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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. Does not have an equal sign (3x+5) (2a+9b)
The real number a of the complex number z = a + bi
expression
Commutative Law of Multiplication
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
2. Any number that is not a multiple of 2 is an
Number fields
Positional notation (place value)
subtraction
Odd Number
3. 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
Base of the number system
a curve - a surface or some other such object in n-dimensional space
Algebraic number theory
F - F+1 - F+2.......answer is F+2
4. LAWS FOR COMBINING NUMBERS
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
T+9
the sum of its digits is divisible by 9
5. Any number that la a multiple of 2 is an
Even Number
a curve - a surface or some other such object in n-dimensional space
Q-16
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
6. The defining characteristic of a position vector is that it has
Odd Number
magnitude and direction
Braces
algebraic number
7. An equation - or system of equations - in two or more variables defines
Prime Factor
consecutive whole numbers
The multiplication of two complex numbers is defined by the following formula:
a curve - a surface or some other such object in n-dimensional space
8. 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.
addition
Associative Law of Multiplication
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
multiplication
9. 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
multiplication
Set
The multiplication of two complex numbers is defined by the following formula:
Absolute value and argument
10. 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.
addition
Commutative Law of Addition
The numbers are conventionally plotted using the real part
complex number
11. Has an equal sign (3x+5 = 14)
equation
Multiple of the given number
Analytic number theory
addition
12. 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
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
constructing a parallelogram
Set
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.
(x-12)/40
C or
Commutative Law of Multiplication
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
14. Implies a collection or grouping of similar - objects or symbols.
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.
(x-12)/40
Downward
Set
15. A number is divisible by 9 if
magnitude and direction
the sum of its digits is divisible by 9
Place Value Concept
counterclockwise through 90
16. As shown earlier - c - di is the complex conjugate of the denominator c + di.
subtraction
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
the sum of its digits is divisible by 9
a complex number is real if and only if it equals its conjugate.
17. Number X decreased by 12 divided by forty
Inversive geometry
Third Axiom of Equality
(x-12)/40
Commutative Law of Addition
18. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
Absolute value and argument
In Diophantine geometry
variable
19. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Commutative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
magnitude and direction
variable
20. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
a complex number is real if and only if it equals its conjugate.
Place Value Concept
Distributive Law
21. The number touching the variable (in the case of 5x - would be 5)
Downward
coefficient
Definition of genus
addition
22. Number symbols
Composite Number
upward
Numerals
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
23. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
consecutive whole numbers
Numerals
positive
24. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Second Axiom of Equality
subtraction
Number fields
Inversive geometry
25. 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
Equal
Second Axiom of Equality
a complex number is real if and only if it equals its conjugate.
Digits
26. Remainder
The real number a of the complex number z = a + bi
subtraction
Analytic number theory
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
27. A number is divisible by 2 if
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
repeated elements
right-hand digit is even
Complex numbers
28. The relative greatness of positive and negative numbers
magnitude
negative
Prime Factor
Numerals
29. 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.
T+9
Third Axiom of Equality
Commutative Law of Addition
a complex number is real if and only if it equals its conjugate.
30. 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.)
Number fields
the number formed by the two right-hand digits is divisible by 4
rectangular coordinates
base-ten number
31. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
division
Associative Law of Addition
upward
To separate a number into prime factors
32. A number is divisible by 3 if
counterclockwise through 90
Multiple of the given number
its the sum of its digits is divisible by 3
Downward
33. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
upward
division
K+6 - K+5 - K+4 K+3.........answer is K+3
Odd Number
34. 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
Inversive geometry
Positional notation (place value)
C or
T+9
35. The objects in a set have at least
an equation in two variables defines
one characteristic in common such as similarity of appearance or purpose
Distributive Law
algebraic number
36. 2 -3 -4 -5 -6
Definition of genus
consecutive whole numbers
the number formed by the two right-hand digits is divisible by 4
upward
37. A number is divisible by 6 if it is
expression
even and the sum of its digits is divisible by 3
base-ten number
Prime Factor
38. 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 -
constant
Analytic number theory
upward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
39. Any number that is exactly divisible by a given number is a
coefficient
Multiple of the given number
the number formed by the three right-hand digits is divisible by 8
rectangular coordinates
40. A curve in the plane
the number formed by the three right-hand digits is divisible by 8
righthand digit is 0 or 5
an equation in two variables defines
a curve - a surface or some other such object in n-dimensional space
41. 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.
Equal
Forth Axiom of Equality
counterclockwise through 90
Base of the number system
42. 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.
right-hand digit is even
constant
complex number
Commutative Law of Addition
43. Plus
addition
even and the sum of its digits is divisible by 3
the sum of its digits is divisible by 9
Even Number
44. Integers greater than zero and less than 5 form a set - as follows:
magnitude
16(5+R)
its the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
45. 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.
C or
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Associative Law of Addition
division
46. A number is divisible by 5 if its
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
righthand digit is 0 or 5
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Algebraic number theory
47. 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
positive
In Diophantine geometry
algebraic number
Absolute value and argument
48. Decreased by
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
positive
subtraction
rectangular coordinates
49. 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
Set
Definition of genus
In Diophantine geometry
Forth Axiom of Equality
50. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Set
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).
K+6 - K+5 - K+4 K+3.........answer is K+3
rectangular coordinates