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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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 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.
order of operations
Natural Numbers
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Complex numbers

2. 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
Third Axiom of Equality
Numerals
negative

3. Total
Associative Law of Addition
the genus of the curve
monomial
addition

4. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
variable
consecutive whole numbers
coefficient

5. 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
Q-16
base-ten number
Natural Numbers
Absolute value and argument

6. No short method has been found for determining whether a number is divisible by
7
Natural Numbers
upward
Even Number

7. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
right-hand digit is even
7
Downward

8. A number is divisible by 8 if
the sum of its digits is divisible by 9
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
variable

9. Quotient
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Inversive geometry
division
polynomial

10. 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.
C or
Inversive geometry
counterclockwise through 90

11. 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.
The multiplication of two complex numbers is defined by the following formula:
Members of Elements of the Set
Inversive geometry
Analytic number theory

12. The objects in a set have at least
counterclockwise through 90
one characteristic in common such as similarity of appearance or purpose
righthand digit is 0 or 5
Digits

13. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
negative
K+6 - K+5 - K+4 K+3.........answer is K+3
rectangular coordinates

14. Product
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
multiplication
Place Value Concept
To separate a number into prime factors

15. Number T increased by 9
T+9
even and the sum of its digits is divisible by 3
magnitude
Composite Number

16. The relative greatness of positive and negative numbers
Set
Commutative Law of Addition
magnitude
Commutative Law of Multiplication

17. A curve in the plane
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.
Algebraic number theory
Forth Axiom of Equality
an equation in two variables defines

18. 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
subtraction
base-ten number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
division

19. Has an equal sign (3x+5 = 14)
algebraic number
equation
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
base-ten number

20. Decreased by
variable
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
subtraction

21. Remainder
Composite Number
subtraction
Set
Definition of genus

22. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
multiplication
To separate a number into prime factors

23. Subtraction
F - F+1 - F+2.......answer is F+2
difference
the number formed by the three right-hand digits is divisible by 8
C or

24. 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.
variable
righthand digit is 0 or 5
Second Axiom of Equality
subtraction

25. A number is divisible by 9 if
magnitude and direction
In Diophantine geometry
the sum of its digits is divisible by 9
Positional notation (place value)

26. 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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27. A number that has factors other than itself and 1 is a
16(5+R)
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Composite Number
Third Axiom of Equality

28. As shown earlier - c - di is the complex conjugate of the denominator c + di.
coefficient
addition
a curve - a surface or some other such object in n-dimensional space
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

29. The number without a variable (5m+2). In this case - 2
Second Axiom of Equality
magnitude and direction
constant
Place Value Concept

30. 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.
Absolute value and argument
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.
quadratic field
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

31. Sixteen less than number Q
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Q-16
solutions

32. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
Numerals
Associative Law of Addition
equation

33. 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.
subtraction
repeated elements
rectangular coordinates
Associative Law of Multiplication

34. 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.
Number fields
Commutative Law of Addition
magnitude
Associative Law of Multiplication

35. Implies a collection or grouping of similar - objects or symbols.
Definition of genus
consecutive whole numbers
Set
Inversive geometry

36. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Complex numbers
Natural Numbers
solutions
upward

37. 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
Place Value Concept
quadratic field
algebraic number
K+6 - K+5 - K+4 K+3.........answer is K+3

38. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
equation
a curve - a surface or some other such object in n-dimensional space
K+6 - K+5 - K+4 K+3.........answer is K+3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

39. 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
Positional notation (place value)
base-ten number
magnitude
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

40. 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.
its the sum of its digits is divisible by 3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
constructing a parallelogram
Associative Law of Addition

41. 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
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).
expression
Braces
Algebraic number theory

42. Sum
monomial
T+9
addition
one characteristic in common such as similarity of appearance or purpose

43. Increased by
magnitude
Commutative Law of Addition
the genus of the curve
addition

44. Product of 16 and the sum of 5 and number R
Prime Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
quadratic field
16(5+R)

45. 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
Second Axiom of Equality
Set
division
complex number

46. 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
division
(x-12)/40
Even Number
To separate a number into prime factors

47. 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
Digits
Place Value Concept
Forth Axiom of Equality
constant

48. 2 -3 -4 -5 -6
solutions
consecutive whole numbers
variable
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

49. Any number that is not a multiple of 2 is an
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.
Odd Number
T+9
negative

50. A number is divisible by 6 if it is
order of operations
expression
even and the sum of its digits is divisible by 3
Second Axiom of Equality