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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. 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.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

2. 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.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Set
Commutative Law of Addition
quadratic field

3. Are used to indicate sets
Braces
Factor of the given number
expression
K+6 - K+5 - K+4 K+3.........answer is K+3

4. 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.
a curve - a surface or some other such object in n-dimensional space
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Analytic number theory
Factor of the given number

5. In particular - the square of the imaginary unit is -1: The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed - if i is treated as a number so that di mean
The multiplication of two complex numbers is defined by the following formula:
Positional notation (place value)
addition
Base of the number system

6. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
In Diophantine geometry
Associative Law of Addition
Inversive geometry
(x-12)/40

7. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Q-16
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Second Axiom of Equality

8. 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.
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).
Associative Law of Addition
Composite Number
The numbers are conventionally plotted using the real part

9. The number without a variable (5m+2). In this case - 2
The real number a of the complex number z = a + bi
constant
upward
In Diophantine geometry

10. The number touching the variable (in the case of 5x - would be 5)
K+6 - K+5 - K+4 K+3.........answer is K+3
coefficient
base-ten number
To separate a number into prime factors

11. 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
the number formed by the three right-hand digits is divisible by 8
base-ten number
Place Value Concept
difference

12. A number is divisible by 6 if it is
magnitude and direction
right-hand digit is even
Commutative Law of Addition
even and the sum of its digits is divisible by 3

13. A number is divisible by 2 if
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 curve - a surface or some other such object in n-dimensional space
Commutative Law of Multiplication
right-hand digit is even

14. The defining characteristic of a position vector is that it has
magnitude and direction
one characteristic in common such as similarity of appearance or purpose
counterclockwise through 90
monomial

15. A number is divisible by 9 if
monomial
the sum of its digits is divisible by 9
polynomial
constant

16. 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
complex number
polynomial
the sum of its digits is divisible by 9
The numbers are conventionally plotted using the real part

17. No short method has been found for determining whether a number is divisible by
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Odd Number
Numerals
7

18. One term (5x or 4)
the sum of its digits is divisible by 9
Algebraic number theory
negative
monomial

19. A number is divisible by 3 if
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
its the sum of its digits is divisible by 3
quadratic field
Downward

20. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
equation
order of operations
Second Axiom of Equality
C or

21. 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
Downward
expression
base-ten number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

22. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
rectangular coordinates
positive
Distributive Law
magnitude and direction

23. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude and direction
Braces

24. Any number that is exactly divisible by a given number is a
Multiple of the given number
Equal
its the sum of its digits is divisible by 3
the sum of its digits is divisible by 9

25. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Downward
Commutative Law of Addition

26. Does not have an equal sign (3x+5) (2a+9b)
expression
constructing a parallelogram
complex number
the number formed by the two right-hand digits is divisible by 4

27. Product
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
multiplication
upward
The numbers are conventionally plotted using the real part

28. Total
Even Number
Q-16
addition
Multiple of the given number

29. 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.
16(5+R)
Second Axiom of Equality
In Diophantine geometry
Associative Law of Addition

30. 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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31. Implies a collection or grouping of similar - objects or symbols.
Third Axiom of Equality
Absolute value and argument
Set
Commutative Law of Multiplication

32. The objects or symbols in a set are called Numerals - Lines - or Points
division
Members of Elements of the Set
the sum of its digits is divisible by 9
multiplication

33. LAWS FOR COMBINING NUMBERS
difference
(x-12)/40
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The multiplication of two complex numbers is defined by the following formula:

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.
even and the sum of its digits is divisible by 3
Commutative Law of Addition
Multiple of the given number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

35. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
In Diophantine geometry
The real number a of the complex number z = a + bi
an equation in two variables defines
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

36. The central problem of Diophantine geometry is to determine when a Diophantine equation has
magnitude
solutions
In Diophantine geometry
monomial

37. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
quadratic field
addition
a complex number is real if and only if it equals its conjugate.

38. Decreased by
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Q-16
The multiplication of two complex numbers is defined by the following formula:
subtraction

39. 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
16(5+R)
righthand digit is 0 or 5
an equation in two variables defines
Equal

40. 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.
Q-16
Absolute value and argument
Commutative Law of Multiplication
Members of Elements of the Set

41. Number X decreased by 12 divided by forty
(x-12)/40
Commutative Law of Addition
Complex numbers
subtraction

42. Number T increased by 9
T+9
Multiple of the given number
its the sum of its digits is divisible by 3
addition

43. As shown earlier - c - di is the complex conjugate of the denominator c + di.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
polynomial
Forth Axiom of Equality
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

44. 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.
Odd Number
Digits
Second Axiom of Equality
Third Axiom of Equality

45. 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.
addition
monomial
Third Axiom of Equality
quadratic field

46. 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
Commutative Law of Addition
upward
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

47. Quotient
positive
Definition of genus
Commutative Law of Multiplication
division

48. Remainder
rectangular coordinates
Positional notation (place value)
subtraction
an equation in two variables defines

49. 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
positive
base-ten 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).

50. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
subtraction
equation
T+9