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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. Number T increased by 9
righthand digit is 0 or 5
Base of the number system
T+9
The multiplication of two complex numbers is defined by the following formula:
2. 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.
addition
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
3. A number is divisible by 4 if
righthand digit is 0 or 5
positive
the number formed by the two right-hand digits is divisible by 4
monomial
4. Quotient
division
the genus of the curve
magnitude
complex number
5. First axiom of equality
even and the sum of its digits is divisible by 3
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.
Factor of the given number
6. 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
F - F+1 - F+2.......answer is F+2
Algebraic number theory
rectangular coordinates
Associative Law of Addition
7. Product
multiplication
subtraction
Associative Law of Addition
even and the sum of its digits is divisible by 3
8. 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.
algebraic number
right-hand digit is even
Set
Third Axiom of Equality
9. 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.
Factor of the given number
Prime Number
In Diophantine geometry
10. Decreased by
Number fields
Commutative Law of Multiplication
Distributive Law
subtraction
11. Sum
a complex number is real if and only if it equals its conjugate.
Composite Number
addition
subtraction
12. 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
To separate a number into prime factors
In Diophantine geometry
division
even and the sum of its digits is divisible by 3
13. 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
expression
Equal
Place Value Concept
subtraction
14. 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
Algebraic number theory
Members of Elements of the Set
addition
15. Less than
constructing a parallelogram
Inversive geometry
subtraction
addition
16. 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.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Place Value Concept
Analytic number theory
algebraic number
17. A letter tat represents a number that is unknown (usually X or Y)
quadratic field
addition
variable
upward
18. 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.
positive
The real number a of the complex number z = a + bi
constructing a parallelogram
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
19. A curve in the plane
F - F+1 - F+2.......answer is F+2
right-hand digit is even
Equal
an equation in two variables defines
20. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
Members of Elements of the Set
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).
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
21. 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 -
Positional notation (place value)
Factor of the given number
(x-12)/40
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
22. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Braces
positive
Base of the number system
Algebraic number theory
23. Does not have an equal sign (3x+5) (2a+9b)
quadratic field
multiplication
expression
Downward
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 number formed by the three right-hand digits is divisible by 8
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Definition of genus
positive
25. Any number that is exactly divisible by a given number is a
constant
Numerals
Multiple of the given number
Commutative Law of Addition
26. Implies a collection or grouping of similar - objects or symbols.
Set
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
right-hand digit is even
variable
27. The numbers which are used for counting in our number system are sometimes called
Definition of genus
a curve - a surface or some other such object in n-dimensional space
Natural Numbers
(x-12)/40
28. The Arabic numerals from 0 through 9 are called
Digits
Natural Numbers
difference
a complex number is real if and only if it equals its conjugate.
29. A number is divisible by 2 if
subtraction
right-hand digit is even
Absolute value and argument
Second Axiom of Equality
30. 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
Natural Numbers
Commutative Law of Addition
To separate a number into prime factors
counterclockwise through 90
31. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
division
quadratic field
upward
one characteristic in common such as similarity of appearance or purpose
32. Number symbols
upward
Numerals
Algebraic number theory
Members of Elements of the Set
33. 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
complex number
Base of the number system
subtraction
34. A number is divisible by 5 if its
righthand digit is 0 or 5
expression
T+9
Commutative Law of Addition
35. The place value which corresponds to a given position in a number is determined by the
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).
right-hand digit is even
quadratic field
Base of the number system
36. More than one term (5x+4 contains two)
Number fields
polynomial
positive
a complex number is real if and only if it equals its conjugate.
37. Any number that is not a multiple of 2 is an
Commutative Law of Addition
negative
Odd Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
38. More than
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).
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
addition
Factor of the given number
39. Increased by
the number formed by the three right-hand digits is divisible by 8
addition
Associative Law of Addition
F - F+1 - F+2.......answer is F+2
40. 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.
Base of the number system
Distributive Law
Forth Axiom of Equality
Inversive geometry
41. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
The multiplication of two complex numbers is defined by the following formula:
16(5+R)
Second Axiom of Equality
42. 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.
Factor of the given number
Downward
Digits
43. The number touching the variable (in the case of 5x - would be 5)
Second Axiom of Equality
the number formed by the two right-hand digits is divisible by 4
Prime Number
coefficient
44. 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
Natural Numbers
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
45. 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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
even and the sum of its digits is divisible by 3
right-hand digit is even
Commutative Law of Multiplication
46. The number without a variable (5m+2). In this case - 2
expression
constant
Commutative Law of Multiplication
even and the sum of its digits is divisible by 3
47. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
a curve - a surface or some other such object in n-dimensional space
48. 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
base-ten number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
the number formed by the three right-hand digits is divisible by 8
coefficient
49. 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)
Set
F - F+1 - F+2.......answer is F+2
Commutative Law of Multiplication
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
addition
the number formed by the three right-hand digits is divisible by 8
F - F+1 - F+2.......answer is F+2