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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 finiteness or not of the number of rational or integer points on an algebraic curve
upward
rectangular coordinates
the genus of the curve
Q-16
2. A letter tat represents a number that is unknown (usually X or Y)
subtraction
variable
order of operations
In Diophantine geometry
3. First axiom of equality
Q-16
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
Place Value Concept
4. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Analytic number theory
an equation in two variables defines
algebraic number
counterclockwise through 90
5. The set of all complex numbers is denoted 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).
a complex number is real if and only if it equals its conjugate.
addition
C or
6. 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.)
Members of Elements of the Set
Number fields
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Equal
7. 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
addition
In Diophantine geometry
a complex number is real if and only if it equals its conjugate.
The real number a of the complex number z = a + bi
8. 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
rectangular coordinates
7
variable
9. 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.
Equal
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Braces
Third Axiom of Equality
10. The Arabic numerals from 0 through 9 are called
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.
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
Digits
11. 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.
magnitude
Definition of genus
Complex numbers
Equal
12. Quotient
division
the number formed by the three right-hand digits is divisible by 8
Natural Numbers
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
13. 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.
order of operations
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Forth Axiom of Equality
T+9
14. 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
righthand digit is 0 or 5
variable
Absolute value and argument
To separate a number into prime factors
15. Implies a collection or grouping of similar - objects or symbols.
(x-12)/40
constructing a parallelogram
To separate a number into prime factors
Set
16. 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.
addition
coefficient
The numbers are conventionally plotted using the real part
The real number a of the complex number z = a + bi
17. One term (5x or 4)
Factor of the given number
Braces
Place Value Concept
monomial
18. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Analytic number theory
order of operations
negative
19. The place value which corresponds to a given position in a number is determined by the
expression
righthand digit is 0 or 5
coefficient
Base of the number system
20. Increased by
Equal
addition
expression
order of operations
21. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
subtraction
upward
righthand digit is 0 or 5
a curve - a surface or some other such object in n-dimensional space
22. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
the number formed by the two right-hand digits is divisible by 4
addition
positive
negative
23. 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 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).
subtraction
F - F+1 - F+2.......answer is F+2
Associative Law of Multiplication
24. Less than
Members of Elements of the Set
T+9
an equation in two variables defines
subtraction
25. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
Forth Axiom of Equality
In Diophantine geometry
Numerals
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
Inversive geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
base-ten number
27. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Equal
Prime Factor
K+6 - K+5 - K+4 K+3.........answer is K+3
Distributive Law
28. The relative greatness of positive and negative numbers
magnitude
Digits
Commutative Law of Addition
Braces
29. 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.
Commutative Law of Addition
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
Absolute value and argument
30. A number is divisible by 2 if
Prime Factor
right-hand digit is even
C or
quadratic field
31. The central problem of Diophantine geometry is to determine when a Diophantine equation has
right-hand digit is even
polynomial
solutions
In Diophantine geometry
32. Total
the number formed by the two right-hand digits is divisible by 4
an equation in two variables defines
counterclockwise through 90
addition
33. 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.
K+6 - K+5 - K+4 K+3.........answer is K+3
Third Axiom of Equality
upward
algebraic number
34. 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.
variable
Braces
Complex numbers
Commutative Law of Addition
35. The real and imaginary parts of a complex number can be extracted using the conjugate:
algebraic number
the number formed by the two right-hand digits is divisible by 4
a complex number is real if and only if it equals its conjugate.
Composite Number
36. 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
Prime Factor
To separate a number into prime factors
Braces
Algebraic number theory
37. 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
coefficient
Algebraic number theory
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
addition
38. The objects in a set have at least
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
one characteristic in common such as similarity of appearance or purpose
Even Number
39. 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
Associative Law of Multiplication
upward
right-hand digit is even
40. 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
Positional notation (place value)
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Third Axiom of Equality
Equal
41. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Place Value Concept
Set
quadratic field
42. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
addition
Positional notation (place value)
Downward
addition
43. Plus
addition
(x-12)/40
K+6 - K+5 - K+4 K+3.........answer is K+3
its the sum of its digits is divisible by 3
44. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
an equation in two variables defines
upward
C or
45. As shown earlier - c - di is the complex conjugate of the denominator c + di.
repeated elements
variable
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
the genus of the curve
46. A number is divisible by 3 if
Complex numbers
Absolute value and argument
its the sum of its digits is divisible by 3
Commutative Law of Multiplication
47. More than
addition
coefficient
Members of Elements of the Set
the number formed by the three right-hand digits is divisible by 8
48. Decreased by
subtraction
T+9
Associative Law of Addition
The numbers are conventionally plotted using the real part
49. 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
Definition of genus
Second Axiom of Equality
magnitude and direction
Commutative Law of Multiplication
50. Any number that is not a multiple of 2 is an
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Odd Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
difference