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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. 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.
In Diophantine geometry
Commutative Law of Addition
algebraic number
Associative Law of Multiplication
2. 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
positive
Absolute value and argument
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Inversive geometry
3. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
division
Braces
positive
one characteristic in common such as similarity of appearance or purpose
4. 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
negative
right-hand digit is even
addition
Algebraic number theory
5. 2 -3 -4 -5 -6
Base of the number system
consecutive whole numbers
magnitude
The multiplication of two complex numbers is defined by the following formula:
6. 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.
its the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
Distributive Law
the sum of its digits is divisible by 9
7. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Set
Q-16
Inversive geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
8. Increased by
complex number
addition
an equation in two variables defines
Distributive Law
9. A number is divisible by 5 if its
righthand digit is 0 or 5
Base of the number system
the number formed by the three right-hand digits is divisible by 8
algebraic number
10. 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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11. A number is divisible by 9 if
Algebraic number theory
subtraction
an equation in two variables defines
the sum of its digits is divisible by 9
12. 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.
Inversive geometry
Composite Number
an equation in two variables defines
Commutative Law of Addition
13. Does not have an equal sign (3x+5) (2a+9b)
righthand digit is 0 or 5
Forth Axiom of Equality
expression
Equal
14. 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
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).
magnitude
algebraic number
quadratic field
15. Total
addition
Second Axiom of Equality
Definition of genus
the sum of its digits is divisible by 9
16. 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
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.
Absolute value and argument
F - F+1 - F+2.......answer is F+2
17. 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:
Positional notation (place value)
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).
Members of Elements of the Set
Place Value Concept
18. The place value which corresponds to a given position in a number is determined by the
Braces
Inversive geometry
Base of the number system
Odd Number
19. Plus
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
Inversive geometry
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
20. Has an equal sign (3x+5 = 14)
Commutative Law of Multiplication
Third Axiom of Equality
equation
Associative Law of Addition
21. 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.
constant
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
base-ten number
Forth Axiom of Equality
22. LAWS FOR COMBINING NUMBERS
the sum of its digits is divisible by 9
Members of Elements of the Set
a curve - a surface or some other such object in n-dimensional space
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
23. Product of 16 and the sum of 5 and number R
16(5+R)
Even Number
expression
the number formed by the two right-hand digits is divisible by 4
24. First axiom of equality
subtraction
monomial
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
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.
25. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The real number a of the complex number z = a + bi
the number formed by the two right-hand digits is divisible by 4
subtraction
26. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
monomial
Downward
Distributive Law
expression
27. A number is divisible by 2 if
the genus of the curve
K+6 - K+5 - K+4 K+3.........answer is K+3
its the sum of its digits is divisible by 3
right-hand digit is even
28. Decreased by
In Diophantine geometry
subtraction
positive
Equal
29. Sixteen less than number Q
upward
variable
Q-16
The real number a of the complex number z = a + bi
30. 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.)
Number fields
Third Axiom of Equality
quadratic field
a curve - a surface or some other such object in n-dimensional space
31. 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.
negative
Third Axiom of Equality
F - F+1 - F+2.......answer is F+2
the number formed by the three right-hand digits is divisible by 8
32. As shown earlier - c - di is the complex conjugate of the denominator c + di.
polynomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Associative Law of Multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
33. Sum
addition
subtraction
Inversive geometry
Factor of the given number
34. Addition of two complex numbers can be done geometrically by
In Diophantine geometry
constructing a parallelogram
the number formed by the two right-hand digits is divisible by 4
Base of the number system
35. Number T increased by 9
T+9
monomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
addition
36. More than
Complex numbers
addition
upward
a curve - a surface or some other such object in n-dimensional space
37. One term (5x or 4)
monomial
Positional notation (place value)
expression
Digits
38. The greatest of 3 consecutive whole numbers - the smallest of which is F
subtraction
Absolute value and argument
F - F+1 - F+2.......answer is F+2
rectangular coordinates
39. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Base of the number system
Associative Law of Addition
In Diophantine geometry
40. Are used to indicate sets
an equation in two variables defines
expression
Braces
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
41. 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.
the sum of its digits is divisible by 9
Definition of genus
the genus of the curve
quadratic field
42. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
upward
Associative Law of Multiplication
repeated elements
43. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
quadratic field
subtraction
In Diophantine geometry
order of operations
44. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Distributive Law
Commutative Law of Addition
45. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
upward
the number formed by the three right-hand digits is divisible by 8
46. More than one term (5x+4 contains two)
polynomial
upward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
consecutive whole numbers
47. 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.
Absolute value and argument
Second Axiom of Equality
variable
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. Number X decreased by 12 divided by forty
solutions
(x-12)/40
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
49. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
difference
Braces
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
50. Subtraction
Definition of genus
rectangular coordinates
difference
Commutative Law of Multiplication