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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. 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.
an equation in two variables defines
order of operations
Commutative Law of Addition
expression

2. A number is divisible by 2 if
order of operations
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
right-hand digit is even

3. Any number that is exactly divisible by a given number is a
Distributive Law
righthand digit is 0 or 5
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).
Multiple of the given number

4. The greatest of 3 consecutive whole numbers - the smallest of which is F
base-ten number
Odd Number
a complex number is real if and only if it equals its conjugate.
F - F+1 - F+2.......answer is F+2

5. 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
negative
a curve - a surface or some other such object in n-dimensional space
addition

6. More than
repeated elements
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition

7. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Associative Law of Addition
Downward
Members of Elements of the Set
To separate a number into prime factors

8. 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.
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 number formed by the two right-hand digits is divisible by 4
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Commutative Law of Addition

9. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
Forth Axiom of Equality
Commutative Law of Addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

10. 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
The real number a of the complex number z = a + bi
addition
Natural Numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

11. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Multiple of the given number
base-ten number
the number formed by the two right-hand digits is divisible by 4

12. The relative greatness of positive and negative numbers
addition
magnitude
Complex numbers
Associative Law of Addition

13. 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
Odd Number
In Diophantine geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

14. 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.
7
K+6 - K+5 - K+4 K+3.........answer is K+3
Analytic number theory
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).

15. 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
Third Axiom of Equality
the number formed by the three right-hand digits is divisible by 8
Algebraic number theory
Base of the number system

16. The numbers which are used for counting in our number system are sometimes called
quadratic field
Factor of the given number
Natural Numbers
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

17. A letter tat represents a number that is unknown (usually X or Y)
order of operations
Number fields
variable
subtraction

18. The defining characteristic of a position vector is that it has
equation
Digits
magnitude and direction
Composite Number

19. Remainder
The multiplication of two complex numbers is defined by the following formula:
subtraction
addition
Members of Elements of the Set

20. 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
Absolute value and argument
the number formed by the three right-hand digits is divisible by 8
a curve - a surface or some other such object in n-dimensional space
Definition of genus

21. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Third Axiom of Equality
Commutative Law of Addition
rectangular coordinates
Commutative Law of Multiplication

22. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Commutative Law of Addition
counterclockwise through 90
polynomial
quadratic field

23. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
the number formed by the three right-hand digits is divisible by 8
The real number a of the complex number z = a + bi
addition

24. 2 -3 -4 -5 -6
the number formed by the two right-hand digits is divisible by 4
Associative Law of Multiplication
consecutive whole numbers
equation

25. A number is divisible by 8 if
subtraction
the number formed by the three right-hand digits is divisible by 8
Base of the number system
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

26. 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 numbers are conventionally plotted using the real part
Prime Factor
In Diophantine geometry

27. One term (5x or 4)
Odd Number
monomial
(x-12)/40
quadratic field

28. Total
16(5+R)
the number formed by the two right-hand digits is divisible by 4
one characteristic in common such as similarity of appearance or purpose
addition

29. The place value which corresponds to a given position in a number is determined by the
addition
algebraic number
Base of the number system
solutions

30. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Forth Axiom of Equality
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Complex numbers
division

31. 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.
algebraic number
K+6 - K+5 - K+4 K+3.........answer is K+3
Number fields

32. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
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.
negative
Base of the number system

33. 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
Number fields
the sum of its digits is divisible by 9
Positional notation (place value)
complex number

34. 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.
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
quadratic field
16(5+R)

35. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Distributive Law
algebraic number
the number formed by the three right-hand digits is divisible by 8

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.
its the sum of its digits is divisible by 3
16(5+R)
Complex numbers
algebraic number

37. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
a curve - a surface or some other such object in n-dimensional space
coefficient
Commutative Law of Multiplication

38. Integers greater than zero and less than 5 form a set - as follows:
Commutative Law of Addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Prime Number
quadratic field

39. A number that has no factors except itself and 1 is a
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the number formed by the three right-hand digits is divisible by 8
Prime Number
righthand digit is 0 or 5

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.
subtraction
C or
Associative Law of Addition
Third Axiom of Equality

41. Product of 16 and the sum of 5 and number R
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
16(5+R)
Digits
consecutive whole numbers

42. Are used to indicate sets
base-ten number
Braces
Place Value Concept
Numerals

43. 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
its the sum of its digits is divisible by 3
To separate a number into prime factors
repeated elements

44. A curve in the plane
an equation in two variables defines
7
In Diophantine geometry
upward

45. 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.
Associative Law of Multiplication
Third Axiom of Equality
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.
Complex numbers

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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Positional notation (place value)
an equation in two variables defines
Equal

47. Increased by
quadratic field
addition
complex number
counterclockwise through 90

48. A number is divisible by 4 if
the genus of the curve
quadratic field
the number formed by the two right-hand digits is divisible by 4
Analytic number theory

49. A number is divisible by 9 if
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
the sum of its digits is divisible by 9
Commutative Law of Multiplication
16(5+R)

50. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Associative Law of Multiplication
Number fields
addition
solutions