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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. 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.
quadratic field
Commutative Law of Addition
solutions
addition

2. Any number that la a multiple of 2 is an
Even Number
division
counterclockwise through 90
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

3. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Factor of the given number
polynomial
K+6 - K+5 - K+4 K+3.........answer is K+3
Definition of genus

4. 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.
consecutive whole numbers
division
solutions

5. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
a curve - a surface or some other such object in n-dimensional space
Place Value Concept

6. Decreased by
Base of the number system
subtraction
In Diophantine geometry
positive

7. The relative greatness of positive and negative numbers
magnitude
Natural Numbers
addition
consecutive whole numbers

8. A number that has factors other than itself and 1 is a
Composite Number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
(x-12)/40

9. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
addition
positive
negative
Third Axiom of Equality

10. The number without a variable (5m+2). In this case - 2
counterclockwise through 90
consecutive whole numbers
constant
subtraction

11. 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
Digits
the sum of its digits is divisible by 9
algebraic number
right-hand digit is even

12. One term (5x or 4)
The numbers are conventionally plotted using the real part
(x-12)/40
monomial
upward

13. Implies a collection or grouping of similar - objects or symbols.
expression
K+6 - K+5 - K+4 K+3.........answer is K+3
Set
the number formed by the two right-hand digits is divisible by 4

14. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Number

15. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
The numbers are conventionally plotted using the real part
polynomial
C or

16. 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
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:
division
expression

17. 2 -3 -4 -5 -6
Associative Law of Multiplication
addition
consecutive whole numbers
variable

18. Product of 16 and the sum of 5 and number R
16(5+R)
In Diophantine geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
subtraction

19. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Analytic number theory
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).
Positional notation (place value)

20. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
addition
the sum of its digits is divisible by 9
addition

21. The finiteness or not of the number of rational or integer points on an algebraic curve
its the sum of its digits is divisible by 3
the genus of the curve
base-ten number
Definition of genus

22. 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
Braces
Second Axiom of Equality
In Diophantine geometry
Q-16

23. 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.
even and the sum of its digits is divisible by 3
To separate a number into prime factors
Complex numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

24. 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 Addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
addition
Inversive geometry

25. A number is divisible by 6 if it is
base-ten number
Members of Elements of the Set
equation
even and the sum of its digits is divisible by 3

26. Sum
addition
Associative Law of Addition
Forth Axiom of Equality
Second Axiom of Equality

27. A number is divisible by 5 if its
Distributive Law
Factor of the given number
Associative Law of Multiplication
righthand digit is 0 or 5

28. Has an equal sign (3x+5 = 14)
Commutative Law of Addition
Multiple of the given number
equation
Downward

29. The greatest of 3 consecutive whole numbers - the smallest of which is F
Second Axiom of Equality
Inversive geometry
F - F+1 - F+2.......answer is F+2
the number formed by the two right-hand digits is divisible by 4

30. Remainder
16(5+R)
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Natural Numbers

31. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
magnitude
constant
counterclockwise through 90

32. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Commutative Law of Addition
addition
repeated elements

33. The defining characteristic of a position vector is that it has
magnitude and direction
consecutive whole numbers
To separate a number into prime factors
In Diophantine geometry

34. 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
monomial
algebraic number
Inversive geometry
The real number a of the complex number z = a + bi

35. The Arabic numerals from 0 through 9 are called
the number formed by the two right-hand digits is divisible by 4
polynomial
Digits
Number fields

36. The set of all complex numbers is denoted by
C or
Associative Law of Multiplication
Algebraic number theory
Composite Number

37. 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.
Positional notation (place value)
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.
the sum of its digits is divisible by 9
Commutative Law of Multiplication

38. The objects or symbols in a set are called Numerals - Lines - or Points
one characteristic in common such as similarity of appearance or purpose
Absolute value and argument
repeated elements
Members of Elements of the Set

39. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
solutions
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Forth Axiom of Equality

40. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
equation
division
constructing a parallelogram

41. More than one term (5x+4 contains two)
polynomial
Associative Law of Addition
Associative Law of Multiplication
the number formed by the two right-hand digits is divisible by 4

42. A number that has no factors except itself and 1 is a
Definition of genus
Numerals
Prime Number
Q-16

43. 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.)
constructing a parallelogram
Number fields
righthand digit is 0 or 5
To separate a number into prime factors

44. 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
7
rectangular coordinates
In Diophantine geometry
constant

45. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Associative Law of Addition
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

46. 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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47. Sixteen less than number Q
To separate a number into prime factors
constant
Q-16
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

48. More than
Q-16
addition
negative
the number formed by the three right-hand digits is divisible by 8

49. No short method has been found for determining whether a number is divisible by
monomial
7
F - F+1 - F+2.......answer is F+2
difference

50. A curve in the plane
an equation in two variables defines
negative
the number formed by the three right-hand digits is divisible by 8
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation: