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CLEP General Mathematics: Number Systems And Sets
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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. Integers greater than zero and less than 5 form a set - as follows:
Braces
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
2. Quotient
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
rectangular coordinates
division
constant
3. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
constructing a parallelogram
its the sum of its digits is divisible by 3
Q-16
Inversive geometry
4. The greatest of 3 consecutive whole numbers - the smallest of which is F
Braces
difference
F - F+1 - F+2.......answer is F+2
coefficient
5. 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
F - F+1 - F+2.......answer is F+2
16(5+R)
C or
Place Value Concept
6. 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
Definition of genus
In Diophantine geometry
Number fields
coefficient
7. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
division
negative
Associative Law of Multiplication
8. A number is divisible by 3 if
its the sum of its digits is divisible by 3
(x-12)/40
solutions
The numbers are conventionally plotted using the real part
9. The numbers which are used for counting in our number system are sometimes called
The multiplication of two complex numbers is defined by the following formula:
a complex number is real if and only if it equals its conjugate.
righthand digit is 0 or 5
Natural Numbers
10. 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
Equal
Set
Second Axiom of Equality
complex number
11. Any number that is not a multiple of 2 is an
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Factor
difference
Odd Number
12. The real and imaginary parts of a complex number can be extracted using the conjugate:
Number fields
In Diophantine geometry
a complex number is real if and only if it equals its conjugate.
expression
13. Number X decreased by 12 divided by forty
magnitude
(x-12)/40
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
its the sum of its digits is divisible by 3
14. Any number that can be divided lnto a given number without a remainder is a
Even Number
Digits
Factor of the given number
Number fields
15. Less than
subtraction
In Diophantine geometry
Forth Axiom of Equality
The real number a of the complex number z = a + bi
16. The place value which corresponds to a given position in a number is determined by the
Base of the number system
an equation in two variables defines
one characteristic in common such as similarity of appearance or purpose
Associative Law of Addition
17. Remainder
negative
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Commutative Law of Addition
subtraction
18. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Even Number
variable
even and the sum of its digits is divisible by 3
Downward
19. 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
Members of Elements of the Set
Analytic number theory
To separate a number into prime factors
division
20. If a factor of a number is prime - it is called a
addition
Prime Factor
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.
Even Number
21. 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.
constant
Commutative Law of Addition
subtraction
Even Number
22. Any number that la a multiple of 2 is an
The real number a of the complex number z = a + bi
Even Number
Forth Axiom of Equality
In Diophantine geometry
23. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
T+9
subtraction
Absolute value and argument
upward
24. Number T increased by 9
T+9
positive
(x-12)/40
Composite Number
25. No short method has been found for determining whether a number is divisible by
addition
constructing a parallelogram
Base of the number system
7
26. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
base-ten number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Commutative Law of Multiplication
27. The finiteness or not of the number of rational or integer points on an algebraic curve
The multiplication of two complex numbers is defined by the following formula:
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
subtraction
the genus of the curve
28. A number that has no factors except itself and 1 is a
In Diophantine geometry
Set
the number formed by the two right-hand digits is divisible by 4
Prime Number
29. The relative greatness of positive and negative numbers
Associative Law of Addition
Natural Numbers
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
magnitude
30. Any number that is exactly divisible by a given number is a
rectangular coordinates
the number formed by the three right-hand digits is divisible by 8
Definition of genus
Multiple of the given number
31. Implies a collection or grouping of similar - objects or symbols.
C or
Set
Odd Number
F - F+1 - F+2.......answer is F+2
32. 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
Natural Numbers
In Diophantine geometry
addition
Downward
33. A number is divisible by 8 if
coefficient
the number formed by the three right-hand digits is divisible by 8
Odd Number
Natural Numbers
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
base-ten number
Positional notation (place value)
right-hand digit is even
multiplication
35. Decreased by
division
subtraction
In Diophantine geometry
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).
36. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
equation
counterclockwise through 90
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
variable
37. 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
coefficient
Number fields
repeated elements
38. 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
its the sum of its digits is divisible by 3
Algebraic number theory
39. Sum
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
counterclockwise through 90
(x-12)/40
addition
40. 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 -
subtraction
upward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Positional notation (place value)
41. A letter tat represents a number that is unknown (usually X or Y)
Prime Factor
Definition of genus
variable
Braces
42. Number symbols
Inversive geometry
Numerals
equation
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
43. 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:
C or
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).
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
44. A number is divisible by 2 if
Distributive Law
Factor of the given number
The real number a of the complex number z = a + bi
right-hand digit is even
45. A number that has factors other than itself and 1 is a
addition
Composite Number
Positional notation (place value)
Odd Number
46. A curve in the plane
Odd Number
an equation in two variables defines
even and the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
47. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Multiple of the given number
Second Axiom of Equality
repeated elements
the number formed by the two right-hand digits is divisible by 4
48. 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.
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.
The numbers are conventionally plotted using the real part
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
49. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Commutative Law of Addition
order of operations
Factor of the given number
even and the sum of its digits is divisible by 3
50. 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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Multiplication
polynomial
right-hand digit is even
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