SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
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. 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.
Set
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
quadratic field
Place Value Concept
2. 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
Inversive geometry
Definition of genus
multiplication
algebraic number
3. LAWS FOR COMBINING NUMBERS
addition
constant
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Composite Number
4. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Factor of the given number
Downward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
a curve - a surface or some other such object in n-dimensional space
5. The numbers which are used for counting in our number system are sometimes called
Prime Number
Natural Numbers
complex number
variable
6. 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.)
addition
Q-16
algebraic number
Number fields
7. Quotient
Third Axiom of Equality
Q-16
division
addition
8. 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
Forth Axiom of Equality
constant
Q-16
Positional notation (place value)
9. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
counterclockwise through 90
difference
rectangular coordinates
10. Product
Commutative Law of Addition
Forth Axiom of Equality
multiplication
the number formed by the three right-hand digits is divisible by 8
11. A number is divisible by 3 if
Analytic number theory
In Diophantine geometry
its the sum of its digits is divisible by 3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
12. Decreased by
Associative Law of Addition
subtraction
algebraic number
F - F+1 - F+2.......answer is F+2
13. A number that has factors other than itself and 1 is a
Place Value Concept
consecutive whole numbers
Composite Number
addition
14. Has an equal sign (3x+5 = 14)
Associative Law of Addition
its the sum of its digits is divisible by 3
Base of the number system
equation
15. Number T increased by 9
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 genus of the curve
T+9
Multiple of the given number
16. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
rectangular coordinates
complex number
variable
17. 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 genus of the curve
Definition of genus
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
18. 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 real number a of the complex number z = a + bi
Place Value Concept
addition
the genus of the curve
19. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
K+6 - K+5 - K+4 K+3.........answer is K+3
addition
the number formed by the two right-hand digits is divisible by 4
20. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Forth Axiom of Equality
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
21. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
algebraic number
Composite Number
righthand digit is 0 or 5
22. More than
Natural Numbers
Inversive geometry
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
23. A letter tat represents a number that is unknown (usually X or Y)
variable
Factor of the given number
Digits
the number formed by the two right-hand digits is divisible by 4
24. 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.
Absolute value and argument
expression
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Associative Law of Addition
25. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
monomial
addition
26. 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.
Forth Axiom of Equality
Natural Numbers
quadratic field
Third Axiom of Equality
27. The set of all complex numbers is denoted by
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.
Members of Elements of the Set
C or
28. 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:
addition
even and the sum of its digits is divisible by 3
complex number
29. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
the number formed by the three right-hand digits is divisible by 8
C or
base-ten number
30. This law can be applied to subtraction by changing signs in such a way that all negative signs are treated as number signs rather than operational signs.That is - some of the addends can be negative numbers.
right-hand digit is even
subtraction
Associative Law of Addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
31. 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.
subtraction
16(5+R)
Odd Number
Commutative Law of Addition
32. Number X decreased by 12 divided by forty
Numerals
Even Number
(x-12)/40
Commutative Law of Addition
33. 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
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
algebraic number
7
addition
34. Implies a collection or grouping of similar - objects or symbols.
Third Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
Prime Factor
Set
35. Are used to indicate sets
In Diophantine geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Braces
subtraction
36. 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
rectangular coordinates
subtraction
addition
The real number a of the complex number z = a + bi
37. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
To separate a number into prime factors
positive
C or
its the sum of its digits is divisible by 3
38. 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
complex number
division
Inversive geometry
counterclockwise through 90
39. 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
negative
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
In Diophantine geometry
Number fields
40. The finiteness or not of the number of rational or integer points on an algebraic curve
In Diophantine geometry
one characteristic in common such as similarity of appearance or purpose
solutions
the genus of the curve
41. A number is divisible by 9 if
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 sum of its digits is divisible by 9
monomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
42. A number is divisible by 2 if
Equal
Absolute value and argument
right-hand digit is even
7
43. A curve in the plane
Set
an equation in two variables defines
addition
Composite Number
44. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
coefficient
difference
Associative Law of Addition
45. 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:
one characteristic in common such as similarity of appearance or purpose
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).
Absolute value and argument
Even Number
46. One term (5x or 4)
Third Axiom of Equality
monomial
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
47. The number touching the variable (in the case of 5x - would be 5)
To separate a number into prime factors
Digits
a curve - a surface or some other such object in n-dimensional space
coefficient
48. No short method has been found for determining whether a number is divisible by
7
K+6 - K+5 - K+4 K+3.........answer is K+3
16(5+R)
counterclockwise through 90
49. Any number that is not a multiple of 2 is an
The multiplication of two complex numbers is defined by the following formula:
Odd Number
addition
F - F+1 - F+2.......answer is F+2
50. A number is divisible by 4 if
constant
the number formed by the two right-hand digits is divisible by 4
an equation in two variables defines
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation: