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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. 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
consecutive whole numbers
The numbers are conventionally plotted using the real part
algebraic number
monomial
2. Sixteen less than number Q
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Q-16
monomial
3. One term (5x or 4)
complex number
monomial
multiplication
a curve - a surface or some other such object in n-dimensional space
4. Remainder
subtraction
righthand digit is 0 or 5
an equation in two variables defines
Even Number
5. More than
equation
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Associative Law of Addition
addition
6. The greatest of 3 consecutive whole numbers - the smallest of which is F
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
a curve - a surface or some other such object in n-dimensional space
F - F+1 - F+2.......answer is F+2
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).
7. 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
Numerals
Equal
Prime Number
upward
8. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Equal
addition
the number formed by the two right-hand digits is divisible by 4
negative
9. Product
multiplication
Composite Number
coefficient
Prime Number
10. Addition of two complex numbers can be done geometrically by
subtraction
its the sum of its digits is divisible by 3
Associative Law of Multiplication
constructing a parallelogram
11. Any number that is not a multiple of 2 is an
T+9
Odd Number
variable
monomial
12. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
C or
counterclockwise through 90
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.
13. 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:
7
Absolute value and argument
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).
positive
14. A number that has no factors except itself and 1 is a
Absolute value and argument
Commutative Law of Multiplication
Prime Number
solutions
15. Integers greater than zero and less than 5 form a set - as follows:
multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
difference
variable
16. 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
right-hand digit is even
Positional notation (place value)
Commutative Law of Addition
negative
17. Subtraction
Composite Number
difference
multiplication
Prime Factor
18. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
counterclockwise through 90
repeated elements
Commutative Law of Multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
19. 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
complex number
In Diophantine geometry
Base of the number system
even and the sum of its digits is divisible by 3
20. LAWS FOR COMBINING NUMBERS
F - F+1 - F+2.......answer is F+2
The numbers are conventionally plotted using the real part
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
21. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Addition
upward
In Diophantine geometry
22. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Number fields
complex number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
23. 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.
addition
the sum of its digits is divisible by 9
Associative Law of Multiplication
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).
24. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
complex number
In Diophantine geometry
rectangular coordinates
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
25. The place value which corresponds to a given position in a number is determined by the
Associative Law of Addition
Base of the number system
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The numbers are conventionally plotted using the real part
26. No short method has been found for determining whether a number is divisible by
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
7
equation
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
27. Any number that is exactly divisible by a given number is a
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Multiple of the given number
Numerals
28. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
a complex number is real if and only if it equals its conjugate.
polynomial
Multiple of the given number
Inversive geometry
29. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
algebraic number
subtraction
Place Value Concept
K+6 - K+5 - K+4 K+3.........answer is K+3
30. More than one term (5x+4 contains two)
Second Axiom of Equality
addition
Number fields
polynomial
31. 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
subtraction
Set
one characteristic in common such as similarity of appearance or purpose
32. The objects in a set have at least
T+9
one characteristic in common such as similarity of appearance or purpose
In Diophantine geometry
constant
33. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
magnitude and direction
(x-12)/40
upward
34. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
7
Analytic number theory
Positional notation (place value)
35. Implies a collection or grouping of similar - objects or symbols.
equation
Numerals
the sum of its digits is divisible by 9
Set
36. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
right-hand digit is even
Base of the number system
order of operations
equation
37. 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
difference
In Diophantine geometry
To separate a number into prime factors
subtraction
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
right-hand digit is even
Commutative Law of Addition
complex number
righthand digit is 0 or 5
39. The numbers which are used for counting in our number system are sometimes called
F - F+1 - F+2.......answer is F+2
Natural 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.
addition
40. A curve in the plane
complex number
Prime Factor
an equation in two variables defines
Commutative Law of Addition
41. Any number that la a multiple of 2 is an
Prime Number
Even Number
base-ten number
Algebraic number theory
42. The Arabic numerals from 0 through 9 are called
addition
even and the sum of its digits is divisible by 3
complex number
Digits
43. 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
magnitude and direction
Odd Number
Definition of genus
Forth Axiom of Equality
44. 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
Absolute value and argument
addition
Analytic number theory
Positional notation (place value)
45. A number that has factors other than itself and 1 is a
Associative Law of Multiplication
Composite Number
negative
quadratic field
46. If a factor of a number is prime - it is called a
Prime Factor
difference
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
subtraction
47. Number T increased by 9
T+9
a curve - a surface or some other such object in n-dimensional space
positive
7
48. Increased by
F - F+1 - F+2.......answer is F+2
addition
equation
the genus of the curve
49. 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.
Algebraic number theory
Forth Axiom of Equality
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.
50. An equation - or system of equations - in two or more variables defines
Commutative Law of Multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Set
a curve - a surface or some other such object in n-dimensional space