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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. 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.
16(5+R)
Q-16
Commutative Law of Addition
Set
2. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Odd Number
Braces
positive
even and the sum of its digits is divisible by 3
3. Number X decreased by 12 divided by forty
the genus of the curve
(x-12)/40
variable
Digits
4. A number is divisible by 4 if
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
the number formed by the two right-hand digits is divisible by 4
solutions
5. The number touching the variable (in the case of 5x - would be 5)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Natural Numbers
In Diophantine geometry
coefficient
6. The Arabic numerals from 0 through 9 are called
its the sum of its digits is divisible by 3
solutions
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Digits
7. 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.)
a complex number is real if and only if it equals its conjugate.
rectangular coordinates
counterclockwise through 90
Number fields
8. 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.
Prime Factor
Complex numbers
Place Value Concept
Commutative Law of Addition
9. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
subtraction
The numbers are conventionally plotted using the real part
Complex numbers
10. 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
monomial
Second Axiom of Equality
the number formed by the three right-hand digits is divisible by 8
11. LAWS FOR COMBINING NUMBERS
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
In Diophantine geometry
Absolute value and argument
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
12. A number is divisible by 2 if
subtraction
right-hand digit is even
constant
Number fields
13. Are used to indicate sets
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
Set
Braces
14. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
The real number a of the complex number z = a + bi
T+9
K+6 - K+5 - K+4 K+3.........answer is K+3
15. 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
polynomial
counterclockwise through 90
Positional notation (place value)
Equal
16. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
division
Absolute value and argument
Prime Number
17. Total
addition
Q-16
Even Number
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.
18. 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
Downward
righthand digit is 0 or 5
equation
19. 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.
Composite Number
Associative Law of Addition
Odd Number
Distributive Law
20. Has an equal sign (3x+5 = 14)
Algebraic number theory
subtraction
equation
quadratic field
21. 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
Place Value Concept
Numerals
difference
22. Any number that is not a multiple of 2 is an
Distributive Law
Commutative Law of Addition
magnitude
Odd Number
23. A letter tat represents a number that is unknown (usually X or Y)
Prime Factor
16(5+R)
subtraction
variable
24. 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.
16(5+R)
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).
Inversive geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
25. Decreased by
equation
subtraction
Commutative Law of Addition
quadratic field
26. The real and imaginary parts of a complex number can be extracted using the conjugate:
Natural Numbers
coefficient
a complex number is real if and only if it equals its conjugate.
Associative Law of Addition
27. 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.
Commutative Law of Multiplication
Third Axiom of Equality
the genus of the curve
Odd Number
28. 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.
the number formed by the three right-hand digits is divisible by 8
Third Axiom of Equality
Absolute value and argument
Associative Law of Addition
29. A number that has factors other than itself and 1 is a
the sum of its digits is divisible by 9
Members of Elements of the Set
negative
Composite Number
30. An equation - or system of equations - in two or more variables defines
subtraction
Analytic number theory
addition
a curve - a surface or some other such object in n-dimensional space
31. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Braces
the sum of its digits is divisible by 9
Distributive Law
Associative Law of Addition
32. 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
Q-16
a complex number is real if and only if it equals its conjugate.
Distributive Law
In Diophantine geometry
33. More than one term (5x+4 contains two)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
polynomial
Natural Numbers
34. 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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35. Number T increased by 9
order of operations
equation
Even Number
T+9
36. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Place Value Concept
Forth Axiom of Equality
variable
37. 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
complex number
Definition of genus
Set
Commutative Law of Addition
38. Remainder
Braces
constant
subtraction
difference
39. 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.
Even Number
Set
Associative Law of Multiplication
variable
40. One term (5x or 4)
monomial
the genus of the curve
Members of Elements of the Set
its the sum of its digits is divisible by 3
41. Product of 16 and the sum of 5 and number R
Number fields
a curve - a surface or some other such object in n-dimensional space
positive
16(5+R)
42. Quotient
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
division
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
43. No short method has been found for determining whether a number is divisible by
base-ten number
solutions
addition
7
44. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
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.
(x-12)/40
45. Does not have an equal sign (3x+5) (2a+9b)
expression
repeated elements
Analytic number theory
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
46. 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.
the number formed by the three right-hand digits is divisible by 8
equation
the number formed by the two right-hand digits is divisible by 4
47. 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:
Odd Number
rectangular coordinates
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).
48. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Algebraic number theory
Members of Elements of the Set
Multiple of the given number
49. A number is divisible by 3 if
its the sum of its digits is divisible by 3
Number fields
coefficient
magnitude
50. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
16(5+R)
rectangular coordinates
algebraic number
subtraction