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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 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
(x-12)/40
upward
The multiplication of two complex numbers is defined by the following formula:
subtraction
2. Plus
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.
upward
Complex numbers
addition
3. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
The multiplication of two complex numbers is defined by the following formula:
the number formed by the three right-hand digits is divisible by 8
an equation in two variables defines
4. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Set
coefficient
5. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
counterclockwise through 90
In Diophantine geometry
righthand digit is 0 or 5
6. 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
Absolute value and argument
coefficient
Multiple of the given number
(x-12)/40
7. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
16(5+R)
Base of the number system
coefficient
8. A number is divisible by 6 if it is
magnitude and direction
magnitude
even and the sum of its digits is divisible by 3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
9. 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
magnitude
complex number
repeated elements
a complex number is real if and only if it equals its conjugate.
10. 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
Forth Axiom of Equality
algebraic number
upward
one characteristic in common such as similarity of appearance or purpose
11. Product
Commutative Law of Multiplication
multiplication
addition
consecutive whole numbers
12. More than one term (5x+4 contains two)
polynomial
Inversive geometry
equation
base-ten number
13. Are used to indicate sets
Equal
addition
C or
Braces
14. 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
Positional notation (place value)
C or
Place Value Concept
15. The greatest of 3 consecutive whole numbers - the smallest of which is F
righthand digit is 0 or 5
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
F - F+1 - F+2.......answer is F+2
quadratic field
16. Subtraction
Complex numbers
To separate a number into prime factors
difference
solutions
17. Integers greater than zero and less than 5 form a set - as follows:
7
Natural Numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Place Value Concept
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.
Q-16
difference
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Equal
19. 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
Natural Numbers
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Definition of genus
20. If a factor of a number is prime - it is called a
Number fields
Prime Factor
7
Positional notation (place value)
21. 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
Place Value Concept
addition
polynomial
22. 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
Associative Law of Multiplication
The real number a of the complex number z = a + bi
Number fields
Algebraic number theory
23. Quotient
constructing a parallelogram
negative
division
Downward
24. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Complex numbers
an equation in two variables defines
complex number
25. One term (5x or 4)
monomial
Associative Law of Multiplication
Base of the number system
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
26. The number touching the variable (in the case of 5x - would be 5)
To separate a number into prime factors
coefficient
magnitude and direction
the number formed by the three right-hand digits is divisible by 8
27. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:
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).
In Diophantine geometry
Analytic number theory
monomial
28. 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.)
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
a complex number is real if and only if it equals its conjugate.
Number fields
its the sum of its digits is divisible by 3
29. The objects or symbols in a set are called Numerals - Lines - or Points
equation
Members of Elements of the Set
F - F+1 - F+2.......answer is F+2
positive
30. This law can be applied to subtraction by changing signs so that all negative signs become number signs and all signs of operation are positive.
its the sum of its digits is divisible by 3
upward
Commutative Law of Addition
coefficient
31. 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.
the sum of its digits is divisible by 9
an equation in two variables defines
Associative Law of Addition
base-ten number
32. Total
addition
the sum of its digits is divisible by 9
base-ten number
Associative Law of Multiplication
33. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Distributive Law
an equation in two variables defines
one characteristic in common such as similarity of appearance or purpose
34. 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.
Equal
Base of the number system
Second Axiom of Equality
subtraction
35. Implies a collection or grouping of similar - objects or symbols.
Set
quadratic field
constant
16(5+R)
36. A curve in the plane
counterclockwise through 90
an equation in two variables defines
righthand digit is 0 or 5
Base of the number system
37. 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
Commutative Law of Multiplication
Equal
the sum of its digits is divisible by 9
order of operations
38. Product of 16 and the sum of 5 and number R
16(5+R)
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.
Positional notation (place value)
Even Number
39. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
even and the sum of its digits is divisible by 3
Distributive Law
Absolute value and argument
C or
40. 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.
Q-16
constructing a parallelogram
Associative Law of Multiplication
Numerals
41. An equation - or system of equations - in two or more variables defines
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
a curve - a surface or some other such object in n-dimensional space
addition
42. Any number that is not a multiple of 2 is an
coefficient
Odd Number
Prime Number
magnitude
43. 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
multiplication
C or
one characteristic in common such as similarity of appearance or purpose
The real number a of the complex number z = a + bi
44. Has an equal sign (3x+5 = 14)
Natural Numbers
7
equation
subtraction
45. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
addition
counterclockwise through 90
polynomial
negative
46. Any number that la a multiple of 2 is an
equation
Downward
Even Number
repeated elements
47. A number is divisible by 9 if
subtraction
Associative Law of Addition
the sum of its digits is divisible by 9
F - F+1 - F+2.......answer is F+2
48. Number X decreased by 12 divided by forty
(x-12)/40
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
an equation in two variables defines
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
49. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Algebraic number theory
constructing a parallelogram
Braces
rectangular coordinates
50. The real and imaginary parts of a complex number can be extracted using the conjugate:
Digits
a complex number is real if and only if it equals its conjugate.
algebraic number
K+6 - K+5 - K+4 K+3.........answer is K+3