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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

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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. Number T increased by 9
the number formed by the three right-hand digits is divisible by 8
addition
The real number a of the complex number z = a + bi
T+9

2. 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
Forth Axiom of Equality
the genus of the curve
Absolute value and argument
rectangular coordinates

3. LAWS FOR COMBINING NUMBERS
magnitude and direction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Base of the number system
difference

4. The relative greatness of positive and negative numbers
Prime Number
constructing a parallelogram
magnitude
counterclockwise through 90

5. 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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6. A form of coding in which the value of each digit of a number depends upon its position in relation to the other digits of the number. The convention used in our number system is that each digit has a higher place value than those digits to the right
the sum of its digits is divisible by 9
Positional notation (place value)
Second Axiom of Equality
polynomial

7. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
addition
magnitude and direction
Commutative Law of Multiplication

8. 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
Prime Number
division
algebraic number
negative

9. 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
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).
repeated elements
equation

10. Number symbols
the genus of the curve
Numerals
order of operations
even and the sum of its digits is divisible by 3

11. A letter tat represents a number that is unknown (usually X or Y)
addition
Number fields
variable
Third Axiom of Equality

12. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
In Diophantine geometry
a complex number is real if and only if it equals its conjugate.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Inversive geometry

13. The objects or symbols in a set are called Numerals - Lines - or Points
variable
C or
positive
Members of Elements of the Set

14. Quotient
its the sum of its digits is divisible by 3
Braces
division
Number fields

15. A number is divisible by 3 if
its the sum of its digits is divisible by 3
subtraction
an equation in two variables defines
F - F+1 - F+2.......answer is F+2

16. The numbers which are used for counting in our number system are sometimes called
Base of the number system
rectangular coordinates
monomial
Natural Numbers

17. Has an equal sign (3x+5 = 14)
addition
Prime Number
equation
constant

18. 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
Forth Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
order of operations
In Diophantine geometry

19. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
multiplication
F - F+1 - F+2.......answer is F+2
Prime Number

20. A number that has no factors except itself and 1 is a
16(5+R)
Prime Number
quadratic field
addition

21. More than one term (5x+4 contains two)
polynomial
Numerals
constructing a parallelogram
Members of Elements of the Set

22. A number is divisible by 5 if its
righthand digit is 0 or 5
Composite Number
(x-12)/40
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

23. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Natural Numbers
Commutative Law of Multiplication
(x-12)/40

24. Product
multiplication
Natural Numbers
addition
algebraic number

25. An equation - or system of equations - in two or more variables defines
equation
one characteristic in common such as similarity of appearance or purpose
Set
a curve - a surface or some other such object in n-dimensional space

26. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
The numbers are conventionally plotted using the real part
Complex numbers
Q-16

27. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag
negative
magnitude
Commutative Law of Addition
complex number

28. 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
negative
Odd Number
To separate a number into prime factors
addition

29. 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.
The real number a of the complex number z = a + bi
Commutative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space
subtraction

30. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
negative
In Diophantine geometry
positive

31. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Composite Number
The real number a of the complex number z = a + bi
Natural Numbers

32. Less than
16(5+R)
The multiplication of two complex numbers is defined by the following formula:
subtraction
Prime Factor

33. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Prime Number
solutions
16(5+R)
rectangular coordinates

34. 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.)
Inversive geometry
Number fields
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

35. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
addition
Prime Number
addition

36. 2 -3 -4 -5 -6
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
consecutive whole numbers
repeated elements
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

37. The Arabic numerals from 0 through 9 are called
Digits
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
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).

38. A number is divisible by 2 if
upward
Prime Number
right-hand digit is even
solutions

39. 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.
variable
Complex numbers
Base of the number system
equation

40. Plus
Odd Number
constant
addition
In Diophantine geometry

41. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
Associative Law of Multiplication
the genus of the curve
quadratic field

42. No short method has been found for determining whether a number is divisible by
magnitude and direction
Forth Axiom of Equality
Number fields
7

43. Number X decreased by 12 divided by forty
(x-12)/40
Positional notation (place value)
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Number fields

44. The objects in a set have at least
Commutative Law of Addition
Equal
one characteristic in common such as similarity of appearance or purpose
Multiple of the given number

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.
Distributive Law
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
16(5+R)
expression

46. 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}
Distributive Law
addition
order of operations

47. 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 -
magnitude and direction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
counterclockwise through 90
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

48. 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
16(5+R)
negative
the number formed by the two right-hand digits is divisible by 4
The multiplication of two complex numbers is defined by the following formula:

49. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
coefficient
Factor of the given number
Even Number

50. 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
magnitude and direction
Place Value Concept
addition
quadratic field