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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. 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
Absolute value and argument
Algebraic number theory
Second Axiom of Equality
Commutative Law of Multiplication

2. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
the genus of the curve
Braces
counterclockwise through 90
base-ten number

3. Plus
negative
constant
a complex number is real if and only if it equals its conjugate.
addition

4. Product of 16 and the sum of 5 and number R
16(5+R)
solutions
Forth Axiom of Equality
7

5. A number is divisible by 9 if
positive
addition
the genus of the curve
the sum of its digits is divisible by 9

6. 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.
F - F+1 - F+2.......answer is F+2
positive
Third Axiom of Equality
Associative Law of Multiplication

7. The greatest of 3 consecutive whole numbers - the smallest of which is F
magnitude and direction
F - F+1 - F+2.......answer is F+2
K+6 - K+5 - K+4 K+3.........answer is K+3
variable

8. Implies a collection or grouping of similar - objects or symbols.
Number fields
equation
Set
Prime Number

9. A number is divisible by 3 if
Factor of the given number
monomial
its the sum of its digits is divisible by 3
Commutative Law of Addition

10. 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.
7
the number formed by the three right-hand digits is divisible by 8
Third Axiom of Equality
Braces

11. LAWS FOR COMBINING NUMBERS
division
Third Axiom of Equality
Commutative Law of Multiplication
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

12. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Q-16
Associative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

13. More than
a complex number is real if and only if it equals its conjugate.
complex number
solutions
addition

14. 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
base-ten number
The multiplication of two complex numbers is defined by the following formula:
counterclockwise through 90
righthand digit is 0 or 5

15. A number that has factors other than itself and 1 is a
the sum of its digits is divisible by 9
a complex number is real if and only if it equals its conjugate.
Prime Number
Composite Number

16. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
algebraic number
one characteristic in common such as similarity of appearance or purpose
addition

17. Sum
Braces
a curve - a surface or some other such object in n-dimensional space
base-ten number
addition

18. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Place Value Concept
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
solutions

19. 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
Prime Factor
Distributive Law
In Diophantine geometry
Composite Number

20. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
its the sum of its digits is divisible by 3
addition
F - F+1 - F+2.......answer is F+2

21. The real and imaginary parts of a complex number can be extracted using the conjugate:
base-ten number
the number formed by the two right-hand digits is divisible by 4
a complex number is real if and only if it equals its conjugate.
even and the sum of its digits is divisible by 3

22. A number is divisible by 6 if it is
multiplication
the genus of the curve
consecutive whole numbers
even and the sum of its digits is divisible by 3

23. 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
Braces
counterclockwise through 90
Positional notation (place value)
T+9

24. A number is divisible by 5 if its
Numerals
Braces
righthand digit is 0 or 5
Q-16

25. A number is divisible by 8 if
expression
order of operations
Downward
the number formed by the three right-hand digits is divisible by 8

26. 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:
the number formed by the two right-hand digits is divisible by 4
16(5+R)
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).

27. Addition of two complex numbers can be done geometrically by
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 complex number is real if and only if it equals its conjugate.
constructing a parallelogram
a curve - a surface or some other such object in n-dimensional space

28. Decreased by
subtraction
Q-16
Analytic number theory
one characteristic in common such as similarity of appearance or purpose

29. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
equation
Commutative Law of Addition
Commutative Law of Multiplication
Place Value Concept

30. Any number that la a multiple of 2 is an
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Q-16
Even Number
Positional notation (place value)

31. Product
the genus of the curve
multiplication
Natural Numbers
Members of Elements of the Set

32. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Absolute value and argument
positive
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Odd Number

33. 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
7
The numbers are conventionally plotted using the real part
quadratic field

34. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
coefficient
rectangular coordinates
F - F+1 - F+2.......answer is F+2
upward

35. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Equal

36. 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
Prime Factor
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Absolute value and argument
complex number

37. A number is divisible by 4 if
an equation in two variables defines
algebraic number
the number formed by the two right-hand digits is divisible by 4
constructing a parallelogram

38. Subtraction
a complex number is real if and only if it equals its conjugate.
difference
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).
even and the sum of its digits is divisible by 3

39. 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
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.
constant
an equation in two variables defines
To separate a number into prime factors

40. 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
positive
Odd Number
Definition of genus
Inversive geometry

41. No short method has been found for determining whether a number is divisible by
Set
7
Number fields
monomial

42. Has an equal sign (3x+5 = 14)
Numerals
equation
The multiplication of two complex numbers is defined by the following formula:
complex number

43. Number T increased by 9
Numerals
Associative Law of Addition
magnitude and direction
T+9

44. One term (5x or 4)
monomial
Complex numbers
In Diophantine geometry
constructing a parallelogram

45. The defining characteristic of a position vector is that it has
its the sum of its digits is divisible by 3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
16(5+R)
magnitude and direction

46. 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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47. A letter tat represents a number that is unknown (usually X or Y)
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Factor of the given number
Q-16
variable

48. A number is divisible by 2 if
Members of Elements of the Set
multiplication
one characteristic in common such as similarity of appearance or purpose
right-hand digit is even

49. If a factor of a number is prime - it is called a
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Numerals
the genus of the curve
Prime Factor

50. More than one term (5x+4 contains two)
right-hand digit is even
the genus of the curve
polynomial
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.