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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. Does not have an equal sign (3x+5) (2a+9b)
expression
a curve - a surface or some other such object in n-dimensional space
subtraction
Forth Axiom of Equality
2. Quotient
division
Commutative Law of Multiplication
Algebraic number theory
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).
3. Any number that is exactly divisible by a given number is a
constructing a parallelogram
T+9
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Multiple of the given number
4. Are used to indicate sets
magnitude and direction
Braces
Odd Number
equation
5. A letter tat represents a number that is unknown (usually X or Y)
Associative Law of Multiplication
Definition of genus
variable
algebraic number
6. Sum
7
addition
The multiplication of two complex numbers is defined by the following formula:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
7. A number that has factors other than itself and 1 is a
repeated elements
Natural Numbers
Composite Number
To separate a number into prime factors
8. 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
the number formed by the two right-hand digits is divisible by 4
addition
The real number a of the complex number z = a + bi
expression
9. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
division
upward
Associative Law of Addition
10. No short method has been found for determining whether a number is divisible by
addition
Prime Factor
a curve - a surface or some other such object in n-dimensional space
7
11. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
positive
expression
12. 2 -3 -4 -5 -6
consecutive whole numbers
Multiple of the given number
righthand digit is 0 or 5
an equation in two variables defines
13. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Multiple of the given number
Inversive geometry
the number formed by the two right-hand digits is divisible by 4
16(5+R)
14. 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.
complex number
positive
even and the sum of its digits is divisible by 3
Second Axiom of Equality
15. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
(x-12)/40
order of operations
addition
In Diophantine geometry
16. 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 -
Numerals
16(5+R)
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
repeated elements
17. Total
16(5+R)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Distributive Law
addition
18. Any number that is not a multiple of 2 is an
Odd Number
addition
Inversive geometry
Factor of the given number
19. 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.
Downward
addition
Algebraic number theory
Commutative Law of Addition
20. The relative greatness of positive and negative numbers
K+6 - K+5 - K+4 K+3.........answer is K+3
magnitude
Complex numbers
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
21. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Odd Number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Digits
22. More than
Positional notation (place value)
addition
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.
negative
23. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
In Diophantine geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
one characteristic in common such as similarity of appearance or purpose
Number fields
24. 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
Definition of genus
base-ten number
T+9
Inversive geometry
25. The set of all complex numbers is denoted by
difference
C or
Digits
complex number
26. A number is divisible by 5 if its
righthand digit is 0 or 5
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Place Value Concept
Odd Number
27. A number is divisible by 4 if
one characteristic in common such as similarity of appearance or purpose
monomial
repeated elements
the number formed by the two right-hand digits is divisible by 4
28. The number touching the variable (in the case of 5x - would be 5)
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
coefficient
righthand digit is 0 or 5
(x-12)/40
29. Product
magnitude
the number formed by the three right-hand digits is divisible by 8
Number fields
multiplication
30. 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 sum of its digits is divisible by 9
Members of Elements of the Set
division
Place Value Concept
31. 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
Definition of genus
Downward
Prime Factor
upward
32. Product of 16 and the sum of 5 and number R
K+6 - K+5 - K+4 K+3.........answer is K+3
16(5+R)
7
To separate a number into prime factors
33. A number is divisible by 3 if
addition
Third Axiom of Equality
consecutive whole numbers
its the sum of its digits is divisible by 3
34. 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.
Complex numbers
the number formed by the three right-hand digits is divisible by 8
subtraction
Multiple of the given number
35. Any number that la a multiple of 2 is an
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Even Number
Composite Number
36. 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.
Base of the number system
Commutative Law of Addition
C or
The numbers are conventionally plotted using the real part
37. 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}
solutions
polynomial
Braces
38. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Complex numbers
upward
variable
multiplication
39. A number is divisible by 9 if
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the sum of its digits is divisible by 9
subtraction
addition
40. 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:
addition
The real number a of the complex number z = a + bi
Associative Law of Addition
41. Subtraction
addition
addition
difference
quadratic field
42. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Digits
subtraction
repeated elements
16(5+R)
43. If a factor of a number is prime - it is called a
Prime Factor
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Third Axiom of Equality
44. A number is divisible by 2 if
right-hand digit is even
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 number formed by the three right-hand digits is divisible by 8
Associative Law of Addition
45. A number is divisible by 6 if it is
T+9
7
K+6 - K+5 - K+4 K+3.........answer is K+3
even and the sum of its digits is divisible by 3
46. 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.
16(5+R)
polynomial
Associative Law of Addition
Number fields
47. 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
addition
Algebraic number theory
right-hand digit is even
the sum of its digits is divisible by 9
48. The defining characteristic of a position vector is that it has
complex number
magnitude and direction
right-hand digit is even
Definition of genus
49. 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
Positional notation (place value)
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Prime Factor
50. Number symbols
Numerals
the number formed by the two right-hand digits is divisible by 4
a complex number is real if and only if it equals its conjugate.
Positional notation (place value)