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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 real and imaginary parts of a complex number can be extracted using the conjugate:
Braces
a complex number is real if and only if it equals its conjugate.
To separate a number into prime factors
C or

2. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
16(5+R)
counterclockwise through 90
C or

3. 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.
F - F+1 - F+2.......answer is F+2
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.
Complex numbers
The numbers are conventionally plotted using the real part

4. 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.
equation
addition
Even Number
Associative Law of Multiplication

5. 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 and direction
Associative Law of Addition
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is

6. A number is divisible by 8 if
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).
Analytic number theory
the number formed by the three right-hand digits is divisible by 8
Prime Number

7. 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
In Diophantine geometry
algebraic number
a complex number is real if and only if it equals its conjugate.
Third Axiom of Equality

8. 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.
Downward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
repeated elements
Algebraic number theory

9. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
consecutive whole numbers
Number fields
negative
a complex number is real if and only if it equals its conjugate.

10. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
Downward
multiplication
complex number

11. 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
Positional notation (place value)
Q-16
one characteristic in common such as similarity of appearance or purpose
variable

12. The number without a variable (5m+2). In this case - 2
righthand digit is 0 or 5
In Diophantine geometry
constant
The real number a of the complex number z = a + bi

13. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
Prime Factor
counterclockwise through 90
repeated elements

14. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The numbers are conventionally plotted using the real part
16(5+R)
Second Axiom of Equality

15. Product
K+6 - K+5 - K+4 K+3.........answer is K+3
repeated elements
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
multiplication

16. Sum
Second Axiom of Equality
In Diophantine geometry
addition
Natural Numbers

17. Consists of all numbers of the form - where a and b are rational numbers and d is a fixed rational number whose square root is not rational.
the number formed by the three right-hand digits is divisible by 8
C or
quadratic field
Downward

18. Any number that can be divided lnto a given number without a remainder is a
16(5+R)
its the sum of its digits is divisible by 3
Factor of the given number
In Diophantine geometry

19. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Base of the number system
Positional notation (place value)
counterclockwise through 90
repeated elements

20. 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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21. 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
Number fields
To separate a number into prime factors
the sum of its digits is divisible by 9
Associative Law of Addition

22. 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
righthand digit is 0 or 5
7
Q-16

23. The objects in a set have at least
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Commutative Law of Addition
difference
one characteristic in common such as similarity of appearance or purpose

24. 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
multiplication
In Diophantine geometry
Members of Elements of the Set
difference

25. No short method has been found for determining whether a number is divisible by
addition
the number formed by the three right-hand digits is divisible by 8
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7

26. The number touching the variable (in the case of 5x - would be 5)
coefficient
Downward
Natural Numbers
Set

27. A number is divisible by 3 if
its the sum of its digits is divisible by 3
counterclockwise through 90
Second Axiom of Equality
The numbers are conventionally plotted using the real part

28. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Complex numbers
righthand digit is 0 or 5
The real number a of the complex number z = a + bi

29. A number that has factors other than itself and 1 is a
Composite Number
Definition of genus
Number fields
the number formed by the two right-hand digits is divisible by 4

30. The objects or symbols in a set are called Numerals - Lines - or Points
Set
addition
Members of Elements of the Set
complex number

31. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Composite Number
Prime Factor
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Downward

32. 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.
upward
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.
Number fields

33. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
Algebraic number theory
even and the sum of its digits is divisible by 3
consecutive whole numbers

34. More than one term (5x+4 contains two)
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
polynomial
one characteristic in common such as similarity of appearance or purpose
quadratic field

35. Number T increased by 9
consecutive whole numbers
Equal
T+9
Commutative Law of Multiplication

36. Has an equal sign (3x+5 = 14)
(x-12)/40
Inversive geometry
equation
Base of the number system

37. Any number that is exactly divisible by a given number is a
Multiple of the given number
complex number
a complex number is real if and only if it equals its conjugate.
To separate a number into prime factors

38. 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.
addition
Second Axiom of Equality
Definition of genus
Distributive Law

39. Number X decreased by 12 divided by forty
positive
solutions
(x-12)/40
constant

40. Quotient
the genus of the curve
a curve - a surface or some other such object in n-dimensional space
Prime Factor
division

41. A curve in the plane
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
T+9
an equation in two variables defines
Downward

42. Product of 16 and the sum of 5 and number R
16(5+R)
the number formed by the two right-hand digits is divisible by 4
Definition of genus
Multiple of the given number

43. Any number that la a multiple of 2 is an
Algebraic number theory
right-hand digit is even
positive
Even Number

44. The central problem of Diophantine geometry is to determine when a Diophantine equation has
constant
negative
Associative Law of Addition
solutions

45. 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:
expression
Positional notation (place value)
its the sum of its digits is divisible by 3

46. 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.
one characteristic in common such as similarity of appearance or purpose
Prime Number
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3

47. 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.
constructing a parallelogram
magnitude and direction
Place Value Concept
Analytic number theory

48. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
To separate a number into prime factors
multiplication
Associative Law of Addition

49. 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
equation
base-ten number
Analytic number theory
repeated elements

50. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
division
coefficient
magnitude
Inversive geometry