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CLEP General Mathematics: Number Systems And Sets
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Subjects
:
clep
,
math
Instructions:
Answer 50 questions in 15 minutes.
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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. 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.
expression
Q-16
Composite Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
2. Integers greater than zero and less than 5 form a set - as follows:
F - F+1 - F+2.......answer is F+2
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
In Diophantine geometry
3. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Odd Number
consecutive whole numbers
negative
difference
4. Subtraction
difference
Numerals
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Commutative Law of Addition
5. Implies a collection or grouping of similar - objects or symbols.
addition
Set
magnitude
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
6. 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
complex number
base-ten number
order of operations
F - F+1 - F+2.......answer is F+2
7. 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
one characteristic in common such as similarity of appearance or purpose
the number formed by the two right-hand digits is divisible by 4
the genus of the curve
Absolute value and argument
8. 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 genus of the curve
magnitude
Place Value Concept
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
9. The objects in a set have at least
even and the sum of its digits is divisible by 3
one characteristic in common such as similarity of appearance or purpose
Even Number
The real number a of the complex number z = a + bi
10. 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
Base of the number system
Odd Number
algebraic number
In Diophantine geometry
11. More than one term (5x+4 contains two)
difference
Odd Number
polynomial
expression
12. The relative greatness of positive and negative numbers
quadratic field
The numbers are conventionally plotted using the real part
upward
magnitude
13. A number is divisible by 2 if
magnitude
Downward
right-hand digit is even
Place Value Concept
14. 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.
Number fields
Second Axiom of Equality
Prime Factor
subtraction
15. 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.
Associative Law of Multiplication
Complex numbers
rectangular coordinates
its the sum of its digits is divisible by 3
16. Any number that is not a multiple of 2 is an
Downward
expression
the number formed by the two right-hand digits is divisible by 4
Odd Number
17. Sixteen less than number Q
Q-16
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
consecutive whole numbers
Commutative Law of Addition
18. Number T increased by 9
magnitude
16(5+R)
T+9
Second Axiom of Equality
19. 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
Commutative Law of Addition
Numerals
the number formed by the three right-hand digits is divisible by 8
20. 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.
righthand digit is 0 or 5
The real number a of the complex number z = a + bi
rectangular coordinates
Commutative Law of Multiplication
21. The set of all complex numbers is denoted by
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
C or
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
22. Quotient
The real number a of the complex number z = a + bi
constructing a parallelogram
division
variable
23. Number X decreased by 12 divided by forty
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
(x-12)/40
Natural Numbers
Digits
24. 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.
subtraction
Associative Law of Addition
Commutative Law of Addition
upward
25. The objects or symbols in a set are called Numerals - Lines - or Points
addition
Downward
Members of Elements of the Set
Braces
26. A letter tat represents a number that is unknown (usually X or Y)
variable
Associative Law of Addition
Commutative Law of Addition
F - F+1 - F+2.......answer is F+2
27. First axiom of equality
addition
Absolute value and argument
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.
difference
28. 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.
constant
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
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.
29. 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
Number fields
To separate a number into prime factors
algebraic number
polynomial
30. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
one characteristic in common such as similarity of appearance or purpose
Multiple of the given number
upward
constructing a parallelogram
31. 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
(x-12)/40
The real number a of the complex number z = a + bi
Q-16
Composite Number
32. Are used to indicate sets
addition
Prime Number
addition
Braces
33. Decreased by
addition
Commutative Law of Addition
subtraction
multiplication
34. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
C or
Inversive geometry
Q-16
rectangular coordinates
35. A number is divisible by 9 if
the sum of its digits is divisible by 9
7
counterclockwise through 90
Forth Axiom of Equality
36. 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
Set
repeated elements
Equal
Positional notation (place value)
37. A number is divisible by 6 if it is
subtraction
quadratic field
even and the sum of its digits is divisible by 3
coefficient
38. No short method has been found for determining whether a number is divisible by
algebraic number
7
multiplication
negative
39. The Arabic numerals from 0 through 9 are called
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Digits
the sum of its digits is divisible by 9
40. More than
the genus of the curve
upward
Equal
addition
41. Number symbols
Numerals
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition
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. A number that has factors other than itself and 1 is a
coefficient
Composite Number
right-hand digit is even
the number formed by the three right-hand digits is divisible by 8
43. 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.
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).
Braces
an equation in two variables defines
Commutative Law of Addition
44. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Prime Factor
Braces
Definition of genus
Downward
45. Sum
a curve - a surface or some other such object in n-dimensional space
addition
Base of the number system
upward
46. The place value which corresponds to a given position in a number is determined by the
Prime Factor
difference
Base of the number system
variable
47. 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.
The real number a of the complex number z = a + bi
equation
Associative Law of Multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
48. One term (5x or 4)
addition
monomial
the number formed by the three right-hand digits is divisible by 8
addition
49. Total
Set
variable
addition
subtraction
50. A number is divisible by 5 if its
In Diophantine geometry
constructing a parallelogram
righthand digit is 0 or 5
The multiplication of two complex numbers is defined by the following formula:
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