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. A number is divisible by 6 if it is
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
rectangular coordinates
even and the sum of its digits is divisible by 3
Complex numbers
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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Definition of genus
subtraction
Associative Law of Multiplication
3. Does not have an equal sign (3x+5) (2a+9b)
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).
addition
quadratic field
expression
4. 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.
complex number
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
T+9
5. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
an equation in two variables defines
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Addition
order of operations
6. 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.
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).
Second Axiom of Equality
difference
Analytic number theory
7. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
consecutive whole numbers
positive
quadratic field
Inversive geometry
8. The numbers which are used for counting in our number system are sometimes called
T+9
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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Natural Numbers
9. Integers greater than zero and less than 5 form a set - as follows:
Commutative Law of Multiplication
Positional notation (place value)
a complex number is real if and only if it equals its conjugate.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
10. 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 part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Place Value Concept
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Second Axiom of Equality
11. Increased by
an equation in two variables defines
magnitude
addition
Commutative Law of Addition
12. A curve in the plane
quadratic field
Commutative Law of Multiplication
an equation in two variables defines
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
13. Remainder
an equation in two variables defines
Third Axiom of Equality
coefficient
subtraction
14. 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
coefficient
even and the sum of its digits is divisible by 3
In Diophantine geometry
15. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Q-16
the number formed by the two right-hand digits is divisible by 4
Absolute value and argument
upward
16. A number is divisible by 5 if its
constant
Factor of the given number
righthand digit is 0 or 5
Composite Number
17. 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
consecutive whole numbers
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 multiplication of two complex numbers is defined by the following formula:
Odd Number
18. More than one term (5x+4 contains two)
Prime Number
polynomial
addition
quadratic field
19. Sixteen less than number Q
righthand digit is 0 or 5
Number fields
Definition of genus
Q-16
20. If a factor of a number is prime - it is called a
F - F+1 - F+2.......answer is F+2
Composite Number
solutions
Prime Factor
21. Product
multiplication
To separate a number into prime factors
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
rectangular coordinates
22. A number is divisible by 4 if
righthand digit is 0 or 5
addition
the number formed by the two right-hand digits is divisible by 4
Members of Elements of the Set
23. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
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.
variable
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
24. Has an equal sign (3x+5 = 14)
The real number a of the complex number z = a + bi
consecutive whole numbers
equation
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
25. Less than
(x-12)/40
subtraction
Numerals
Third Axiom of Equality
26. The set of all complex numbers is denoted by
The real number a of the complex number z = a + bi
C or
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition
27. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
multiplication
Number fields
The multiplication of two complex numbers is defined by the following formula:
positive
28. LAWS FOR COMBINING NUMBERS
Algebraic number theory
Natural Numbers
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
subtraction
29. Product of 16 and the sum of 5 and number R
magnitude and direction
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.
16(5+R)
Place Value Concept
30. 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.
Distributive Law
a complex number is real if and only if it equals its conjugate.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
solutions
31. One term (5x or 4)
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
monomial
Distributive Law
32. 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 -
7
algebraic number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Addition
33. 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
quadratic field
In Diophantine geometry
monomial
addition
34. Total
(x-12)/40
subtraction
a curve - a surface or some other such object in n-dimensional space
addition
35. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Equal
Composite Number
Definition of genus
36. 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.)
Number fields
addition
expression
The multiplication of two complex numbers is defined by the following formula:
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.
positive
Commutative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Complex numbers
38. 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
solutions
a complex number is real if and only if it equals its conjugate.
right-hand digit is even
39. 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
C or
Number fields
consecutive whole numbers
40. Another way of encoding points in the complex plane other than using the x- and y-coordinates is to use the distance of a point P to O - the point whose coordinates are (0 - 0) (the origin) - and the angle of the line through P and O. This idea leads
magnitude and direction
Absolute value and argument
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Second Axiom of Equality
41. 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.
Complex numbers
Absolute value and argument
Commutative Law of Addition
subtraction
42. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
algebraic number
negative
complex number
The numbers are conventionally plotted using the real part
43. The defining characteristic of a position vector is that it has
Prime Number
magnitude and direction
Forth Axiom of Equality
division
44. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.
even and the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
multiplication
Commutative Law of Addition
45. Any number that la a multiple of 2 is an
constructing a parallelogram
Q-16
righthand digit is 0 or 5
Even Number
46. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.
Third Axiom of Equality
expression
16(5+R)
multiplication
47. The central problem of Diophantine geometry is to determine when a Diophantine equation has
F - F+1 - F+2.......answer is F+2
solutions
the number formed by the two right-hand digits is divisible by 4
division
48. Number T increased by 9
quadratic field
Set
T+9
variable
49. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
a curve - a surface or some other such object in n-dimensional space
counterclockwise through 90
the sum of its digits is divisible by 9
Definition of genus
50. 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
Members of Elements of the Set
the genus of the curve
complex number
Inversive geometry