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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 branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
constant
addition

2. The Arabic numerals from 0 through 9 are called
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
rectangular coordinates
Digits
Complex numbers

3. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
rectangular coordinates
counterclockwise through 90
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Second Axiom of Equality

4. Number symbols
Numerals
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Inversive geometry
order of operations

5. 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.
Complex numbers
16(5+R)
even and the sum of its digits is divisible by 3
Analytic number theory

6. If a factor of a number is prime - it is called a
Composite Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Prime Factor
The numbers are conventionally plotted using the real part

7. One term (5x or 4)
The multiplication of two complex numbers is defined by the following formula:
constant
Analytic number theory
monomial

8. 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
In Diophantine geometry
Absolute value and argument
multiplication
the number formed by the three right-hand digits is divisible by 8

9. 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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10. 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
subtraction
a curve - a surface or some other such object in n-dimensional space
Absolute value and argument
solutions

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
algebraic number
subtraction
In Diophantine geometry
Base of the number system

12. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
quadratic field
Commutative Law of Addition
constant

13. A number is divisible by 5 if its
Q-16
upward
righthand digit is 0 or 5
Odd Number

14. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Numerals
Prime Factor
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
positive

15. 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
16(5+R)
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

16. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Braces
order of operations
Second Axiom of Equality
counterclockwise through 90

17. A letter tat represents a number that is unknown (usually X or Y)
order of operations
variable
T+9
Associative Law of Addition

18. Addition of two complex numbers can be done geometrically by
To separate a number into prime factors
variable
Odd Number
constructing a parallelogram

19. 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.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Commutative Law of Addition
Associative Law of Addition
the number formed by the three right-hand digits is divisible by 8

20. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
consecutive whole numbers
The multiplication of two complex numbers is defined by the following formula:
upward
Absolute value and argument

21. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Place Value Concept
Complex numbers
Multiple of the given number

22. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
The real number a of the complex number z = a + bi
positive
K+6 - K+5 - K+4 K+3.........answer is K+3
polynomial

23. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
monomial
7
difference

24. Has an equal sign (3x+5 = 14)
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
magnitude and direction
In Diophantine geometry
equation

25. No short method has been found for determining whether a number is divisible by
7
Place Value Concept
constructing a parallelogram
C or

26. The number without a variable (5m+2). In this case - 2
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
the genus of the curve
constant
magnitude and direction

27. Product
Composite Number
subtraction
Members of Elements of the Set
multiplication

28. 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.
coefficient
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
counterclockwise through 90
The numbers are conventionally plotted using the real part

29. The defining characteristic of a position vector is that it has
constructing a parallelogram
addition
rectangular coordinates
magnitude and direction

30. The real and imaginary parts of a complex number can be extracted using the conjugate:
16(5+R)
a complex number is real if and only if it equals its conjugate.
positive
constant

31. 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.
positive
Associative Law of Addition
coefficient
equation

32. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
monomial
Downward
addition
righthand digit is 0 or 5

33. 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.
a curve - a surface or some other such object in n-dimensional space
positive
Second Axiom of Equality
Commutative Law of Addition

34. Remainder
a complex number is real if and only if it equals its conjugate.
Q-16
subtraction
counterclockwise through 90

35. Any number that la a multiple of 2 is an
Even Number
Digits
The real number a of the complex number z = a + bi
solutions

36. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Prime Number
upward
Distributive Law
The multiplication of two complex numbers is defined by the following formula:

37. As shown earlier - c - di is the complex conjugate of the denominator c + di.
repeated elements
Forth Axiom of Equality
Digits
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

38. The objects or symbols in a set are called Numerals - Lines - or Points
its the sum of its digits is divisible by 3
right-hand digit is even
quadratic field
Members of Elements of the Set

39. 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
The multiplication of two complex numbers is defined by the following formula:
16(5+R)
base-ten number
right-hand digit is even

40. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.
algebraic number
addition
To separate a number into prime factors
Third Axiom of Equality

41. Does not have an equal sign (3x+5) (2a+9b)
The numbers are conventionally plotted using the real part
its the sum of its digits is divisible by 3
expression
Set

42. Sum
addition
polynomial
Second Axiom of Equality
Even Number

43. A number is divisible by 3 if
its the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
addition
coefficient

44. Implies a collection or grouping of similar - objects or symbols.
Set
complex number
quadratic field
Braces

45. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a
multiplication
equation
Algebraic number theory
Commutative Law of Addition

46. A number is divisible by 9 if
the sum of its digits is divisible by 9
the genus of the curve
one characteristic in common such as similarity of appearance or purpose
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. If two equal quantities are divided by the same quantity - the resulting quotients are equal. If equals are divided by equals - the results are equal.
monomial
Members of Elements of the Set
Forth Axiom of Equality
Distributive Law

48. Number X decreased by 12 divided by forty
magnitude
subtraction
(x-12)/40
Positional notation (place value)

49. 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.
Base of the number system
a complex number is real if and only if it equals its conjugate.
Associative Law of Multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

50. Sixteen less than number Q
Q-16
monomial
an equation in two variables defines
Even Number