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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
quadratic field
Inversive geometry
the sum of its digits is divisible by 9
2. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
Associative Law of Addition
magnitude
addition
3. The central problem of Diophantine geometry is to determine when a Diophantine equation has
constructing a parallelogram
variable
Algebraic number theory
solutions
4. First axiom of equality
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.
Definition of genus
Associative Law of Addition
equation
5. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
magnitude and direction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
division
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
6. The relative greatness of positive and negative numbers
rectangular coordinates
Inversive geometry
magnitude
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. 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:
Equal
Base of the number system
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 number formed by the three right-hand digits is divisible by 8
8. 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
base-ten number
Distributive Law
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).
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
9. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
The multiplication of two complex numbers is defined by the following formula:
even and the sum of its digits is divisible by 3
Downward
addition
10. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Number fields
the number formed by the three right-hand digits is divisible by 8
Analytic number theory
positive
11. A number that has factors other than itself and 1 is a
magnitude and direction
7
Composite Number
The multiplication of two complex numbers is defined by the following formula:
12. 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.
positive
addition
16(5+R)
Commutative Law of Addition
13. Any number that la a multiple of 2 is an
Factor of the given number
the number formed by the three right-hand digits is divisible by 8
Even Number
Multiple of the given number
14. The numbers which are used for counting in our number system are sometimes called
difference
righthand digit is 0 or 5
Natural Numbers
a complex number is real if and only if it equals its conjugate.
15. The Arabic numerals from 0 through 9 are called
the sum of its digits is divisible by 9
difference
Digits
Inversive geometry
16. The place value which corresponds to a given position in a number is determined by the
Base of the number system
upward
Natural Numbers
The real number a of the complex number z = a + bi
17. Total
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
Commutative Law of Addition
subtraction
18. Sum
addition
The multiplication of two complex numbers is defined by the following formula:
Prime Number
an equation in two variables defines
19. Number symbols
Digits
consecutive whole numbers
Numerals
base-ten number
20. 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.
right-hand digit is even
addition
T+9
Forth Axiom of Equality
21. 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.
subtraction
division
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
22. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
a curve - a surface or some other such object in n-dimensional space
negative
In Diophantine geometry
23. A number is divisible by 2 if
right-hand digit is even
the number formed by the three right-hand digits is divisible by 8
algebraic number
upward
24. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
one characteristic in common such as similarity of appearance or purpose
Factor of the given number
The real number a of the complex number z = a + bi
counterclockwise through 90
25. 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
Positional notation (place value)
In Diophantine geometry
addition
Prime Factor
26. 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
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).
Third Axiom of Equality
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
27. A number is divisible by 5 if its
righthand digit is 0 or 5
coefficient
Definition of genus
Commutative Law of Multiplication
28. The defining characteristic of a position vector is that it has
the genus of the curve
The multiplication of two complex numbers is defined by the following formula:
counterclockwise through 90
magnitude and direction
29. 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.
righthand digit is 0 or 5
Prime Number
Analytic number theory
Complex numbers
30. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
Set
Associative Law of Multiplication
complex number
31. 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.
Set
one characteristic in common such as similarity of appearance or purpose
the genus of the curve
Commutative Law of Multiplication
32. Increased by
quadratic field
right-hand digit is even
Set
addition
33. 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
Factor of the given number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
K+6 - K+5 - K+4 K+3.........answer is K+3
Place Value Concept
34. The objects or symbols in a set are called Numerals - Lines - or Points
Commutative Law of Multiplication
negative
Members of Elements of the Set
Inversive geometry
35. 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
even and the sum of its digits is divisible by 3
complex number
Braces
Place Value Concept
36. 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
addition
order of operations
37. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
a complex number is real if and only if it equals its conjugate.
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).
equation
38. 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.
Associative Law of Addition
Even Number
addition
difference
39. A number that has no factors except itself and 1 is a
Braces
Prime Number
expression
polynomial
40. Are used to indicate sets
Braces
Odd Number
subtraction
magnitude and direction
41. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
7
order of operations
algebraic number
Second Axiom of Equality
42. 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.
righthand digit is 0 or 5
Place Value Concept
consecutive whole numbers
Commutative Law of Addition
43. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
even and the sum of its digits is divisible by 3
To separate a number into prime factors
polynomial
44. 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
Definition of genus
Commutative Law of Addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
positive
45. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
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46. 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
Base of the number system
Algebraic number theory
Associative Law of Multiplication
order of operations
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.
solutions
Number fields
Second Axiom of Equality
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
48. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Third Axiom of Equality
division
subtraction
K+6 - K+5 - K+4 K+3.........answer is K+3
49. Integers greater than zero and less than 5 form a set - as follows:
Set
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
repeated elements
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
50. Decreased by
Braces
subtraction
Distributive Law
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.