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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. The number touching the variable (in the case of 5x - would be 5)
coefficient
T+9
solutions
constant
2. LAWS FOR COMBINING NUMBERS
a curve - a surface or some other such object in n-dimensional space
Numerals
Inversive geometry
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
3. 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.)
T+9
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Number fields
Place Value Concept
4. Number X decreased by 12 divided by forty
Factor of the given number
Third Axiom of Equality
subtraction
(x-12)/40
5. 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
The multiplication of two complex numbers is defined by the following formula:
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.
Algebraic number theory
coefficient
6. 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.
consecutive whole numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
division
magnitude and direction
7. Plus
expression
magnitude and direction
addition
the sum of its digits is divisible by 9
8. An equation - or system of equations - in two or more variables defines
Distributive Law
positive
a curve - a surface or some other such object in n-dimensional space
righthand digit is 0 or 5
9. Less than
subtraction
complex number
Base of the number system
a curve - a surface or some other such object in n-dimensional space
10. 2 -3 -4 -5 -6
consecutive whole numbers
positive
Factor of the given number
the genus of the curve
11. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
equation
addition
the number formed by the two right-hand digits is divisible by 4
12. A number is divisible by 4 if
Commutative Law of Addition
Commutative Law of Addition
the number formed by the two right-hand digits is divisible by 4
consecutive whole numbers
13. More than one term (5x+4 contains two)
difference
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
solutions
polynomial
14. The set of all complex numbers is denoted by
positive
a complex number is real if and only if it equals its conjugate.
C or
Absolute value and argument
15. Subtraction
difference
Definition of genus
Odd Number
base-ten number
16. Remainder
righthand digit is 0 or 5
constant
Numerals
subtraction
17. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Associative Law of Addition
repeated elements
Absolute value and argument
In Diophantine geometry
18. The number without a variable (5m+2). In this case - 2
addition
Third Axiom of Equality
constant
Factor of the given number
19. A number is divisible by 2 if
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
C or
right-hand digit is even
rectangular coordinates
20. 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
The real number a of the complex number z = a + bi
variable
(x-12)/40
quadratic field
21. More than
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
negative
constructing a parallelogram
addition
22. 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.
complex number
subtraction
Third Axiom of Equality
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
23. 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
a curve - a surface or some other such object in n-dimensional space
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Absolute value and argument
a complex number is real if and only if it equals its conjugate.
24. Product of 16 and the sum of 5 and number R
16(5+R)
Even Number
addition
addition
25. 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.
Commutative Law of Addition
Second Axiom of Equality
Inversive geometry
Multiple of the given number
26. Are used to indicate sets
solutions
Braces
Associative Law of Addition
Third Axiom of Equality
27. A curve in the plane
an equation in two variables defines
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Composite Number
28. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
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).
Commutative Law of Addition
Commutative Law of Multiplication
29. The Arabic numerals from 0 through 9 are called
Digits
Associative Law of Addition
Absolute value and argument
Third Axiom of Equality
30. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
rectangular coordinates
addition
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).
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.
order of operations
addition
solutions
Commutative Law of Multiplication
32. 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.
Place Value Concept
Number fields
expression
Associative Law of Addition
33. 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.
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).
Complex numbers
order of operations
Commutative Law of Addition
34. 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.
T+9
Associative Law of Addition
even and the sum of its digits is divisible by 3
subtraction
35. A number that has factors other than itself and 1 is a
one characteristic in common such as similarity of appearance or purpose
subtraction
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.
Composite Number
36. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Numerals
rectangular coordinates
Commutative Law of Addition
the number formed by the three right-hand digits is divisible by 8
37. Number T increased by 9
addition
positive
Members of Elements of the Set
T+9
38. 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
Equal
Associative Law of Addition
To separate a number into prime factors
constructing a parallelogram
39. 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.
Definition of genus
To separate a number into prime factors
repeated elements
Second Axiom of Equality
40. The central problem of Diophantine geometry is to determine when a Diophantine equation has
repeated elements
solutions
The real number a of the complex number z = a + bi
Set
41. A number is divisible by 9 if
consecutive whole numbers
the sum of its digits is divisible by 9
Even Number
Definition of genus
42. No short method has been found for determining whether a number is divisible by
right-hand digit is even
Third Axiom of Equality
7
equation
43. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
polynomial
K+6 - K+5 - K+4 K+3.........answer is K+3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Associative Law of Addition
44. Total
repeated elements
positive
addition
In Diophantine geometry
45. The relative greatness of positive and negative numbers
Complex numbers
addition
magnitude
Digits
46. 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.
The numbers are conventionally plotted using the real part
a complex number is real if and only if it equals its conjugate.
positive
In Diophantine geometry
47. 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
Place Value Concept
expression
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.
base-ten number
48. 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
Positional notation (place value)
Algebraic number theory
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Multiplication
49. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Braces
counterclockwise through 90
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).
(x-12)/40
50. 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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