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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. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
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
base-ten number
2. The set of all complex numbers is denoted by
constructing a parallelogram
T+9
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
C or
3. First axiom of equality
algebraic 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.
variable
upward
4. Are used to indicate sets
Braces
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
multiplication
the genus of the curve
5. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
division
(x-12)/40
the number formed by the two right-hand digits is divisible by 4
rectangular coordinates
6. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Associative Law of Multiplication
algebraic number
multiplication
7. Addition of two complex numbers can be done geometrically by
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
subtraction
monomial
constructing a parallelogram
8. A number is divisible by 6 if it is
T+9
even and the sum of its digits is divisible by 3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
a curve - a surface or some other such object in n-dimensional space
9. 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
consecutive whole numbers
right-hand digit is even
Positional notation (place value)
counterclockwise through 90
10. 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
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.
right-hand digit is even
Place Value Concept
Multiple of the given number
11. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Place Value Concept
upward
Base of the number system
its the sum of its digits is divisible by 3
12. The Arabic numerals from 0 through 9 are called
Base of the number system
Distributive Law
Digits
Algebraic number theory
13. Remainder
Prime Factor
a complex number is real if and only if it equals its conjugate.
subtraction
Commutative Law of Addition
14. More than one term (5x+4 contains two)
polynomial
Associative Law of Addition
positive
16(5+R)
15. Increased by
Positional notation (place value)
Definition of genus
K+6 - K+5 - K+4 K+3.........answer is K+3
addition
16. A curve in the plane
Second Axiom of Equality
an equation in two variables defines
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
17. An equation - or system of equations - in two or more variables defines
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
a curve - a surface or some other such object in n-dimensional space
Digits
Positional notation (place value)
18. The place value which corresponds to a given position in a number is determined by the
Factor of the given number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Q-16
Base of the number system
19. More than
addition
Equal
Positional notation (place value)
a curve - a surface or some other such object in n-dimensional space
20. The central problem of Diophantine geometry is to determine when a Diophantine equation has
subtraction
Even Number
solutions
addition
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
algebraic number
Number fields
a curve - a surface or some other such object in n-dimensional space
22. 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.
Forth Axiom of Equality
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
K+6 - K+5 - K+4 K+3.........answer is K+3
In Diophantine geometry
23. Less than
subtraction
expression
Commutative Law of Multiplication
constant
24. 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.
Definition of genus
multiplication
order of operations
The numbers are conventionally plotted using the real part
25. 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
Numerals
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
26. Any number that is not a multiple of 2 is an
repeated elements
Forth Axiom of Equality
Odd Number
C or
27. 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
Even Number
K+6 - K+5 - K+4 K+3.........answer is K+3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
28. 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.
Analytic number theory
7
the number formed by the two right-hand digits is divisible by 4
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
29. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
division
positive
algebraic number
30. Any number that can be divided lnto a given number without a remainder is a
subtraction
positive
Factor of the given number
algebraic number
31. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
righthand digit is 0 or 5
Third Axiom of Equality
32. Sixteen less than number Q
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.
Q-16
positive
a curve - a surface or some other such object in n-dimensional space
33. A letter tat represents a number that is unknown (usually X or Y)
Multiple of the given number
Factor of the given number
Number fields
variable
34. A number is divisible by 8 if
The real number a of the complex number z = a + bi
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
negative
the number formed by the three right-hand digits is divisible by 8
35. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
equation
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
positive
a curve - a surface or some other such object in n-dimensional space
36. Sum
K+6 - K+5 - K+4 K+3.........answer is K+3
In Diophantine geometry
monomial
addition
37. A number that has no factors except itself and 1 is a
rectangular coordinates
the genus of the curve
Prime Number
Associative Law of Addition
38. A number is divisible by 4 if
variable
addition
polynomial
the number formed by the two right-hand digits is divisible by 4
39. 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.
Inversive geometry
algebraic number
the genus of the curve
40. Integers greater than zero and less than 5 form a set - as follows:
Prime Factor
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Braces
monomial
41. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Composite Number
upward
42. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
consecutive whole numbers
Distributive Law
Algebraic number theory
Definition of genus
43. 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:
Associative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
Inversive geometry
44. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
Commutative Law of Addition
subtraction
Prime Factor
45. 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
magnitude and direction
monomial
base-ten number
Numerals
46. The defining characteristic of a position vector is that it has
an equation in two variables defines
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
magnitude and direction
a complex number is real if and only if it equals its conjugate.
47. 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.
solutions
Braces
Absolute value and argument
quadratic field
48. Quotient
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Factor
Base of the number system
division
49. The objects or symbols in a set are called Numerals - Lines - or Points
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.
Members of Elements of the Set
its the sum of its digits is divisible by 3
division
50. 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.
Associative Law of Addition
expression
counterclockwise through 90
subtraction