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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 number is divisible by 5 if its
7
division
expression
righthand digit is 0 or 5

2. Less than
Associative Law of Multiplication
Equal
subtraction
The multiplication of two complex numbers is defined by the following formula:

3. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
addition
T+9
a curve - a surface or some other such object in n-dimensional space
K+6 - K+5 - K+4 K+3.........answer is K+3

4. 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 -
Composite Number
The multiplication of two complex numbers is defined by the following formula:
counterclockwise through 90
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

5. A number is divisible by 9 if
constructing a parallelogram
the sum of its digits is divisible by 9
Complex numbers
Third Axiom of Equality

6. Any number that la a multiple of 2 is an
Even Number
its the sum of its digits is divisible by 3
order of operations
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:

7. 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
Members of Elements of the Set
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
constructing a parallelogram
In Diophantine geometry

8. A number is divisible by 3 if
positive
Multiple of the given number
the genus of the curve
its the sum of its digits is divisible by 3

9. A letter tat represents a number that is unknown (usually X or Y)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
righthand digit is 0 or 5
Analytic number theory
variable

10. 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.
positive
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
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.

11. Number T increased by 9
one characteristic in common such as similarity of appearance or purpose
T+9
addition
The numbers are conventionally plotted using the real part

12. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
The real number a of the complex number z = a + bi
positive
Odd Number

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
Braces
16(5+R)
Place Value Concept
Analytic number theory

14. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
base-ten number
addition
Distributive Law

15. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
monomial
rectangular coordinates
To separate a number into prime factors
Positional notation (place value)

16. 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.
Analytic number theory
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
magnitude and direction
F - F+1 - F+2.......answer is F+2

17. 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
Algebraic number theory
In Diophantine geometry
In Diophantine geometry
constant

18. One term (5x or 4)
Braces
16(5+R)
monomial
the genus of the curve

19. Number X decreased by 12 divided by forty
(x-12)/40
Q-16
complex number
In Diophantine geometry

20. 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}
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
coefficient
In Diophantine geometry

21. 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.
Q-16
Commutative Law of Multiplication
Commutative Law of Addition
Forth Axiom of Equality

22. 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
righthand digit is 0 or 5
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The multiplication of two complex numbers is defined by the following formula:
Commutative Law of Multiplication

23. Remainder
subtraction
repeated elements
its the sum of its digits is divisible by 3
a curve - a surface or some other such object in n-dimensional space

24. A curve in the plane
an equation in two variables defines
variable
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).
Base of the number system

25. 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
Set
Numerals
addition

26. Product
variable
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
solutions
multiplication

27. The place value which corresponds to a given position in a number is determined by the
expression
Base of the number system
magnitude and direction
difference

28. The central problem of Diophantine geometry is to determine when a Diophantine equation has
subtraction
solutions
K+6 - K+5 - K+4 K+3.........answer is K+3
Multiple of the given number

29. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Numerals
solutions
repeated elements
The multiplication of two complex numbers is defined by the following formula:

30. 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
Inversive geometry
Even Number
Definition of genus
algebraic number

31. 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.
subtraction
Members of Elements of the Set
Second Axiom of Equality
difference

32. 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).
Factor of the given number
Braces
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.

33. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
16(5+R)
variable
Prime Number

34. Sixteen less than number Q
magnitude and direction
Q-16
equation
Commutative Law of Addition

35. 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.
Associative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
base-ten number

36. 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.
equation
positive
To separate a number into prime factors
Associative Law of Addition

37. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
an equation in two variables defines
Multiple of the given number
positive
the number formed by the two right-hand digits is divisible by 4

38. 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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39. 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
consecutive whole numbers
Forth Axiom of Equality
F - F+1 - F+2.......answer is F+2
Positional notation (place value)

40. Increased by
righthand digit is 0 or 5
addition
Complex numbers
algebraic number

41. Plus
The real number a of the complex number z = a + bi
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Associative Law of Addition
addition

42. If a factor of a number is prime - it is called a
C or
Prime Factor
T+9
The real number a of the complex number z = a + bi

43. 2 -3 -4 -5 -6
In Diophantine geometry
Distributive Law
consecutive whole numbers
negative

44. 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.
Third Axiom of Equality
Equal
constant
constructing a parallelogram

45. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
subtraction
Members of Elements of the Set
Absolute value and argument

46. The relative greatness of positive and negative numbers
its the sum of its digits is divisible by 3
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude

47. A number that has factors other than itself and 1 is a
difference
Distributive Law
The numbers are conventionally plotted using the real part
Composite Number

48. The objects or symbols in a set are called Numerals - Lines - or Points
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Absolute value and argument
polynomial
Members of Elements of the Set

49. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
difference
Even Number
addition

50. The real and imaginary parts of a complex number can be extracted using the conjugate:
Associative Law of Multiplication
a complex number is real if and only if it equals its conjugate.
Complex numbers
16(5+R)