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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. The central problem of Diophantine geometry is to determine when a Diophantine equation has
subtraction
solutions
Definition of genus
expression

2. Sum
addition
7
order of operations
Inversive geometry

3. A number is divisible by 2 if
subtraction
division
K+6 - K+5 - K+4 K+3.........answer is K+3
right-hand digit is even

4. 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
Definition of genus
Absolute value and argument
In Diophantine geometry
Commutative Law of Addition

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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
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:
The multiplication of two complex numbers is defined by the following formula:

6. 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
Distributive Law
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
expression

7. 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.
Associative Law of Addition
solutions
Forth Axiom of Equality
Associative Law of Addition

8. 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
16(5+R)
To separate a number into prime factors
Algebraic number theory
complex number

9. More than
addition
the number formed by the three right-hand digits is divisible by 8
Downward
Forth Axiom of Equality

10. Remainder
subtraction
complex number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The real number a of the complex number z = a + bi

11. 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
addition
Algebraic number theory
To separate a number into prime factors
Even Number

12. If a factor of a number is prime - it is called a
Numerals
Inversive geometry
Prime Factor
Base of the number system

13. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
algebraic number
negative
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).

14. 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
equation
The real number a of the complex number z = a + bi
addition
addition

15. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th
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
Definition of genus
a complex number is real if and only if it equals its conjugate.

16. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
Associative Law of Addition
its the sum of its digits is divisible by 3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

17. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
K+6 - K+5 - K+4 K+3.........answer is K+3
base-ten number
Inversive geometry

18. 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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19. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
The numbers are conventionally plotted using the real part
Digits
K+6 - K+5 - K+4 K+3.........answer is K+3

20. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Numerals
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
Positional notation (place value)

21. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Composite Number
constant
Prime Number

22. Does not have an equal sign (3x+5) (2a+9b)
expression
Downward
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.

23. First axiom of equality
K+6 - K+5 - K+4 K+3.........answer is K+3
Prime 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.
a curve - a surface or some other such object in n-dimensional space

24. Any number that is exactly divisible by a given number is a
base-ten number
Multiple of the given number
Prime Factor
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

25. 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.
order of operations
Natural Numbers
Second Axiom of Equality
subtraction

26. Has an equal sign (3x+5 = 14)
constructing a parallelogram
equation
expression
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).

27. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
variable
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
one characteristic in common such as similarity of appearance or purpose
even and the sum of its digits is divisible by 3

28. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
addition
The numbers are conventionally plotted using the real part
positive
Set

29. A number is divisible by 9 if
Downward
coefficient
variable
the sum of its digits is divisible by 9

30. A number is divisible by 5 if its
Positional notation (place value)
righthand digit is 0 or 5
Distributive Law
Set

31. 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.)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Number fields
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Commutative Law of Addition

32. Plus
Even Number
consecutive whole numbers
addition
subtraction

33. Implies a collection or grouping of similar - objects or symbols.
the genus of the curve
Multiple of the given number
Set
Place Value Concept

34. 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.
Digits
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
repeated elements

35. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
a curve - a surface or some other such object in n-dimensional space
The numbers are conventionally plotted using the real part
positive

36. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
solutions
To separate a number into prime factors
addition

37. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
one characteristic in common such as similarity of appearance or purpose
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
counterclockwise through 90

38. Integers greater than zero and less than 5 form a set - as follows:
constructing a parallelogram
The numbers are conventionally plotted using the real part
complex number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}

39. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The multiplication of two complex numbers is defined by the following formula:
base-ten number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

40. Product of 16 and the sum of 5 and number R
Complex numbers
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.
16(5+R)
Odd Number

41. Number T increased by 9
Factor of the given number
division
Associative Law of Addition
T+9

42. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
an equation in two variables defines
Odd Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

43. The numbers which are used for counting in our number system are sometimes called
Third 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.
Natural Numbers
constant

44. 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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
To separate a number into prime factors
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
constant

45. As shown earlier - c - di is the complex conjugate of the denominator c + di.
constructing a parallelogram
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
even and the sum of its digits is divisible by 3
Place Value Concept

46. Any number that la a multiple of 2 is an
K+6 - K+5 - K+4 K+3.........answer is K+3
To separate a number into prime factors
Distributive Law
Even Number

47. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Definition of genus
order of operations
Number fields
the number formed by the two right-hand digits is divisible by 4

48. 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
even and the sum of its digits is divisible by 3
one characteristic in common such as similarity of appearance or purpose
Absolute value and argument
subtraction

49. More than one term (5x+4 contains two)
16(5+R)
The multiplication of two complex numbers is defined by the following formula:
Positional notation (place value)
polynomial

50. One term (5x or 4)
The numbers are conventionally plotted using the real part
In Diophantine geometry
monomial
Definition of genus