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CLEP General Mathematics: Number Systems And Sets

Subjects : clep, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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 branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Inversive geometry
Even Number
an equation in two variables defines

2. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
its the sum of its digits is divisible by 3
To separate a number into prime factors
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.
upward

3. If a factor of a number is prime - it is called a
F - F+1 - F+2.......answer is F+2
Prime Factor
base-ten number
negative

4. 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.
Digits
difference
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
To separate a number into prime factors

5. 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
Algebraic number theory
Commutative Law of Multiplication
To separate a number into prime factors
Composite Number

6. 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
monomial
addition
its the sum of its digits is divisible by 3

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
Set
algebraic number
a complex number is real if and only if it equals its conjugate.

8. Any number that is exactly divisible by a given number is a
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Second Axiom of Equality
positive
Multiple of the given number

9. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
16(5+R)
its the sum of its digits is divisible by 3
right-hand digit is even

10. Are used to indicate sets
magnitude and direction
Braces
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
difference

11. Product
multiplication
complex number
upward
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

12. A letter tat represents a number that is unknown (usually X or Y)
Factor of the given number
division
variable
subtraction

13. Any number that is not a multiple of 2 is an
coefficient
addition
Odd Number
subtraction

14. No short method has been found for determining whether a number is divisible by
multiplication
the number formed by the two right-hand digits is divisible by 4
negative
7

15. 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.
Forth Axiom of Equality
Associative Law of Addition
variable
solutions

16. Product of 16 and the sum of 5 and number R
coefficient
Members of Elements of the Set
16(5+R)
upward

17. An equation - or system of equations - in two or more variables defines
subtraction
the sum of its digits is divisible by 9
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
a curve - a surface or some other such object in n-dimensional space

18. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
The multiplication of two complex numbers is defined by the following formula:
Forth Axiom of Equality
algebraic number

19. Addition of two complex numbers can be done geometrically by
Q-16
Equal
Inversive geometry
constructing a parallelogram

20. 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.
(x-12)/40
Commutative Law of Multiplication
Associative Law of Addition
the number formed by the two right-hand digits is divisible by 4

21. A number is divisible by 2 if
rectangular coordinates
quadratic field
Commutative Law of Multiplication
right-hand digit is even

22. Any number that can be divided lnto a given number without a remainder is a
Distributive Law
Even Number
Factor of the given number
Q-16

23. Implies a collection or grouping of similar - objects or symbols.
Even Number
Set
Positional notation (place value)
counterclockwise through 90

24. 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 Number
Commutative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
complex number

25. One term (5x or 4)
monomial
complex number
right-hand digit is even
algebraic number

26. Sixteen less than number Q
Q-16
algebraic number
To separate a number into prime factors
Complex numbers

27. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Analytic number theory
Positional notation (place value)
The real number a of the complex number z = a + bi

28. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
repeated elements
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Prime Number

29. The real and imaginary parts of a complex number can be extracted using the conjugate:
the number formed by the two right-hand digits is divisible by 4
polynomial
counterclockwise through 90
a complex number is real if and only if it equals its conjugate.

30. The relative greatness of positive and negative numbers
multiplication
complex number
addition
magnitude

31. Less than
counterclockwise through 90
magnitude
subtraction
Even Number

32. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.
Commutative Law of Addition
Number fields
counterclockwise through 90
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.

33. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.
Algebraic number theory
Composite Number
righthand digit is 0 or 5
Associative Law of Addition

34. 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
base-ten number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the genus of the curve

35. The number touching the variable (in the case of 5x - would be 5)
Base of the number system
coefficient
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

36. A number is divisible by 8 if
Analytic number theory
Commutative Law of Addition
Associative Law of Addition
the number formed by the three right-hand digits is divisible by 8

37. Sum
addition
The multiplication of two complex numbers is defined by the following formula:
16(5+R)
Commutative Law of Addition

38. A number that has no factors except itself and 1 is a
Commutative Law of Addition
addition
Prime Number
equation

39. Number X decreased by 12 divided by forty
(x-12)/40
the genus of the curve
K+6 - K+5 - K+4 K+3.........answer is K+3
monomial

40. A number is divisible by 9 if
(x-12)/40
the sum of its digits is divisible by 9
Natural Numbers
Commutative Law of Addition

41. Decreased 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.
subtraction
Complex numbers
The multiplication of two complex numbers is defined by the following formula:

42. 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
The numbers are conventionally plotted using the real part
7
Equal
In Diophantine geometry

43. 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.
quadratic field
Prime Number
Algebraic number theory
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

44. 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.
Associative Law of Addition
Base of the number system
Commutative Law of Addition
Associative Law of Multiplication

45. 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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46. 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
The real number a of the complex number z = a + bi
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
coefficient
Place Value Concept

47. Quotient
monomial
division
Associative Law of Addition
negative

48. The set of all complex numbers is denoted by
variable
Natural Numbers
base-ten number
C or

49. Does not have an equal sign (3x+5) (2a+9b)
variable
Second Axiom of Equality
expression
Even Number

50. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
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.
polynomial
Downward
Positional notation (place value)