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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. 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
To separate a number into prime factors
F - F+1 - F+2.......answer is F+2
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
algebraic number
2. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Second Axiom of Equality
Definition of genus
C or
3. Total
Natural Numbers
Multiple of the given number
a curve - a surface or some other such object in n-dimensional space
addition
4. A letter tat represents a number that is unknown (usually X or Y)
Prime Number
Commutative Law of Addition
Analytic number theory
variable
5. 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
Equal
Base of the number system
The real number a of the complex number z = a + bi
6. 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
Base of the number system
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
In Diophantine geometry
Even Number
7. The relative greatness of positive and negative numbers
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
a curve - a surface or some other such object in n-dimensional space
magnitude
magnitude and direction
8. Increased by
even and the sum of its digits is divisible by 3
addition
C or
rectangular coordinates
9. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
In Diophantine geometry
solutions
the number formed by the three right-hand digits is divisible by 8
10. Any number that is exactly divisible by a given number is a
In Diophantine geometry
Absolute value and argument
Braces
Multiple of the given number
11. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Distributive Law
monomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
right-hand digit is even
12. If z is a real number (i.e. - y = 0) - then r = |x|. In general - by Pythagoras' theorem - r is the distance of the point P representing the complex number z to the origin.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Equal
the number formed by the three right-hand digits is divisible by 8
13. Quotient
Odd Number
Absolute value and argument
division
a curve - a surface or some other such object in n-dimensional space
14. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Set
Positional notation (place value)
order of operations
Analytic number theory
15. 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
constant
Absolute value and argument
Odd Number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
16. The greatest of 3 consecutive whole numbers - the smallest of which is F
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
F - F+1 - F+2.......answer is F+2
(x-12)/40
variable
17. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.
Number fields
Associative Law of Addition
Place Value Concept
the genus of the curve
18. 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.)
Number fields
right-hand digit is even
negative
Multiple of the given number
19. First axiom of equality
base-ten number
a complex number is real if and only if it equals its conjugate.
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.
(x-12)/40
20. The number without a variable (5m+2). In this case - 2
Prime Number
upward
constant
counterclockwise through 90
21. The set of all complex numbers is denoted by
C or
The real number a of the complex number z = a + bi
Q-16
T+9
22. 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.
Factor of the given number
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).
To separate a number into prime factors
quadratic field
23. 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
Composite Number
the sum of its digits is divisible by 9
In Diophantine geometry
24. A number is divisible by 3 if
its the sum of its digits is divisible by 3
Associative Law of Addition
The multiplication of two complex numbers is defined by the following formula:
Even Number
25. A number is divisible by 9 if
a complex number is real if and only if it equals its conjugate.
a curve - a surface or some other such object in n-dimensional space
the sum of its digits is divisible by 9
an equation in two variables defines
26. 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.
Complex numbers
In Diophantine geometry
complex number
subtraction
27. A number that has factors other than itself and 1 is a
(x-12)/40
Composite Number
Numerals
Commutative Law of Addition
28. The defining characteristic of a position vector is that it has
counterclockwise through 90
constant
Complex numbers
magnitude and direction
29. Are used to indicate sets
Associative Law of Addition
expression
Braces
consecutive whole numbers
30. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
repeated elements
the genus of the curve
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).
31. 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.
addition
Associative Law of Multiplication
order of operations
coefficient
32. Any number that is not a multiple of 2 is an
Multiple of the given number
Odd Number
Numerals
The numbers are conventionally plotted using the real part
33. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
34. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Algebraic number theory
Natural Numbers
35. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Natural Numbers
Prime Factor
36. 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.
polynomial
algebraic number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
37. 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
addition
Braces
Inversive geometry
38. The place value which corresponds to a given position in a number is determined by the
right-hand digit is even
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
an equation in two variables defines
Base of the number system
39. Product of 16 and the sum of 5 and number R
addition
To separate a number into prime factors
addition
16(5+R)
40. 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
subtraction
Associative Law of Addition
In Diophantine geometry
an equation in two variables defines
41. The numbers which are used for counting in our number system are sometimes called
The multiplication of two complex numbers is defined by the following formula:
multiplication
Natural Numbers
Even Number
42. 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
Place Value Concept
Braces
even and the sum of its digits is divisible by 3
Commutative Law of Addition
43. 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
Algebraic number theory
The real number a of the complex number z = a + bi
Downward
base-ten number
44. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Algebraic number theory
counterclockwise through 90
difference
Distributive Law
45. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
coefficient
Downward
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
46. The finiteness or not of the number of rational or integer points on an algebraic curve
16(5+R)
Complex numbers
magnitude
the genus of the curve
47. No short method has been found for determining whether a number is divisible by
Prime Factor
Prime Number
7
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
48. The number touching the variable (in the case of 5x - would be 5)
Q-16
coefficient
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Second Axiom of Equality
49. 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.
Factor of the given number
addition
Downward
Third Axiom of Equality
50. Sixteen less than number Q
addition
Base of the number system
C or
Q-16