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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
Start Test
Study First
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. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
7
2. The relative greatness of positive and negative numbers
Members of Elements of the Set
constructing a parallelogram
equation
magnitude
3. Increased by
righthand digit is 0 or 5
addition
The multiplication of two complex numbers is defined by the following formula:
T+9
4. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
multiplication
constant
Q-16
5. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Natural Numbers
16(5+R)
Associative Law of Multiplication
6. Less than
difference
subtraction
the number formed by the two right-hand digits is divisible by 4
monomial
7. The objects in a set have at least
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
one characteristic in common such as similarity of appearance or purpose
an equation in two variables defines
Composite Number
8. A curve in the plane
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
an equation in two variables defines
Even Number
Analytic number theory
9. Are used to indicate sets
equation
Numerals
Braces
Factor of the given number
10. Any number that is exactly divisible by a given number is a
Multiple of the given number
The multiplication of two complex numbers is defined by the following formula:
Number fields
righthand digit is 0 or 5
11. 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
Natural Numbers
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
12. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
its the sum of its digits is divisible by 3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
counterclockwise through 90
positive
13. 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.
Commutative Law of Multiplication
Absolute value and argument
the sum of its digits is divisible by 9
Associative Law of Addition
14. A number is divisible by 6 if it is
Associative Law of Addition
Set
The numbers are conventionally plotted using the real part
even and the sum of its digits is divisible by 3
15. Subtraction
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).
Odd Number
difference
Number fields
16. First axiom of equality
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
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.
difference
17. 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.
its the sum of its digits is divisible by 3
Members of Elements of the Set
Commutative Law of Addition
Numerals
18. 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}
K+6 - K+5 - K+4 K+3.........answer is K+3
the genus of the curve
Complex numbers
19. 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.
Absolute value and argument
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Members of Elements of the Set
Distributive Law
20. 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.
Inversive geometry
constant
Associative Law of Addition
Odd Number
21. Product of 16 and the sum of 5 and number R
16(5+R)
even and the sum of its digits is divisible by 3
counterclockwise through 90
the genus of the curve
22. The numbers which are used for counting in our number system are sometimes called
constant
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Natural Numbers
addition
23. 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.
Commutative Law of Addition
the genus of the curve
Third Axiom of Equality
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
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
In Diophantine geometry
the genus of the curve
addition
the number formed by the three right-hand digits is divisible by 8
25. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
In Diophantine geometry
order of operations
Associative Law of Multiplication
negative
26. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
In Diophantine geometry
the number formed by the two right-hand digits is divisible by 4
27. Number T increased by 9
Number fields
T+9
Downward
The multiplication of two complex numbers is defined by the following formula:
28. 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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Analytic number theory
Associative Law of Multiplication
Definition of genus
29. The set of all complex numbers is denoted by
complex number
C or
Base of the number system
expression
30. Any number that la a multiple of 2 is an
polynomial
Even Number
even and the sum of its digits is divisible by 3
consecutive whole numbers
31. Remainder
Distributive Law
subtraction
expression
Definition of genus
32. Has an equal sign (3x+5 = 14)
equation
its the sum of its digits is divisible by 3
F - F+1 - F+2.......answer is F+2
a complex number is real if and only if it equals its conjugate.
33. A letter tat represents a number that is unknown (usually X or Y)
variable
Even Number
Braces
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
34. The number without a variable (5m+2). In this case - 2
expression
constant
Absolute value and argument
subtraction
35. A number is divisible by 3 if
Associative Law of Addition
Positional notation (place value)
The real number a of the complex number z = a + bi
its the sum of its digits is divisible by 3
36. Addition of two complex numbers can be done geometrically by
Downward
Associative Law of Multiplication
constructing a parallelogram
the number formed by the two right-hand digits is divisible by 4
37. 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.
Associative Law of Addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
variable
Forth Axiom of Equality
38. Number X decreased by 12 divided by forty
Multiple of the given number
Associative Law of Addition
F - F+1 - F+2.......answer is F+2
(x-12)/40
39. A number that has factors other than itself and 1 is a
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).
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.
constructing a parallelogram
Composite Number
40. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
a complex number is real if and only if it equals its conjugate.
Digits
Inversive geometry
its the sum of its digits is divisible by 3
41. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
one characteristic in common such as similarity of appearance or purpose
Prime Factor
Associative Law of Multiplication
42. 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:
subtraction
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).
its the sum of its digits is divisible by 3
Algebraic number theory
43. 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
Analytic number theory
its the sum of its digits is divisible by 3
The real number a of the complex number z = a + bi
The multiplication of two complex numbers is defined by the following formula:
44. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
negative
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
repeated elements
complex number
45. If a factor of a number is prime - it is called a
Prime Factor
Factor of the given number
an equation in two variables defines
Even Number
46. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
addition
repeated elements
consecutive whole numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
47. 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
Commutative Law of Multiplication
Definition of genus
repeated elements
addition
48. The place value which corresponds to a given position in a number is determined by the
Base of the number system
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
quadratic field
division
49. Total
the number formed by the two right-hand digits is divisible by 4
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Q-16
50. Number symbols
Odd Number
To separate a number into prime factors
Numerals
Second Axiom of Equality