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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. A number is divisible by 3 if
its the sum of its digits is divisible by 3
subtraction
F - F+1 - F+2.......answer is F+2
addition

2. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
expression
order of operations
addition
righthand digit is 0 or 5

3. 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.
Third Axiom of Equality
Braces
addition
quadratic field

4. A number that has factors other than itself and 1 is a
Factor of the given number
equation
Composite Number
The numbers are conventionally plotted using the real part

5. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
polynomial
Distributive Law
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Complex numbers

6. Plus
a curve - a surface or some other such object in n-dimensional space
righthand digit is 0 or 5
addition
Absolute value and argument

7. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Distributive Law
solutions
rectangular coordinates
Set

8. 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 -
Odd Number
To separate a number into prime factors
division
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

9. Less than
Definition of genus
consecutive whole numbers
subtraction
repeated elements

10. 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
Complex numbers
coefficient
The real number a of the complex number z = a + bi
Composite Number

11. 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.
one characteristic in common such as similarity of appearance or purpose
negative
its the sum of its digits is divisible by 3
Complex numbers

12. The real and imaginary parts of a complex number can be extracted using the conjugate:
rectangular coordinates
a complex number is real if and only if it equals its conjugate.
base-ten number
an equation in two variables defines

13. Addition of two complex numbers can be done geometrically by
even and the sum of its digits is divisible by 3
the genus of the curve
its the sum of its digits is divisible by 3
constructing a parallelogram

14. The objects in a set have at least
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.
an equation in two variables defines
magnitude
one characteristic in common such as similarity of appearance or purpose

15. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Composite Number
C or
positive

16. Any number that la a multiple of 2 is an
subtraction
right-hand digit is even
Even 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.

17. 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
To separate a number into prime factors
quadratic field
Commutative Law of Multiplication

18. 2 -3 -4 -5 -6
F - F+1 - F+2.......answer is F+2
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
repeated elements
consecutive whole numbers

19. A letter tat represents a number that is unknown (usually X or Y)
Multiple of the given number
a curve - a surface or some other such object in n-dimensional space
variable
F - F+1 - F+2.......answer is F+2

20. The place value which corresponds to a given position in a number is determined by the
The real number a of the complex number z = a + bi
difference
Braces
Base of the number system

21. The defining characteristic of a position vector is that it has
addition
magnitude and direction
order of operations
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

22. Increased by
addition
Definition of genus
Odd Number
positive

23. 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
expression
Absolute value and argument
positive
16(5+R)

24. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
16(5+R)
Place Value Concept
In Diophantine geometry
positive

25. 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
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
one characteristic in common such as similarity of appearance or purpose
expression

26. 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
right-hand digit is even
In Diophantine geometry
addition
C or

27. 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
solutions
Set
Braces
Definition of genus

28. Number T increased by 9
T+9
division
complex number
Second Axiom of Equality

29. 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.
K+6 - K+5 - K+4 K+3.........answer is K+3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Analytic number theory

30. 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.
quadratic field
the number formed by the three right-hand digits is divisible by 8
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

31. 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.
16(5+R)
complex number
Set
Associative Law of Multiplication

32. Quotient
division
In Diophantine geometry
even and the sum of its digits is divisible by 3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

33. 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
Numerals
Second Axiom of Equality
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
In Diophantine geometry

34. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
division
7
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

35. Implies a collection or grouping of similar - objects or symbols.
coefficient
The real number a of the complex number z = a + bi
Set
Analytic number theory

36. 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.
The numbers are conventionally plotted using the real part
magnitude and direction
Base of the number system
addition

37. The greatest of 3 consecutive whole numbers - the smallest of which is F
Digits
F - F+1 - F+2.......answer is F+2
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
16(5+R)

38. Sixteen less than number Q
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
right-hand digit is even
addition
Q-16

39. More than
quadratic field
Positional notation (place value)
addition
Composite Number

40. More than one term (5x+4 contains two)
subtraction
polynomial
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
counterclockwise through 90

41. Product
a complex number is real if and only if it equals its conjugate.
subtraction
consecutive whole numbers
multiplication

42. 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
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
difference

43. 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.
Associative Law of Addition
Complex numbers
Even Number
difference

44. Any number that is not a multiple of 2 is an
a complex number is real if and only if it equals its conjugate.
Definition of genus
Odd Number
Digits

45. A number is divisible by 8 if
complex number
addition
the number formed by the three right-hand digits is divisible by 8
Braces

46. The number without a variable (5m+2). In this case - 2
constant
order of operations
magnitude
complex number

47. 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
right-hand digit is even
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Associative Law of Addition

48. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Second Axiom of Equality
16(5+R)
the sum of its digits is divisible by 9
upward

49. Are used to indicate sets
subtraction
Braces
C or
algebraic number

50. The number touching the variable (in the case of 5x - would be 5)
16(5+R)
variable
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
coefficient