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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 numbers which are used for counting in our number system are sometimes called
Natural Numbers
coefficient
righthand digit is 0 or 5
algebraic number
2. A number that has factors other than itself and 1 is a
F - F+1 - F+2.......answer is F+2
Composite Number
Commutative Law of Addition
its the sum of its digits is divisible by 3
3. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Even Number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Distributive Law
Natural Numbers
4. More than one term (5x+4 contains two)
Members of Elements of the Set
polynomial
base-ten number
In Diophantine geometry
5. 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
Complex numbers
equation
subtraction
base-ten number
6. A number is divisible by 8 if
Absolute value and argument
the number formed by the three right-hand digits is divisible by 8
upward
complex number
7. A letter tat represents a number that is unknown (usually X or Y)
K+6 - K+5 - K+4 K+3.........answer is K+3
variable
rectangular coordinates
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
8. The real and imaginary parts of a complex number can be extracted using the conjugate:
base-ten number
order of operations
a complex number is real if and only if it equals its conjugate.
coefficient
9. 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
The real number a of the complex number z = a + bi
righthand digit is 0 or 5
Composite Number
10. A number is divisible by 5 if its
coefficient
righthand digit is 0 or 5
the number formed by the three right-hand digits is divisible by 8
Commutative Law of Addition
11. 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
Distributive Law
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Place Value Concept
a complex number is real if and only if it equals its conjugate.
12. Addition of two complex numbers can be done geometrically by
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 Multiplication
constructing a parallelogram
Numerals
13. 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.
even and the sum of its digits is divisible by 3
The numbers are conventionally plotted using the real part
Braces
a curve - a surface or some other such object in n-dimensional space
14. The set of all complex numbers is denoted by
addition
C or
Number fields
Third Axiom of Equality
15. 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
Composite Number
Second Axiom of Equality
Digits
16. Remainder
order of operations
consecutive whole numbers
monomial
subtraction
17. Product
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Place Value Concept
multiplication
18. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
even and the sum of its digits is divisible by 3
subtraction
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.
Associative Law of Addition
upward
Braces
algebraic number
20. 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.
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).
upward
F - F+1 - F+2.......answer is F+2
21. 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.
Second Axiom of Equality
The real number a of the complex number z = a + bi
K+6 - K+5 - K+4 K+3.........answer is K+3
Inversive geometry
22. Any number that is not a multiple of 2 is an
monomial
addition
equation
Odd Number
23. 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
Associative Law of Addition
Numerals
Definition of genus
division
24. 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
Complex numbers
algebraic number
Composite Number
the number formed by the two right-hand digits is divisible by 4
25. 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.
Inversive geometry
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Distributive Law
In Diophantine geometry
26. A number is divisible by 9 if
the sum of its digits is divisible by 9
right-hand digit is even
The numbers are conventionally plotted using the real part
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
27. Product of 16 and the sum of 5 and number R
16(5+R)
one characteristic in common such as similarity of appearance or purpose
Absolute value and argument
Complex numbers
28. 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
a curve - a surface or some other such object in n-dimensional space
consecutive whole numbers
Equal
Distributive Law
29. 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
addition
In Diophantine geometry
difference
Composite Number
30. A curve in the plane
an equation in two variables defines
subtraction
Equal
coefficient
31. First axiom of equality
Inversive geometry
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.
In Diophantine geometry
a curve - a surface or some other such object in n-dimensional space
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.
magnitude and direction
even and the sum of its digits is divisible by 3
expression
Associative Law of Addition
33. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
The multiplication of two complex numbers is defined by the following formula:
variable
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.
34. The objects in a set have at least
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).
one characteristic in common such as similarity of appearance or purpose
Associative Law of Multiplication
even and the sum of its digits is divisible by 3
35. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Downward
multiplication
the genus of the curve
repeated elements
36. Implies a collection or grouping of similar - objects or symbols.
counterclockwise through 90
Set
(x-12)/40
monomial
37. 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
Commutative Law of Addition
The real number a of the complex number z = a + bi
magnitude and direction
a complex number is real if and only if it equals its conjugate.
38. 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
Algebraic number theory
division
expression
its the sum of its digits is divisible by 3
39. The place value which corresponds to a given position in a number is determined by the
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
division
Base of the number system
an equation in two variables defines
40. A number is divisible by 2 if
the genus of the curve
magnitude and direction
right-hand digit is even
upward
41. Sixteen less than number Q
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).
Composite Number
Q-16
the number formed by the two right-hand digits is divisible by 4
42. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
the sum of its digits is divisible by 9
expression
Base of the number system
Inversive geometry
43. Subtraction
expression
difference
its the sum of its digits is divisible by 3
even and the sum of its digits is divisible by 3
44. A number that has no factors except itself and 1 is a
Prime Number
magnitude
7
16(5+R)
45. An equation - or system of equations - in two or more variables defines
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).
T+9
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
46. 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 -
solutions
rectangular coordinates
Number fields
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
47. Increased by
In Diophantine geometry
right-hand digit is even
Forth Axiom of Equality
addition
48. Less than
subtraction
Numerals
magnitude and direction
In Diophantine geometry
49. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag
righthand digit is 0 or 5
complex number
a complex number is real if and only if it equals its conjugate.
Prime Number
50. 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.
negative
Analytic number theory
subtraction
the sum of its digits is divisible by 9