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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. Number symbols
Numerals
addition
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).
Factor of the given number

2. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
Q-16
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Equal

3. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Q-16
negative
Commutative Law of Addition
C or

4. 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.
addition
Natural Numbers
right-hand digit is even
Associative Law of Addition

5. Integers greater than zero and less than 5 form a set - as follows:
Distributive Law
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Number fields
expression

6. A number is divisible by 4 if
base-ten number
the number formed by the two right-hand digits is divisible by 4
Second Axiom of Equality
Base of the number system

7. Less than
F - F+1 - F+2.......answer is F+2
(x-12)/40
subtraction
Odd Number

8. A letter tat represents a number that is unknown (usually X or Y)
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
variable
In Diophantine geometry

9. 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
Second Axiom of Equality
The numbers are conventionally plotted using the real part
Absolute value and argument
the number formed by the three right-hand digits is divisible by 8

10. The Arabic numerals from 0 through 9 are called
one characteristic in common such as similarity of appearance or purpose
Absolute value and argument
Digits
even and the sum of its digits is divisible by 3

11. A curve in the plane
Factor of the given number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
an equation in two variables defines
T+9

12. 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
coefficient
The real number a of the complex number z = a + bi
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).
division

13. 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.
Commutative Law of Addition
polynomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

14. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
an equation in two variables defines
subtraction
Number fields

15. 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
Distributive Law
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula:
Commutative Law of Addition

16. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
variable
Commutative Law of Addition
algebraic number

17. More than
addition
constructing a parallelogram
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
magnitude

18. Any number that is exactly divisible by a given number is a
Multiple of the given number
the number formed by the three right-hand digits is divisible by 8
quadratic field
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

19. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
the number formed by the three right-hand digits is divisible by 8
a complex number is real if and only if it equals its conjugate.
F - F+1 - F+2.......answer is F+2
K+6 - K+5 - K+4 K+3.........answer is K+3

20. If a factor of a number is prime - it is called a
Prime Factor
Associative Law of Addition
Downward
right-hand digit is even

21. 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.
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.
Associative Law of Addition
subtraction
upward

22. 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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23. Number X decreased by 12 divided by forty
(x-12)/40
Digits
The real number a of the complex number z = a + bi
division

24. The greatest of 3 consecutive whole numbers - the smallest of which is F
quadratic field
F - F+1 - F+2.......answer is F+2
Prime Factor
division

25. 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.
Forth Axiom of Equality
an equation in two variables defines
Analytic number theory
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

26. A number is divisible by 9 if
the sum of its digits is divisible by 9
Natural Numbers
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
base-ten number

27. 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
a complex number is real if and only if it equals its conjugate.
consecutive whole numbers
Numerals

28. 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.
Commutative Law of Multiplication
division
Commutative Law of Addition
Complex numbers

29. Quotient
algebraic number
Set
division
addition

30. 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
Algebraic number theory
Second Axiom of Equality
magnitude

31. 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 -
one characteristic in common such as similarity of appearance or purpose
Complex numbers
T+9
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

32. 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.
Multiple of the given number
Forth Axiom of Equality
Third Axiom of Equality
a complex number is real if and only if it equals its conjugate.

33. 2 -3 -4 -5 -6
C or
consecutive whole numbers
Positional notation (place value)
Inversive geometry

34. First axiom of equality
In Diophantine geometry
complex number
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.
algebraic 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:
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).
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction

36. Any number that is not a multiple of 2 is an
The multiplication of two complex numbers is defined by the following formula:
The real number a of the complex number z = a + bi
addition
Odd Number

37. No short method has been found for determining whether a number is divisible by
Forth Axiom of Equality
repeated elements
7
even and the sum of its digits is divisible by 3

38. Subtraction
Definition of genus
difference
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Inversive geometry

39. Number T increased by 9
Odd Number
addition
T+9
expression

40. The objects in a set have at least
Second Axiom of Equality
Complex numbers
The numbers are conventionally plotted using the real part
one characteristic in common such as similarity of appearance or purpose

41. More than one term (5x+4 contains two)
righthand digit is 0 or 5
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).
polynomial

42. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
rectangular coordinates
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
complex number

43. The central problem of Diophantine geometry is to determine when a Diophantine equation has
difference
solutions
magnitude and direction
base-ten number

44. 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.
polynomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
C or
The numbers are conventionally plotted using the real part

45. 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
negative
addition
quadratic field

46. Product of 16 and the sum of 5 and number R
multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
16(5+R)
constant

47. Addition of two complex numbers can be done geometrically by
Absolute value and argument
constructing a parallelogram
subtraction
Even Number

48. A number that has no factors except itself and 1 is a
Prime Number
Associative Law of Addition
constructing a parallelogram
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

49. A number is divisible by 3 if
its the sum of its digits is divisible by 3
division
Absolute value and argument
Positional notation (place value)

50. 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
In Diophantine geometry
consecutive whole numbers
rectangular coordinates
expression