Even Number
Digits
40. Any number that is not a multiple of 2 is an
Commutative Law of Addition
subtraction
Odd Number
negative
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 genus of the curve
Second Axiom of Equality
Associative Law of Addition
repeated elements
42. 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
Even Number
difference
algebraic number
43. The number touching the variable (in the case of 5x - would be 5)
the genus of the curve
coefficient
Distributive Law
Digits
44. If a factor of a number is prime - it is called a
base-ten number
In Diophantine geometry
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Prime Factor
45. 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.
multiplication
the number formed by the two right-hand digits is divisible by 4
quadratic field
The numbers are conventionally plotted using the real part
46. 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
the number formed by the three right-hand digits is divisible by 8
negative
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).
Positional notation (place value)
47. Total
the genus of the curve
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
Commutative Law of Multiplication
48. 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.
subtraction
Commutative Law of Addition
order of operations
magnitude
49. Integers greater than zero and less than 5 form a set - as follows:
Factor of the given number
righthand digit is 0 or 5
Natural Numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
50. Number T increased by 9
Composite Number
T+9
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Prime Number