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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. Remainder
Natural Numbers
Forth Axiom of Equality
subtraction
quadratic field
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
Q-16
Commutative Law of Multiplication
In Diophantine geometry
Absolute value and argument
3. Product of 16 and the sum of 5 and number R
16(5+R)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Composite Number
monomial
4. The set of all complex numbers is denoted by
Composite Number
difference
C or
Second Axiom of Equality
5. The relative greatness of positive and negative numbers
magnitude
magnitude and direction
polynomial
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
6. 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
expression
Third Axiom of Equality
Distributive Law
The real number a of the complex number z = a + bi
7. A number that has no factors except itself and 1 is a
Natural Numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Prime Number
Positional notation (place value)
8. Are used to indicate sets
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
In Diophantine geometry
Braces
The real number a of the complex number z = a + bi
9. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
a complex number is real if and only if it equals its conjugate.
Inversive geometry
constant
T+9
10. 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
Natural Numbers
base-ten number
Equal
C or
11. 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
magnitude and direction
one characteristic in common such as similarity of appearance or purpose
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
12. 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.
quadratic field
rectangular coordinates
The real number a of the complex number z = a + bi
Factor of the given number
13. 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.
Members of Elements of the Set
Base of the number system
Associative Law of Multiplication
complex number
14. More than
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Positional notation (place value)
addition
a curve - a surface or some other such object in n-dimensional space
15. 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
F - F+1 - F+2.......answer is F+2
Natural Numbers
subtraction
16. Subtraction
Downward
Distributive Law
difference
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
17. 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
F - F+1 - F+2.......answer is F+2
magnitude
The multiplication of two complex numbers is defined by the following formula:
Prime Number
18. The objects or symbols in a set are called Numerals - Lines - or Points
K+6 - K+5 - K+4 K+3.........answer is K+3
even and the sum of its digits is divisible by 3
Members of Elements of the Set
multiplication
19. Any number that is not a multiple of 2 is an
Odd Number
coefficient
Factor of the given number
K+6 - K+5 - K+4 K+3.........answer is K+3
20. 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 genus of the curve
complex number
Associative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
21. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
right-hand digit is even
Downward
order of operations
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
22. 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.
Second Axiom of Equality
addition
Analytic number theory
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
23. A number is divisible by 4 if
constructing a parallelogram
the number formed by the two right-hand digits is divisible by 4
Composite Number
The multiplication of two complex numbers is defined by the following formula:
24. 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
The real number a of the complex number z = a + bi
Definition of genus
Braces
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
25. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
Complex numbers
addition
Place Value Concept
26. 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
subtraction
Distributive Law
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).
27. A letter tat represents a number that is unknown (usually X or Y)
variable
even and the sum of its digits is divisible by 3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
magnitude
28. The defining characteristic of a position vector is that it has
subtraction
variable
magnitude and direction
T+9
29. Number X decreased by 12 divided by forty
variable
(x-12)/40
algebraic number
repeated elements
30. More than one term (5x+4 contains two)
counterclockwise through 90
polynomial
constructing a parallelogram
Definition of genus
31. 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.
Commutative Law of Multiplication
16(5+R)
Odd Number
equation
32. No short method has been found for determining whether a number is divisible by
7
Complex numbers
expression
Place Value Concept
33. Sum
Prime Number
addition
Braces
righthand digit is 0 or 5
34. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the genus of the curve
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Prime Factor
35. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
the sum of its digits is divisible by 9
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.
Complex numbers
36. Decreased by
subtraction
the number formed by the three right-hand digits is divisible by 8
even and the sum of its digits is divisible by 3
Members of Elements of the Set
37. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
constant
a curve - a surface or some other such object in n-dimensional space
Prime Factor
38. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
rectangular coordinates
positive
Set
Odd Number
39. 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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40. The number without a variable (5m+2). In this case - 2
difference
K+6 - K+5 - K+4 K+3.........answer is K+3
Members of Elements of the Set
constant
41. 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
complex number
solutions
variable
the number formed by the three right-hand digits is divisible by 8
42. Product
T+9
multiplication
Braces
rectangular coordinates
43. A number is divisible by 5 if its
F - F+1 - F+2.......answer is F+2
Prime Factor
Downward
righthand digit is 0 or 5
44. The Arabic numerals from 0 through 9 are called
Braces
Digits
expression
Set
45. Number symbols
base-ten number
Odd Number
Numerals
Third Axiom of Equality
46. A number that has factors other than itself and 1 is a
equation
division
Composite Number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
47. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
subtraction
coefficient
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.
repeated elements
48. Does not have an equal sign (3x+5) (2a+9b)
expression
Equal
Second Axiom of Equality
the sum of its digits is divisible by 9
49. The finiteness or not of the number of rational or integer points on an algebraic curve
Prime Factor
16(5+R)
the genus of the curve
upward
50. A number is divisible by 2 if
right-hand digit is even
Digits
coefficient
Inversive geometry