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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. An equation - or system of equations - in two or more variables defines
the number formed by the three right-hand digits is divisible by 8
a curve - a surface or some other such object in n-dimensional space
Numerals
Inversive geometry

2. 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:
(x-12)/40
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
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).

3. A number that has no factors except itself and 1 is a
righthand digit is 0 or 5
Associative Law of Addition
Prime Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

4. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
righthand digit is 0 or 5
Analytic number theory
repeated elements
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

5. Has an equal sign (3x+5 = 14)
Members of Elements of the Set
equation
subtraction
negative

6. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Associative Law of Addition
Second Axiom of Equality
K+6 - K+5 - K+4 K+3.........answer is K+3
Commutative Law of Multiplication

7. Subtraction
Numerals
Commutative Law of Multiplication
difference
monomial

8. If a factor of a number is prime - it is called a
righthand digit is 0 or 5
magnitude and direction
Prime Factor
magnitude

9. 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
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.
addition
magnitude
complex number

10. Any number that is exactly divisible by a given number is a
Natural Numbers
Definition of genus
Multiple of the given number
Number fields

11. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
magnitude and direction
Inversive geometry
addition
its the sum of its digits is divisible by 3

12. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Multiple of the given number
rectangular coordinates
quadratic field
subtraction

13. 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
Place Value Concept
algebraic number
a curve - a surface or some other such object in n-dimensional space
Base of the number system

14. 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
Odd Number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
constant
base-ten number

15. 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.
Natural Numbers
Third Axiom of Equality
upward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

16. Implies a collection or grouping of similar - objects or symbols.
difference
variable
Set
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .

17. A number is divisible by 6 if it is
Natural Numbers
even and the sum of its digits is divisible by 3
order of operations
Distributive Law

18. A number is divisible by 9 if
the sum of its digits is divisible by 9
counterclockwise through 90
The multiplication of two complex numbers is defined by the following formula:
Definition of genus

19. The defining characteristic of a position vector is that it has
magnitude and direction
Associative Law of Multiplication
The numbers are conventionally plotted using the real part
Second Axiom of Equality

20. Addition of two complex numbers can be done geometrically by
16(5+R)
constructing a parallelogram
a curve - a surface or some other such object in n-dimensional space
difference

21. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
F - F+1 - F+2.......answer is F+2
Algebraic number theory
order of operations
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

22. 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
Natural Numbers
Algebraic number theory
The real number a of the complex number z = a + bi
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

23. Total
Equal
Forth Axiom of Equality
addition
Multiple of the given number

24. Plus
Forth Axiom of Equality
subtraction
addition
Natural Numbers

25. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
In Diophantine geometry
negative
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
upward

26. 2 -3 -4 -5 -6
upward
consecutive whole numbers
constructing a parallelogram
subtraction

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

28. The relative greatness of positive and negative numbers
magnitude
Multiple of the given number
multiplication
its the sum of its digits is divisible by 3

29. The Arabic numerals from 0 through 9 are called
repeated elements
addition
Braces
Digits

30. Sum
In Diophantine geometry
Braces
magnitude and direction
addition

31. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
its the sum of its digits is divisible by 3
Factor of the given number
algebraic number

32. The objects or symbols in a set are called Numerals - Lines - or Points
Base of the number system
Members of Elements of the Set
even and the sum of its digits is divisible by 3
Commutative Law of Addition

33. 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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34. Any number that la a multiple of 2 is an
Q-16
Even Number
7
constant

35. 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
To separate a number into prime factors
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
positive

36. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Digits
solutions
base-ten number
Odd Number

37. A number that has factors other than itself and 1 is a
positive
Composite Number
the sum of its digits is divisible by 9
a curve - a surface or some other such object in n-dimensional space

38. Increased by
Factor of the given number
the sum of its digits is divisible by 9
Composite Number
addition

39. 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
Commutative Law of Multiplication
Equal
variable
The real number a of the complex number z = a + bi

40. The objects in a set have at least
Associative Law of Multiplication
one characteristic in common such as similarity of appearance or purpose
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

41. More than one term (5x+4 contains two)
C or
polynomial
repeated elements
Set

42. 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
The real number a of the complex number z = a + bi
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Commutative Law of Addition

43. The greatest of 3 consecutive whole numbers - the smallest of which is F
Numerals
F - F+1 - F+2.......answer is F+2
The real number a of the complex number z = a + bi
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

44. Any number that is not a multiple of 2 is an
Inversive geometry
magnitude and direction
7
Odd Number

45. A number is divisible by 2 if
Members of Elements of the Set
right-hand digit is even
Positional notation (place value)
repeated elements

46. More than
addition
constant
even and the sum of its digits is divisible by 3
negative

47. A curve in the plane
Downward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
an equation in two variables defines
addition

48. 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
(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.
In Diophantine geometry
monomial

49. 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.
Inversive geometry
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.
Complex numbers

50. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Associative Law of Addition
F - F+1 - F+2.......answer is F+2
equation