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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.
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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 greatest of 3 consecutive whole numbers - the smallest of which is F
negative
constant
difference
F - F+1 - F+2.......answer is F+2
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
Absolute value and argument
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
16(5+R)
variable
3. Number X decreased by 12 divided by forty
subtraction
(x-12)/40
Associative Law of Multiplication
multiplication
4. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
solutions
K+6 - K+5 - K+4 K+3.........answer is K+3
addition
Inversive geometry
5. Integers greater than zero and less than 5 form a set - as follows:
Definition of genus
magnitude and direction
Second Axiom of Equality
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
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.
The numbers are conventionally plotted using the real part
In Diophantine geometry
Equal
complex number
7. Any number that can be divided lnto a given number without a remainder is a
F - F+1 - F+2.......answer is F+2
Composite Number
The multiplication of two complex numbers is defined by the following formula:
Factor of the given number
8. A number is divisible by 4 if
upward
Natural Numbers
the number formed by the two right-hand digits is divisible by 4
variable
9. Sixteen less than number Q
Q-16
an equation in two variables defines
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
righthand digit is 0 or 5
10. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Definition of genus
Equal
repeated elements
Natural Numbers
11. A curve in the plane
multiplication
addition
an equation in two variables defines
right-hand digit is even
12. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Second Axiom of Equality
F - F+1 - F+2.......answer is F+2
magnitude
solutions
13. The relative greatness of positive and negative numbers
Downward
magnitude
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Composite Number
14. Implies a collection or grouping of similar - objects or symbols.
division
Set
coefficient
7
15. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Base of the number system
addition
upward
K+6 - K+5 - K+4 K+3.........answer is K+3
16. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
16(5+R)
consecutive whole numbers
Composite Number
17. 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.
7
addition
Forth Axiom of Equality
addition
18. Increased by
righthand digit is 0 or 5
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).
a complex number is real if and only if it equals its conjugate.
addition
19. 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.
Associative Law of Addition
Commutative Law of Multiplication
rectangular coordinates
constructing a parallelogram
20. A letter tat represents a number that is unknown (usually X or Y)
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Second Axiom of Equality
T+9
variable
21. Product
multiplication
Analytic number theory
Number fields
7
22. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Composite Number
addition
Number fields
23. An equation - or system of equations - in two or more variables defines
Q-16
a curve - a surface or some other such object in n-dimensional space
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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
24. 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.
addition
repeated elements
Associative Law of Multiplication
Numerals
25. The sum of two complex numbers A and B - interpreted as points of the complex plane - is the point X obtained by building a parallelogram three of whose vertices are O - A and B. Equivalently - X is the point such that the triangles with vertices O -
Downward
To separate a number into prime factors
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
variable
26. A number that has no factors except itself and 1 is a
Prime Number
Inversive geometry
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
base-ten number
27. 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
Multiple of the given number
consecutive whole numbers
7
algebraic number
28. More than
Numerals
constant
Commutative Law of Addition
addition
29. 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
constant
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Addition
Braces
30. A number that has factors other than itself and 1 is a
the number formed by the three right-hand digits is divisible by 8
Composite Number
Equal
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
31. The place value which corresponds to a given position in a number is determined by the
(x-12)/40
Commutative Law of Addition
Base of the number system
right-hand digit is even
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.
complex number
Associative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Absolute value and argument
33. Remainder
subtraction
Set
Odd Number
consecutive whole numbers
34. Are used to indicate sets
Braces
C or
Third Axiom of Equality
Even Number
35. Does not have an equal sign (3x+5) (2a+9b)
expression
polynomial
magnitude and direction
Place Value Concept
36. A number is divisible by 3 if
right-hand digit is even
constant
its the sum of its digits is divisible by 3
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
37. 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
The real number a of the complex number z = a + bi
Complex numbers
38. 2 -3 -4 -5 -6
consecutive whole numbers
addition
Prime Number
addition
39. More than one term (5x+4 contains two)
(x-12)/40
polynomial
7
Algebraic number theory
40. 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.
Complex numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Distributive Law
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
41. The objects or symbols in a set are called Numerals - Lines - or Points
The multiplication of two complex numbers is defined by the following formula:
Members of Elements of the Set
7
monomial
42. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
its the sum of its digits is divisible by 3
Distributive Law
C or
43. Any number that is not a multiple of 2 is an
counterclockwise through 90
Associative Law of Multiplication
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Odd Number
44. The Arabic numerals from 0 through 9 are called
the number formed by the three right-hand digits is divisible by 8
Digits
Prime Number
constant
45. Subtraction
Forth Axiom of Equality
7
difference
Numerals
46. Total
polynomial
addition
Equal
magnitude
47. 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
Distributive Law
Equal
subtraction
addition
48. One term (5x or 4)
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
monomial
Set
49. 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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50. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
righthand digit is 0 or 5
positive
variable
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