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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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Subjects
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clep
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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. 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.
base-ten number
Associative Law of Multiplication
Analytic number theory
Set
2. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
The numbers are conventionally plotted using the real part
upward
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.
3. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Downward
Associative Law of Addition
the number formed by the two right-hand digits is divisible by 4
4. 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.
Q-16
subtraction
Third Axiom of Equality
Algebraic number theory
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:
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).
Factor of the given number
Absolute value and argument
6. Addition of two complex numbers can be done geometrically by
solutions
constructing a parallelogram
division
Algebraic number theory
7. An equation - or system of equations - in two or more variables defines
subtraction
a curve - a surface or some other such object in n-dimensional space
division
variable
8. 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.)
monomial
Distributive Law
Number fields
the number formed by the two right-hand digits is divisible by 4
9. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor
Associative Law of Addition
constructing a parallelogram
Third Axiom of Equality
To separate a number into prime factors
10. A number is divisible by 3 if
base-ten number
Forth Axiom of Equality
addition
its the sum of its digits is divisible by 3
11. 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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12. Number X decreased by 12 divided by forty
rectangular coordinates
Braces
In Diophantine geometry
(x-12)/40
13. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
an equation in two variables defines
magnitude
repeated elements
14. Does not have an equal sign (3x+5) (2a+9b)
constructing a parallelogram
Digits
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
expression
15. 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
In Diophantine geometry
rectangular coordinates
Set
the number formed by the three right-hand digits is divisible by 8
16. 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
Associative Law of Multiplication
Complex numbers
Members of Elements of the Set
17. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.
expression
Definition of genus
Analytic number theory
righthand digit is 0 or 5
18. No short method has been found for determining whether a number is divisible by
7
Members of Elements of the Set
subtraction
order of operations
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
expression
addition
Algebraic number theory
Third Axiom of Equality
20. 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.
Braces
Associative Law of Addition
base-ten number
righthand digit is 0 or 5
21. 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 genus of the curve
Positional notation (place value)
multiplication
22. Has an equal sign (3x+5 = 14)
equation
difference
addition
Number fields
23. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
magnitude and direction
order of operations
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.
24. A number that has no factors except itself and 1 is a
Prime Number
Place Value Concept
upward
16(5+R)
25. Product of 16 and the sum of 5 and number R
Commutative Law of Addition
16(5+R)
negative
Composite Number
26. The set of all complex numbers is denoted by
positive
C or
16(5+R)
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
27. A number is divisible by 2 if
right-hand digit is even
addition
its the sum of its digits is divisible by 3
Set
28. Quotient
Number fields
division
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
29. 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
Number fields
expression
multiplication
base-ten number
30. Number symbols
T+9
Numerals
Digits
Associative Law of Addition
31. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
positive
negative
addition
Base of the number system
32. One term (5x or 4)
base-ten number
Equal
division
monomial
33. Number T increased by 9
solutions
magnitude
Commutative Law of Addition
T+9
34. 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
expression
Analytic number theory
In Diophantine geometry
Place Value Concept
35. 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
the sum of its digits is divisible by 9
complex number
Base of the number system
Equal
36. A number is divisible by 6 if it is
Commutative Law of Addition
Associative Law of Addition
even and the sum of its digits is divisible by 3
Prime Factor
37. The number without a variable (5m+2). In this case - 2
constant
(x-12)/40
coefficient
Numerals
38. 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
addition
algebraic number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Positional notation (place value)
39. Product
The real number a of the complex number z = a + bi
multiplication
Associative Law of Addition
the number formed by the two right-hand digits is divisible by 4
40. 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.
Downward
righthand digit is 0 or 5
Commutative Law of Multiplication
addition
41. 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.
subtraction
Commutative Law of Addition
Downward
Composite Number
42. 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
algebraic number
Absolute value and argument
16(5+R)
Numerals
43. Integers greater than zero and less than 5 form a set - as follows:
Associative Law of Addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The multiplication of two complex numbers is defined by the following formula:
a complex number is real if and only if it equals its conjugate.
44. 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.
The numbers are conventionally plotted using the real part
Associative Law of Addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
coefficient
45. 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.
Set
quadratic field
base-ten number
polynomial
46. LAWS FOR COMBINING NUMBERS
righthand digit is 0 or 5
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Odd Number
addition
47. 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.
addition
Forth Axiom of Equality
Composite Number
48. Any number that is not a multiple of 2 is an
even and the sum of its digits is divisible by 3
T+9
Odd Number
magnitude and direction
49. Total
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
monomial
50. 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.
upward
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Second Axiom of Equality
subtraction
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