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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.
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. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Definition of genus
coefficient
righthand digit is 0 or 5
negative

2. The place value which corresponds to a given position in a number is determined by the
subtraction
constructing a parallelogram
Base of the number system
The real number a of the complex number z = a + bi

3. Does not have an equal sign (3x+5) (2a+9b)
magnitude
Associative Law of Addition
a curve - a surface or some other such object in n-dimensional space
expression

4. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Commutative Law of Multiplication
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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
right-hand digit is even

5. 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:
counterclockwise through 90
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
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).

6. If a factor of a number is prime - it is called a
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.
Prime Factor
addition

7. More than one term (5x+4 contains two)
C or
Number fields
Algebraic number theory
polynomial

8. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
quadratic field

9. Number X decreased by 12 divided by forty
(x-12)/40
Members of Elements of the Set
right-hand digit is even
subtraction

10. The finiteness or not of the number of rational or integer points on an algebraic curve
Downward
coefficient
the genus of the curve
constructing a parallelogram

11. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Second Axiom of Equality
algebraic number
solutions
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).

12. 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.
the number formed by the two right-hand digits is divisible by 4
Associative Law of Multiplication
T+9
Definition of genus

13. The greatest of 3 consecutive whole numbers - the smallest of which is F
Inversive geometry
addition
variable
F - F+1 - F+2.......answer is F+2

14. The relative greatness of positive and negative numbers
magnitude
base-ten number
Forth Axiom of Equality
division

15. 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.
T+9
consecutive whole numbers
Definition of genus
Commutative Law of Multiplication

16. Are often studied as extensions of smaller number fields: a field L is said to be an extension of a field K if L contains K. (For example - the complex numbers C are an extension of the reals R - and the reals R are an extension of the rationals Q.)
To separate a number into prime factors
Number fields
the number formed by the three right-hand digits is divisible by 8
Positional notation (place value)

17. The defining characteristic of a position vector is that it has
constructing a parallelogram
its the sum of its digits is divisible by 3
magnitude and direction
Q-16

18. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Multiple of the given number
Prime Factor
K+6 - K+5 - K+4 K+3.........answer is K+3
C or

19. 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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Multiple of the given number
Numerals

20. 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
algebraic number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
equation
difference

21. The set of all complex numbers is denoted by
constructing a parallelogram
C or
subtraction
quadratic field

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
even and the sum of its digits is divisible by 3
counterclockwise through 90
The multiplication of two complex numbers is defined by the following formula:
C or

23. Less than
order of operations
Downward
the number formed by the three right-hand digits is divisible by 8
subtraction

24. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Even Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
even and the sum of its digits is divisible by 3

25. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
a curve - a surface or some other such object in n-dimensional space
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
complex number

26. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th
Composite Number
upward
even and the sum of its digits is divisible by 3
The real number a of the complex number z = a + bi

27. A number is divisible by 8 if
subtraction
Multiple of the given number
Complex numbers
the number formed by the three right-hand digits is divisible by 8

28. Decreased by
The real number a of the complex number z = a + bi
F - F+1 - F+2.......answer is F+2
subtraction
Natural Numbers

29. Total
Commutative Law of Multiplication
addition
difference
Downward

30. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
quadratic field
polynomial
Associative Law of Addition

31. 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 numbers are conventionally plotted using the real part
polynomial
quadratic field
The real number a of the complex number z = a + bi

32. 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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33. The Arabic numerals from 0 through 9 are called
Prime Number
positive
addition
Digits

34. 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.
Inversive geometry
an equation in two variables defines
Associative Law of Addition
Commutative Law of Addition

35. LAWS FOR COMBINING NUMBERS
Braces
even and the sum of its digits is divisible by 3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
C or

36. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
The numbers are conventionally plotted using the real part
expression
addition

37. A curve in the plane
an equation in two variables defines
upward
rectangular coordinates
In Diophantine geometry

38. A number is divisible by 3 if
upward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
its the sum of its digits is divisible by 3
Q-16

39. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Third Axiom of Equality
Natural Numbers
Positional notation (place value)

40. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Downward
Analytic number theory
Set
rectangular coordinates

41. 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.
constant
The real number a of the complex number z = a + bi
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Second Axiom of Equality

42. No short method has been found for determining whether a number is divisible by
equation
the number formed by the two right-hand digits is divisible by 4
7
C or

43. The objects or symbols in a set are called Numerals - Lines - or Points
the number formed by the three right-hand digits is divisible by 8
Members of Elements of the Set
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Definition of genus

44. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Algebraic number theory
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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.

45. The number without a variable (5m+2). In this case - 2
constant
a curve - a surface or some other such object in n-dimensional space
upward
Commutative Law of Addition

46. One term (5x or 4)
negative
addition
monomial
Base of the number system

47. 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
Distributive Law
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
In Diophantine geometry

48. 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.
Braces
To separate a number into prime factors
Base of the number system
Commutative Law of Addition

49. 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
a curve - a surface or some other such object in n-dimensional space
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Equal
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.

50. 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
In Diophantine geometry
addition
Odd Number
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).