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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. 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}
addition
a curve - a surface or some other such object in n-dimensional space
quadratic field
2. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
repeated elements
16(5+R)
Natural Numbers
3. The finiteness or not of the number of rational or integer points on an algebraic curve
Members of Elements of the Set
the genus of the curve
To separate a number into prime factors
Second Axiom of Equality
4. 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:
consecutive whole numbers
right-hand digit is even
Absolute value and argument
5. 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.)
the number formed by the three right-hand digits is divisible by 8
its the sum of its digits is divisible by 3
negative
Number fields
6. 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
solutions
Even Number
The multiplication of two complex numbers is defined by the following formula:
the genus of the curve
7. 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.
coefficient
Associative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Braces
8. 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
Algebraic number theory
the genus of the curve
K+6 - K+5 - K+4 K+3.........answer is K+3
In Diophantine geometry
9. 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
Multiple of the given number
C or
Definition of genus
To separate a number into prime factors
10. 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:
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).
its the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
constant
11. The numbers which are used for counting in our number system are sometimes called
equation
one characteristic in common such as similarity of appearance or purpose
Natural Numbers
magnitude
12. 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
rectangular coordinates
Set
an equation in two variables defines
13. More than one term (5x+4 contains two)
upward
polynomial
one characteristic in common such as similarity of appearance or purpose
F - F+1 - F+2.......answer is F+2
14. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
variable
constructing a parallelogram
consecutive whole numbers
15. The central problem of Diophantine geometry is to determine when a Diophantine equation has
positive
expression
solutions
magnitude
16. 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.
Prime Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Analytic number theory
17. 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
Analytic number theory
constructing a parallelogram
Equal
equation
18. The place value which corresponds to a given position in a number is determined by the
The multiplication of two complex numbers is defined by the following formula:
Analytic number theory
Base of the number system
Definition of genus
19. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Second Axiom of Equality
rectangular coordinates
Q-16
magnitude and direction
20. The number touching the variable (in the case of 5x - would be 5)
coefficient
16(5+R)
expression
upward
21. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
righthand digit is 0 or 5
The numbers are conventionally plotted using the real part
Associative Law of Addition
22. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Complex numbers
subtraction
Odd Number
23. 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
quadratic field
base-ten number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The real number a of the complex number z = a + bi
24. The defining characteristic of a position vector is that it has
multiplication
Place Value Concept
magnitude and direction
its the sum of its digits is divisible by 3
25. 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.
Factor of the given number
Forth Axiom of Equality
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
rectangular coordinates
26. More than
Prime Number
addition
Associative Law of Multiplication
Set
27. 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
base-ten number
Commutative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
28. Total
its the sum of its digits is divisible by 3
complex number
Algebraic number theory
addition
29. If a factor of a number is prime - it is called a
Multiple of the given number
Prime Factor
solutions
the number formed by the two right-hand digits is divisible by 4
30. The Arabic numerals from 0 through 9 are called
Base of the number system
constant
Second Axiom of Equality
Digits
31. A number is divisible by 6 if it is
16(5+R)
even and the sum of its digits is divisible by 3
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The real number a of the complex number z = a + bi
32. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
addition
positive
F - F+1 - F+2.......answer is F+2
constructing a parallelogram
33. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Complex numbers
Distributive Law
its the sum of its digits is divisible by 3
Natural Numbers
34. Addition of two complex numbers can be done geometrically by
difference
an equation in two variables defines
Absolute value and argument
constructing a parallelogram
35. A number is divisible by 2 if
F - F+1 - F+2.......answer is F+2
right-hand digit is even
equation
addition
36. 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
one characteristic in common such as similarity of appearance or purpose
Place Value Concept
the genus of the curve
The numbers are conventionally plotted using the real part
37. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Equal
upward
its the sum of its digits is divisible by 3
Distributive Law
38. One term (5x or 4)
addition
monomial
complex number
Digits
39. 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.
division
Associative Law of Multiplication
Prime Number
Natural Numbers
40. A number that has factors other than itself and 1 is a
Associative Law of Addition
Composite Number
a complex number is real if and only if it equals its conjugate.
Equal
41. Plus
addition
magnitude
Place Value Concept
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.
42. 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.
K+6 - K+5 - K+4 K+3.........answer is K+3
Commutative Law of Addition
magnitude
Base of the number system
43. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
monomial
7
Equal
44. Has an equal sign (3x+5 = 14)
Set
the number formed by the three right-hand digits is divisible by 8
Members of Elements of the Set
equation
45. Quotient
division
Digits
To separate a number into prime factors
Absolute value and argument
46. Number T increased by 9
Associative Law of Addition
T+9
addition
monomial
47. 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.
Associative Law of Addition
Braces
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
K+6 - K+5 - K+4 K+3.........answer is K+3
48. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Composite Number
Numerals
In Diophantine geometry
49. Any number that is exactly divisible by a given number is a
Multiple of the given number
the sum of its digits is divisible by 9
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Braces
50. Implies a collection or grouping of similar - objects or symbols.
T+9
C or
one characteristic in common such as similarity of appearance or purpose
Set