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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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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
a complex number is real if and only if it equals its conjugate.
Prime Factor
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

2. 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
Odd Number
The numbers are conventionally plotted using the real part
To separate a number into prime factors
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

3. 2 -3 -4 -5 -6
consecutive whole numbers
The numbers are conventionally plotted using the real part
Q-16
addition

4. A number is divisible by 5 if its
Definition of genus
righthand digit is 0 or 5
Algebraic number theory
addition

5. Number symbols
rectangular coordinates
positive
Odd Number
Numerals

6. The greatest of 3 consecutive whole numbers - the smallest of which is F
Digits
Inversive geometry
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
F - F+1 - F+2.......answer is F+2

7. A number that has factors other than itself and 1 is a
Set
To separate a number into prime factors
Composite Number
even and the sum of its digits is divisible by 3

8. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Algebraic number theory
16(5+R)
variable

9. The finiteness or not of the number of rational or integer points on an algebraic curve
F - F+1 - F+2.......answer is F+2
the genus of the curve
multiplication
difference

10. If a factor of a number is prime - it is called a
magnitude and direction
addition
To separate a number into prime factors
Prime Factor

11. 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.
Associative Law of Multiplication
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 numbers are conventionally plotted using the real part
addition

12. Plus
Digits
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).
(x-12)/40
addition

13. Sum
Digits
one characteristic in common such as similarity of appearance or purpose
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition

14. 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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15. LAWS FOR COMBINING NUMBERS
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).
coefficient
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The real number a of the complex number z = a + bi

16. 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.)
Number fields
equation
Set
the number formed by the three right-hand digits is divisible by 8

17. Total
addition
the sum of its digits is divisible by 9
magnitude
rectangular coordinates

18. 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.
Complex numbers
Composite Number
upward
a complex number is real if and only if it equals its conjugate.

19. More than one term (5x+4 contains two)
polynomial
(x-12)/40
the sum of its digits is divisible by 9
solutions

20. Increased by
Number fields
addition
division
In Diophantine geometry

21. The Arabic numerals from 0 through 9 are called
Digits
Place Value Concept
variable
(x-12)/40

22. 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
polynomial
Positional notation (place value)
Number fields
The real number a of the complex number z = a + bi

23. Sixteen less than number Q
Distributive Law
Q-16
The multiplication of two complex numbers is defined by the following formula:
Downward

24. 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.
Second Axiom of Equality
Multiple of the given number
Composite Number
even and the sum of its digits is divisible by 3

25. The number without a variable (5m+2). In this case - 2
Forth Axiom of Equality
a complex number is real if and only if it equals its conjugate.
constant
Digits

26. The relative greatness of positive and negative numbers
magnitude
consecutive whole numbers
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Composite Number

27. 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
base-ten number
Absolute value and argument
16(5+R)

28. 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
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
subtraction
a complex number is real if and only if it equals its conjugate.

29. 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.
multiplication
Forth Axiom of Equality
the sum of its digits is divisible by 9
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

30. No short method has been found for determining whether a number is divisible by
Numerals
(x-12)/40
Number fields
7

31. Implies a collection or grouping of similar - objects or symbols.
F - F+1 - F+2.......answer is F+2
Set
(x-12)/40
Odd Number

32. A number is divisible by 6 if it is
Analytic number theory
the genus of the curve
even and the sum of its digits is divisible by 3
Inversive geometry

33. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
T+9
Complex numbers
Base of the number system

34. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Complex numbers
division
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

35. The objects or symbols in a set are called Numerals - Lines - or Points
The numbers are conventionally plotted using the real part
Second Axiom of Equality
Members of Elements of the Set
the genus of the curve

36. 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.
subtraction
Commutative Law of Multiplication
Analytic number theory
Definition of genus

37. Remainder
magnitude
consecutive whole numbers
addition
subtraction

38. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
Downward
Commutative Law of Addition
Inversive geometry

39. The set of all complex numbers is denoted by
Absolute value and argument
Base of the number system
Braces
C or

40. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
K+6 - K+5 - K+4 K+3.........answer is K+3
expression
Forth Axiom of Equality

41. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
Associative Law of Addition
The numbers are conventionally plotted using the real part
negative

42. 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.
subtraction
Associative Law of Addition
Members of Elements of the Set
addition

43. Number X decreased by 12 divided by forty
counterclockwise through 90
(x-12)/40
variable
Associative Law of Multiplication

44. 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
the number formed by the two right-hand digits is divisible by 4
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
T+9

45. An equation - or system of equations - in two or more variables defines
addition
Forth Axiom of Equality
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
a curve - a surface or some other such object in n-dimensional space

46. First axiom of equality
magnitude
consecutive whole numbers
Factor of the given 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.

47. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Members of Elements of the Set
In Diophantine geometry
Distributive Law
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

48. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Associative Law of Addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
negative
polynomial

49. The number touching the variable (in the case of 5x - would be 5)
coefficient
order of operations
Members of Elements of the Set
algebraic number

50. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
repeated elements
Odd Number
upward
consecutive whole numbers