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CLEP General Mathematics: Number Systems And Sets
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Subjects
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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. Remainder
subtraction
Prime Number
Base of the number system
(x-12)/40
2. Product of 16 and the sum of 5 and number R
The numbers are conventionally plotted using the real part
16(5+R)
Third Axiom of Equality
right-hand digit is even
3. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Algebraic number theory
constant
Downward
4. A number is divisible by 8 if
Commutative Law of Multiplication
K+6 - K+5 - K+4 K+3.........answer is K+3
rectangular coordinates
the number formed by the three right-hand digits is divisible by 8
5. More than one term (5x+4 contains two)
polynomial
In Diophantine geometry
Composite Number
Inversive geometry
6. 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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
complex number
Inversive geometry
coefficient
7. 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.)
Associative Law of Addition
Number fields
(x-12)/40
Associative Law of Multiplication
8. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Multiple of the given number
K+6 - K+5 - K+4 K+3.........answer is K+3
repeated elements
Members of Elements of the Set
9. Product
Second Axiom of Equality
The numbers are conventionally plotted using the real part
multiplication
Members of Elements of the Set
10. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
Set
addition
Composite Number
11. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
multiplication
Braces
Multiple of the given number
12. First axiom of equality
Forth Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
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.
13. The finiteness or not of the number of rational or integer points on an algebraic curve
Even Number
addition
the genus of the curve
Natural Numbers
14. Number T increased by 9
upward
Complex numbers
T+9
Prime Number
15. Number symbols
repeated elements
Inversive geometry
Numerals
Natural Numbers
16. 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
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).
a complex number is real if and only if it equals its conjugate.
17. No short method has been found for determining whether a number is divisible by
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.
7
Associative Law of Multiplication
quadratic field
18. Any number that can be divided lnto a given number without a remainder is a
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Factor of the given number
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.
subtraction
19. The number touching the variable (in the case of 5x - would be 5)
Positional notation (place value)
its the sum of its digits is divisible by 3
coefficient
Commutative Law of Addition
20. Less than
The multiplication of two complex numbers is defined by the following formula:
subtraction
upward
rectangular coordinates
21. 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
Factor of the given number
16(5+R)
The real number a of the complex number z = a + bi
Prime Factor
22. Plus
addition
a complex number is real if and only if it equals its conjugate.
Positional notation (place value)
Prime Factor
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.
subtraction
Analytic number theory
Complex numbers
The real number a of the complex number z = a + bi
24. Any number that is exactly divisible by a given number is a
subtraction
Multiple of the given number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
25. 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.
The numbers are conventionally plotted using the real part
Prime Number
Braces
Distributive Law
26. The objects or symbols in a set are called Numerals - Lines - or Points
Prime Number
base-ten number
even and the sum of its digits is divisible by 3
Members of Elements of the Set
27. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
To separate a number into prime factors
Factor of the given number
monomial
K+6 - K+5 - K+4 K+3.........answer is K+3
28. A curve in the plane
an equation in two variables defines
F - F+1 - F+2.......answer is F+2
subtraction
C or
29. The greatest of 3 consecutive whole numbers - the smallest of which is F
The numbers are conventionally plotted using the real part
In Diophantine geometry
F - F+1 - F+2.......answer is F+2
addition
30. 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
counterclockwise through 90
multiplication
subtraction
base-ten number
31. The place value which corresponds to a given position in a number is determined by the
Base of the number system
upward
Place Value Concept
subtraction
32. The set of all complex numbers is denoted by
subtraction
Inversive geometry
Positional notation (place value)
C or
33. Does not have an equal sign (3x+5) (2a+9b)
expression
Members of Elements of the Set
Numerals
equation
34. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
F - F+1 - F+2.......answer is F+2
rectangular coordinates
Numerals
35. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor
C or
The multiplication of two complex numbers is defined by the following formula:
To separate a number into prime factors
base-ten number
36. 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.
constant
C or
Complex numbers
the number formed by the two right-hand digits is divisible by 4
37. A number is divisible by 5 if its
Definition of genus
Third Axiom of Equality
addition
righthand digit is 0 or 5
38. 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
an equation in two variables defines
Commutative Law of Addition
Algebraic number theory
Positional notation (place value)
39. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
In Diophantine geometry
F - F+1 - F+2.......answer is F+2
consecutive whole numbers
40. The numbers which are used for counting in our number system are sometimes called
Digits
Natural Numbers
a complex number is real if and only if it equals its conjugate.
addition
41. 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.
7
Associative Law of Addition
Downward
K+6 - K+5 - K+4 K+3.........answer is K+3
42. 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.
Second Axiom of Equality
the genus of the curve
Third Axiom of Equality
subtraction
43. 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
upward
Factor of the given number
In Diophantine geometry
44. Are used to indicate sets
algebraic number
Set
Braces
addition
45. Quotient
division
counterclockwise through 90
monomial
Downward
46. The defining characteristic of a position vector is that it has
Positional notation (place value)
subtraction
Even Number
magnitude and direction
47. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Absolute value and argument
order of operations
base-ten number
Downward
48. 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
Algebraic number theory
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
consecutive whole numbers
49. A number is divisible by 2 if
right-hand digit is even
even and the sum of its digits is divisible by 3
order of operations
F - F+1 - F+2.......answer is F+2
50. A number is divisible by 3 if
Analytic number theory
algebraic number
Algebraic number theory
its the sum of its digits is divisible by 3
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