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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 states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
Multiple of the given number
negative
its the sum of its digits is divisible by 3
Commutative Law of Multiplication

2. The set of all complex numbers is denoted by
C or
rectangular coordinates
multiplication
16(5+R)

3. A number is divisible by 8 if
Natural Numbers
addition
the number formed by the three right-hand digits is divisible by 8
expression

4. Plus
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
T+9
addition
division

5. 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
base-ten number
Downward
order of operations
addition

6. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Algebraic number theory
Absolute value and argument
repeated elements
K+6 - K+5 - K+4 K+3.........answer is K+3

7. 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.
Associative Law of Multiplication
upward
difference
The numbers are conventionally plotted using the real part

8. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
magnitude and direction
The numbers are conventionally plotted using the real part
To separate a number into prime factors

9. 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.
Equal
Analytic number theory
Definition of genus
the genus of the curve

10. 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.
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.
Forth Axiom of Equality
Third Axiom of Equality
Members of Elements of the Set

11. 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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12. 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.
repeated elements
upward
equation
Second Axiom of Equality

13. The greatest of 3 consecutive whole numbers - the smallest of which is F
Commutative Law of Addition
F - F+1 - F+2.......answer is F+2
difference
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

14. 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.
Commutative Law of Addition
Forth Axiom of Equality
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

15. First axiom of equality
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.
righthand digit is 0 or 5
subtraction

16. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
Q-16
difference
Number fields

17. 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
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).
Commutative Law of Addition
Analytic number theory

18. 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.
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
coefficient

19. 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.
base-ten number
quadratic field
Commutative Law of Addition
order of operations

20. 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
To separate a number into prime factors
Forth Axiom of Equality
subtraction
Members of Elements of the Set

21. Total
addition
Associative Law of Multiplication
Even Number
magnitude and direction

22. As shown earlier - c - di is the complex conjugate of the denominator c + di.
one characteristic in common such as similarity of appearance or purpose
addition
Analytic number theory
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

23. The objects or symbols in a set are called Numerals - Lines - or Points
16(5+R)
Members of Elements of the Set
Complex numbers
The real number a of the complex number z = a + bi

24. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
righthand digit is 0 or 5
repeated elements
Members of Elements of the Set

25. 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
Braces
Odd Number
Algebraic number theory

26. Product of 16 and the sum of 5 and number R
16(5+R)
rectangular coordinates
Commutative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space

27. Integers greater than zero and less than 5 form a set - as follows:
In Diophantine geometry
base-ten number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude

28. Any number that la a multiple of 2 is an
Even Number
negative
Commutative Law of Addition
The multiplication of two complex numbers is defined by the following formula:

29. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:
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).
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

30. The number touching the variable (in the case of 5x - would be 5)
subtraction
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.
the number formed by the three right-hand digits is divisible by 8
coefficient

31. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Inversive geometry
Commutative Law of Addition
counterclockwise through 90
rectangular coordinates

32. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
its the sum of its digits is divisible by 3
F - F+1 - F+2.......answer is F+2
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.

33. A letter tat represents a number that is unknown (usually X or Y)
complex number
base-ten number
variable
right-hand digit is even

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.
consecutive whole numbers
Commutative Law of Addition
Braces
addition

35. One term (5x or 4)
division
monomial
right-hand digit is even
polynomial

36. A number is divisible by 9 if
a curve - a surface or some other such object in n-dimensional space
Place Value Concept
difference
the sum of its digits is divisible by 9

37. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
complex number
Downward
multiplication
rectangular coordinates

38. The Arabic numerals from 0 through 9 are called
subtraction
addition
The real number a of the complex number z = a + bi
Digits

39. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
quadratic field
negative
Distributive Law
K+6 - K+5 - K+4 K+3.........answer is K+3

40. The central problem of Diophantine geometry is to determine when a Diophantine equation has
K+6 - K+5 - K+4 K+3.........answer is K+3
counterclockwise through 90
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
solutions

41. 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
Factor of the given number
The real number a of the complex number z = a + bi
negative
Positional notation (place value)

42. A number is divisible by 5 if its
addition
righthand digit is 0 or 5
Braces
The real number a of the complex number z = a + bi

43. Number X decreased by 12 divided by forty
Equal
magnitude and direction
To separate a number into prime factors
(x-12)/40

44. 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.
Associative Law of Addition
even and the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
addition

45. LAWS FOR COMBINING NUMBERS
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.
the number formed by the three right-hand digits is divisible by 8
constructing a parallelogram

46. A number that has no factors except itself and 1 is a
Prime Number
16(5+R)
Commutative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

47. Remainder
subtraction
division
its the sum of its digits is divisible by 3
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

48. Less than
Definition of genus
subtraction
Composite Number
the genus of the curve

49. 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
algebraic number
consecutive whole numbers
Positional notation (place value)
quadratic field

50. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Associative Law of Multiplication
Base of the number system
even and the sum of its digits is divisible by 3