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. 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.
Associative Law of Multiplication
Complex numbers
multiplication
Digits
2. Total
an equation in two variables defines
In Diophantine geometry
magnitude
addition
3. Number X decreased by 12 divided by forty
16(5+R)
(x-12)/40
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Members of Elements of the Set
4. The number touching the variable (in the case of 5x - would be 5)
addition
To separate a number into prime factors
order of operations
coefficient
5. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
variable
Odd Number
counterclockwise through 90
The numbers are conventionally plotted using the real part
6. Number symbols
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
16(5+R)
Numerals
the number formed by the three right-hand digits is divisible by 8
7. The relative greatness of positive and negative numbers
constructing a parallelogram
Downward
magnitude
subtraction
8. 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.
subtraction
quadratic field
Commutative Law of Multiplication
Associative Law of Addition
9. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
the sum of its digits is divisible by 9
positive
Prime Factor
subtraction
10. A letter tat represents a number that is unknown (usually X or Y)
difference
subtraction
variable
addition
11. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
complex number
righthand digit is 0 or 5
Inversive geometry
12. LAWS FOR COMBINING NUMBERS
Place Value Concept
Numerals
The real number a of the complex number z = a + bi
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
13. One term (5x or 4)
difference
Set
monomial
Braces
14. 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
C or
Members of Elements of the Set
Complex numbers
15. 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:
Positional notation (place value)
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).
In Diophantine geometry
expression
16. 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
To separate a number into prime factors
the sum of its digits is divisible by 9
In Diophantine geometry
positive
17. Decreased by
In Diophantine geometry
constant
Inversive geometry
subtraction
18. 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.
Analytic number theory
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Definition of genus
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.
19. More than one term (5x+4 contains two)
polynomial
Place Value Concept
Equal
its the sum of its digits is divisible by 3
20. The finiteness or not of the number of rational or integer points on an algebraic curve
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
Definition of genus
consecutive whole numbers
21. Sixteen less than number Q
repeated elements
Q-16
expression
even and the sum of its digits is divisible by 3
22. No short method has been found for determining whether a number is divisible by
polynomial
7
constructing a parallelogram
Positional notation (place value)
23. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
variable
Multiple of the given number
Associative Law of Addition
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
Number fields
Third Axiom of Equality
Algebraic number theory
25. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
In Diophantine geometry
subtraction
order of operations
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
26. A curve in the plane
Commutative Law of Multiplication
The numbers are conventionally plotted using the real part
an equation in two variables defines
Even Number
27. A number that has factors other than itself and 1 is a
coefficient
Digits
Place Value Concept
Composite Number
28. More than
solutions
Associative Law of Addition
addition
Inversive geometry
29. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Numerals
rectangular coordinates
Downward
a complex number is real if and only if it equals its conjugate.
30. Any number that can be divided lnto a given number without a remainder is a
multiplication
positive
Set
Factor of the given number
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
addition
addition
C or
Definition of genus
32. The objects or symbols in a set are called Numerals - Lines - or Points
In Diophantine geometry
Members of Elements of the Set
Second Axiom of Equality
counterclockwise through 90
33. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
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 and the sum of its digits is divisible by 3
Numerals
34. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Analytic number theory
coefficient
K+6 - K+5 - K+4 K+3.........answer is K+3
variable
35. A number is divisible by 2 if
C or
Algebraic number theory
right-hand digit is even
magnitude and direction
36. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
Equal
subtraction
Inversive geometry
37. 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
Q-16
Set
The real number a of the complex number z = a + bi
Number fields
38. Product
(x-12)/40
multiplication
Forth Axiom of Equality
the genus of the curve
39. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
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).
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Inversive geometry
In Diophantine geometry
40. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
subtraction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Addition
41. A number that has no factors except itself and 1 is a
magnitude and direction
Distributive Law
the number formed by the two right-hand digits is divisible by 4
Prime Number
42. Integers greater than zero and less than 5 form a set - as follows:
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Base of the number system
In Diophantine geometry
43. A number is divisible by 9 if
C or
K+6 - K+5 - K+4 K+3.........answer is K+3
consecutive whole numbers
the sum of its digits is divisible by 9
44. 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.
upward
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.
Associative Law of Addition
Commutative Law of Addition
45. 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
Algebraic number theory
multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Addition
46. 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
Second Axiom of Equality
even and the sum of its digits is divisible by 3
rectangular coordinates
base-ten number
47. A number is divisible by 6 if it is
polynomial
even and the sum of its digits is divisible by 3
Place Value Concept
Members of Elements of the Set
48. 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
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 multiplication of two complex numbers is defined by the following formula:
equation
Absolute value and argument
49. 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.
F - F+1 - F+2.......answer is F+2
quadratic field
Second Axiom of Equality
Associative Law of Addition
50. 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.)
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.
Number fields
the sum of its digits is divisible by 9
constant