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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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1. 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
Distributive Law
The multiplication of two complex numbers is defined by the following formula:
Positional notation (place value)
Associative Law of Addition

2. 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
algebraic number
solutions
The multiplication of two complex numbers is defined by the following formula:
monomial

3. The objects in a set have at least
Second Axiom of Equality
one characteristic in common such as similarity of appearance or purpose
its the sum of its digits is divisible by 3
positive

4. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
addition
Analytic number theory
7
order of operations

5. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Numerals
magnitude and direction
the sum of its digits is divisible by 9
upward

6. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Number fields
division
negative

7. The real and imaginary parts of a complex number can be extracted using the conjugate:
subtraction
division
a complex number is real if and only if it equals its conjugate.
Equal

8. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
In Diophantine geometry
the sum of its digits is divisible by 9
Distributive Law
T+9

9. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Base of the number system
difference

10. The finiteness or not of the number of rational or integer points on an algebraic curve
a curve - a surface or some other such object in n-dimensional space
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
equation
the genus of the curve

11. 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
upward
constant
Forth Axiom of Equality
In Diophantine geometry

12. Any number that is exactly divisible by a given number is a
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Q-16
Multiple of the given number
one characteristic in common such as similarity of appearance or purpose

13. 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.
Forth Axiom of Equality
Prime Number
To separate a number into prime factors
order of operations

14. The Arabic numerals from 0 through 9 are called
Commutative Law of Multiplication
Digits
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
even and the sum of its digits is divisible by 3

15. LAWS FOR COMBINING NUMBERS
Even Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
T+9
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.

16. 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
Definition of genus
Equal
Odd Number
C or

17. 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.
repeated elements
To separate a number into prime factors
quadratic field
expression

18. Implies a collection or grouping of similar - objects or symbols.
Absolute value and argument
Numerals
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Set

19. 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.
Definition of genus
Even Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
coefficient

20. 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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21. 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.
algebraic number
Even Number
Analytic number theory
The real number a of the complex number z = a + bi

22. Increased by
addition
(x-12)/40
its the sum of its digits is divisible by 3
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).

23. Subtraction
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).
Base of the number system
difference
Odd Number

24. 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.
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Algebraic number theory
Commutative Law of Addition

25. Any number that is not a multiple of 2 is an
Positional notation (place value)
Odd Number
multiplication
Factor of the given number

26. 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.
Digits
In Diophantine geometry
Associative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

27. The relative greatness of positive and negative numbers
magnitude
Commutative Law of Addition
Natural Numbers
Equal

28. Remainder
The numbers are conventionally plotted using the real part
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.
expression
subtraction

29. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Commutative Law of Multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Associative Law of Addition
Complex numbers

30. A number that has no factors except itself and 1 is a
Prime Factor
Prime Number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
In Diophantine geometry

31. A curve in the plane
an equation in two variables defines
the sum of its digits is divisible by 9
Second Axiom of Equality
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

32. Sixteen less than number Q
C or
K+6 - K+5 - K+4 K+3.........answer is K+3
Q-16
magnitude and direction

33. 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
base-ten number
Algebraic number theory
Even Number
Prime Number

34. A number is divisible by 9 if
Algebraic number theory
counterclockwise through 90
the sum of its digits is divisible by 9
Composite Number

35. 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:
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
constant
difference
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).

36. 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
addition
counterclockwise through 90
complex number
F - F+1 - F+2.......answer is F+2

37. Number X decreased by 12 divided by forty
subtraction
Set
Associative Law of Multiplication
(x-12)/40

38. 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.
Distributive Law
Complex numbers
Second Axiom of Equality
complex number

39. Does not have an equal sign (3x+5) (2a+9b)
expression
even and the sum of its digits is divisible by 3
C or
addition

40. Number T increased by 9
the sum of its digits is divisible by 9
Distributive Law
T+9
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

41. Total
Prime Factor
polynomial
addition
Distributive Law

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.
constructing a parallelogram
the genus of the curve
Second Axiom of Equality
subtraction

43. 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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Braces
Commutative Law of Addition
magnitude

44. 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
K+6 - K+5 - K+4 K+3.........answer is K+3
Commutative Law of Multiplication
negative

45. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Commutative Law of Multiplication
equation
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

46. More than one term (5x+4 contains two)
polynomial
addition
Forth Axiom of Equality
repeated elements

47. 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.
Third Axiom of Equality
algebraic number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
even and the sum of its digits is divisible by 3

48. The place value which corresponds to a given position in a number is determined by the
Commutative Law of Addition
Base of the number system
Associative Law of Addition
Braces

49. The numbers which are used for counting in our number system are sometimes called
positive
magnitude
Natural Numbers
(x-12)/40

50. The set of all complex numbers is denoted by
Definition of genus
Even Number
C or
counterclockwise through 90