SUBJECTS
|
BROWSE
|
CAREER CENTER
|
POPULAR
|
JOIN
|
LOGIN
Business Skills
|
Soft Skills
|
Basic Literacy
|
Certifications
About
|
Help
|
Privacy
|
Terms
|
Email
Search
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. 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.
Base of the number system
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
solutions
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
2. Does not have an equal sign (3x+5) (2a+9b)
expression
subtraction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Even Number
3. 2 -3 -4 -5 -6
polynomial
consecutive whole numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude
4. Product
addition
a complex number is real if and only if it equals its conjugate.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
multiplication
5. 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
In Diophantine geometry
algebraic number
To separate a number into prime factors
even and the sum of its digits is divisible by 3
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.)
7
Positional notation (place value)
Number fields
constructing a parallelogram
7. Addition of two complex numbers can be done geometrically by
Prime Factor
base-ten number
constructing a parallelogram
T+9
8. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
repeated elements
(x-12)/40
rectangular coordinates
negative
9. The Arabic numerals from 0 through 9 are called
Definition of genus
Positional notation (place value)
variable
Digits
10. A number that has no factors except itself and 1 is a
Prime Number
Even Number
(x-12)/40
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
11. A number is divisible by 3 if
its 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.
Third Axiom of Equality
difference
12. If a factor of a number is prime - it is called a
quadratic field
monomial
Positional notation (place value)
Prime Factor
13. 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
Definition of genus
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Commutative Law of Addition
14. 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).
Even Number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Algebraic number theory
15. A number that has factors other than itself and 1 is a
Composite Number
monomial
Numerals
Inversive geometry
16. 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
Even Number
Set
an equation in two variables defines
17. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
the genus of the curve
In Diophantine geometry
order of operations
18. 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
F - F+1 - F+2.......answer is F+2
Definition of genus
To separate a number into prime factors
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
algebraic number
Definition of genus
Second Axiom of Equality
T+9
20. 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
addition
Absolute value and argument
16(5+R)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
21. One term (5x or 4)
monomial
Commutative Law of Addition
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).
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.
22. More than
addition
a complex number is real if and only if it equals its conjugate.
an equation in two variables defines
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
23. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
addition
counterclockwise through 90
Absolute value and argument
consecutive whole numbers
24. Sum
addition
Downward
rectangular coordinates
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
25. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
even and the sum of its digits is divisible by 3
Positional notation (place value)
Numerals
26. 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
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).
Members of Elements of the Set
To separate a number into prime factors
Place Value Concept
27. 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
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.
The real number a of the complex number z = a + bi
Commutative Law of Addition
the sum of its digits is divisible by 9
28. 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.
Commutative Law of Addition
16(5+R)
Braces
Associative Law of Multiplication
29. 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.
Downward
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.
30. The number touching the variable (in the case of 5x - would be 5)
Even Number
coefficient
addition
negative
31. The objects or symbols in a set are called Numerals - Lines - or Points
algebraic number
Members of Elements of the Set
addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
32. Product of 16 and the sum of 5 and number R
an equation in two variables defines
Associative Law of Multiplication
Prime Number
16(5+R)
33. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
constructing a parallelogram
multiplication
division
34. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
subtraction
Digits
Number fields
35. As shown earlier - c - di is the complex conjugate of the denominator c + di.
the number formed by the two right-hand digits is divisible by 4
Third Axiom of Equality
Commutative Law of Addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
36. An equation - or system of equations - in two or more variables defines
the genus of the curve
a curve - a surface or some other such object in n-dimensional space
order of operations
magnitude
37. First axiom of equality
Base of the number system
magnitude and direction
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.
one characteristic in common such as similarity of appearance or purpose
38. Quotient
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Positional notation (place value)
division
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
39. 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.
positive
difference
The numbers are conventionally plotted using the real part
Definition of genus
40. The set of all complex numbers is denoted by
C or
Distributive Law
Odd Number
algebraic number
41. A number is divisible by 9 if
Third Axiom of Equality
complex number
addition
the sum of its digits is divisible by 9
42. Remainder
Definition of genus
subtraction
Members of Elements of the Set
division
43. Sixteen less than number Q
negative
multiplication
Base of the number system
Q-16
44. Are used to indicate sets
the number formed by the three right-hand digits is divisible by 8
Numerals
subtraction
Braces
45. Increased by
a curve - a surface or some other such object in n-dimensional space
Complex numbers
even and the sum of its digits is divisible by 3
addition
46. The number without a variable (5m+2). In this case - 2
constant
Associative Law of Multiplication
addition
The numbers are conventionally plotted using the real part
47. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Digits
addition
complex number
K+6 - K+5 - K+4 K+3.........answer is K+3
48. 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
a curve - a surface or some other such object in n-dimensional space
Place Value Concept
Inversive geometry
coefficient
49. 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
Prime Factor
base-ten number
(x-12)/40
Distributive Law
50. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Equal
Factor of the given number
Inversive geometry
monomial