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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. 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).
a curve - a surface or some other such object in n-dimensional space
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

2. 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 sum of its digits is divisible by 9
Associative Law of Addition
even and the sum of its digits is divisible by 3
complex number

3. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Third Axiom of Equality
consecutive whole numbers
repeated elements

4. 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 number formed by the three right-hand digits is divisible by 8
repeated elements
Associative Law of Addition
Positional notation (place value)

5. 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
Even Number
The multiplication of two complex numbers is defined by the following formula:
repeated elements
Place Value Concept

6. No short method has been found for determining whether a number is divisible by
The numbers are conventionally plotted using the real part
Positional notation (place value)
constructing a parallelogram
7

7. The base which is most commonly used is ten - and the system with ten as a base is called the decimal system (decem is the Latin word for ten). Any number is assumed - unless indicated - to be a
base-ten number
subtraction
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The numbers are conventionally plotted using the real part

8. Total
In Diophantine geometry
T+9
addition
even and the sum of its digits is divisible by 3

9. 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
addition
Associative Law of Multiplication
Commutative Law of Addition
In Diophantine geometry

10. A number is divisible by 4 if
order of operations
Distributive Law
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
the number formed by the two right-hand digits is divisible by 4

11. 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
Associative Law of Addition
solutions
In Diophantine geometry
order of operations

12. Product
magnitude
Associative Law of Addition
multiplication
Forth Axiom of Equality

13. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
16(5+R)
Inversive geometry
a curve - a surface or some other such object in n-dimensional space
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

14. Any number that is not a multiple of 2 is an
a complex number is real if and only if it equals its conjugate.
polynomial
Odd Number
the sum of its digits is divisible by 9

15. The real and imaginary parts of a complex number can be extracted using the conjugate:
16(5+R)
C or
a complex number is real if and only if it equals its conjugate.
Place Value Concept

16. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Commutative Law of Addition
Members of Elements of the Set
T+9

17. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
constant
Analytic number theory

18. Any number that is exactly divisible by a given number is a
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Digits
Multiple of the given number
Braces

19. Has an equal sign (3x+5 = 14)
equation
Digits
Inversive geometry
counterclockwise through 90

20. Are used to indicate sets
even and the sum of its digits is divisible by 3
Braces
Analytic number theory
right-hand digit is even

21. The square roots of a + bi (with b ? 0) are - where and where sgn is the signum function. This can be seen by squaring to obtain a + bi.
subtraction
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.
Multiple of the given number

22. Sixteen less than number Q
16(5+R)
difference
C or
Q-16

23. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
order of operations
consecutive whole numbers

24. Less than
one characteristic in common such as similarity of appearance or purpose
subtraction
Absolute value and argument
the number formed by the two right-hand digits is divisible by 4

25. 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
To separate a number into prime factors
Place Value Concept
T+9
Multiple of the given number

26. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Even Number
solutions
algebraic number
Distributive Law

27. A number is divisible by 3 if
T+9
the genus of the curve
upward
its the sum of its digits is divisible by 3

28. The number without a variable (5m+2). In this case - 2
Number fields
constant
division
Associative Law of Multiplication

29. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
rectangular coordinates
To separate a number into prime factors
Place Value Concept

30. Increased by
polynomial
difference
addition
Digits

31. 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.
quadratic field
Absolute value and argument
Complex numbers
Definition of genus

32. 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.
an equation in two variables defines
algebraic number
Second Axiom of Equality
quadratic field

33. The Arabic numerals from 0 through 9 are called
division
consecutive whole numbers
repeated elements
Digits

34. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
Members of Elements of the Set
In Diophantine geometry
subtraction

35. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
(x-12)/40
K+6 - K+5 - K+4 K+3.........answer is K+3
consecutive whole numbers
The multiplication of two complex numbers is defined by the following formula:

36. 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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37. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
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.
Factor of the given number
Associative Law of Multiplication

38. 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
constructing a parallelogram
T+9
The real number a of the complex number z = a + bi
Commutative Law of Addition

39. The set of all complex numbers is denoted by
C or
variable
Composite Number
positive

40. 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
Commutative Law of Multiplication
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
Absolute value and argument

41. Number symbols
Numerals
Composite Number
Third Axiom of Equality
To separate a number into prime factors

42. If a factor of a number is prime - it is called a
Members of Elements of the Set
Prime Factor
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

43. 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.
magnitude and direction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
an equation in two variables defines
Composite Number

44. Implies a collection or grouping of similar - objects or symbols.
Set
a complex number is real if and only if it equals its conjugate.
rectangular coordinates
magnitude and direction

45. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Equal
order of operations
To separate a number into prime factors

46. Integers greater than zero and less than 5 form a set - as follows:
subtraction
Factor of the given number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Forth Axiom of Equality

47. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
Digits
Analytic number theory
Downward

48. As shown earlier - c - di is the complex conjugate of the denominator c + di.
division
negative
counterclockwise through 90
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

49. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
repeated elements
monomial
C or

50. Any number that la a multiple of 2 is an
In Diophantine geometry
C or
Even Number
Composite Number