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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. 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.)
expression
complex number
Prime Number
Number fields

2. Sixteen less than number Q
Complex numbers
Q-16
monomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

3. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Associative Law of Addition
Algebraic number theory
rectangular coordinates
Distributive Law

4. 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.
Positional notation (place value)
Prime Factor
Forth Axiom of Equality
solutions

5. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
order of operations
repeated elements
Distributive Law
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

6. Any number that la a multiple of 2 is an
Digits
subtraction
Even Number
the sum of its digits is divisible by 9

7. More than one term (5x+4 contains two)
polynomial
one characteristic in common such as similarity of appearance or purpose
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

8. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
the number formed by the two right-hand digits is divisible by 4
Absolute value and argument
the genus of the curve

9. 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
Inversive geometry
addition
The multiplication of two complex numbers is defined by the following formula:
T+9

10. Number symbols
subtraction
Positional notation (place value)
Numerals
Composite Number

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. 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.
addition
Prime Number
Complex numbers
(x-12)/40

13. An equation - or system of equations - in two or more variables defines
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Commutative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space
Distributive Law

14. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
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).
quadratic field
Even Number

15. 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.
Commutative Law of Multiplication
Even Number
polynomial
a curve - a surface or some other such object in n-dimensional space

16. 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
Commutative Law of Multiplication
quadratic field
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

17. First axiom of equality
Number fields
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.
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).
its the sum of its digits is divisible by 3

18. 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.
T+9
Second Axiom of Equality
righthand digit is 0 or 5
Associative Law of Addition

19. Less than
The multiplication of two complex numbers is defined by the following formula:
subtraction
solutions
The real number a of the complex number z = a + bi

20. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The real number a of the complex number z = a + bi
Number fields
subtraction

21. The objects in a set have at least
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
righthand digit is 0 or 5
one characteristic in common such as similarity of appearance or purpose
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

22. The Arabic numerals from 0 through 9 are called
Associative Law of Multiplication
Digits
subtraction
rectangular coordinates

23. Integers greater than zero and less than 5 form a set - as follows:
16(5+R)
The multiplication of two complex numbers is defined by the following formula:
Natural Numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

24. A number that has factors other than itself and 1 is a
subtraction
difference
Inversive geometry
Composite Number

25. The number touching the variable (in the case of 5x - would be 5)
F - F+1 - F+2.......answer is F+2
division
Forth Axiom of Equality
coefficient

26. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
an equation in two variables defines
counterclockwise through 90
Even Number

27. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Analytic number theory
Even Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

28. 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
right-hand digit is even
C or
Place Value Concept
Odd Number

29. One term (5x or 4)
Numerals
Braces
monomial
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

30. A number that has no factors except itself and 1 is a
division
subtraction
Prime Number
Composite Number

31. Any number that is exactly divisible by a given number is a
Complex numbers
Multiple of the given number
constant
The real number a of the complex number z = a + bi

32. 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.
Distributive Law
7
Associative Law of Multiplication
Algebraic number theory

33. Product
multiplication
Even Number
Algebraic number theory
a complex number is real if and only if it equals its conjugate.

34. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Natural Numbers
Distributive Law
right-hand digit is even

35. 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
negative
In Diophantine geometry
consecutive whole numbers
the sum of its digits is divisible by 9

36. 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.
Distributive Law
Set
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
quadratic field

37. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Inversive geometry
solutions
Distributive Law
repeated elements

38. The place value which corresponds to a given position in a number is determined by the
Set
repeated elements
polynomial
Base of the number system

39. A number is divisible by 5 if its
upward
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
variable
righthand digit is 0 or 5

40. Are used to indicate sets
positive
Associative Law of Addition
Braces
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

41. Sum
multiplication
addition
quadratic field
algebraic number

42. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
To separate a number into prime factors
Odd Number
The numbers are conventionally plotted using the real part

43. The number without a variable (5m+2). In this case - 2
Place Value Concept
constant
a complex number is real if and only if it equals its conjugate.
positive

44. Number T increased by 9
Commutative Law of Addition
T+9
Q-16
Second Axiom of Equality

45. 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.
an equation in two variables defines
quadratic field
upward
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

46. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Natural Numbers
Inversive geometry
magnitude and direction
monomial

47. 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.
monomial
Commutative Law of Addition
Second Axiom of Equality
Distributive Law

48. 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
equation
K+6 - K+5 - K+4 K+3.........answer is K+3
Absolute value and argument
Factor of the given number

49. Implies a collection or grouping of similar - objects or symbols.
positive
Set
addition
quadratic field

50. The real and imaginary parts of a complex number can be extracted using the conjugate:
Associative Law of Addition
Even Number
a complex number is real if and only if it equals its conjugate.
right-hand digit is even