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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. 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.
Associative Law of Multiplication
The multiplication of two complex numbers is defined by the following formula:
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).
quadratic field
2. If a factor of a number is prime - it is called a
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Definition of genus
repeated elements
Prime Factor
3. The number without a variable (5m+2). In this case - 2
Prime Factor
Positional notation (place value)
constant
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
4. Quotient
The numbers are conventionally plotted using the real part
a complex number is real if and only if it equals its conjugate.
T+9
division
5. More than one term (5x+4 contains two)
Associative Law of Addition
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
polynomial
6. Plus
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Multiplication
addition
counterclockwise through 90
7. An equation - or system of equations - in two or more variables defines
Braces
difference
a curve - a surface or some other such object in n-dimensional space
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
8. The greatest of 3 consecutive whole numbers - the smallest of which is F
subtraction
F - F+1 - F+2.......answer is F+2
addition
Associative Law of Addition
9. First axiom of equality
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.
Members of Elements of the Set
constant
10. Number symbols
positive
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Numerals
repeated elements
11. Product
multiplication
Downward
C or
right-hand digit is even
12. Are used to indicate sets
(x-12)/40
7
Braces
16(5+R)
13. Any number that can be divided lnto a given number without a remainder is a
Place Value Concept
Associative Law of Addition
Factor of the given number
subtraction
14. A number is divisible by 5 if its
polynomial
righthand digit is 0 or 5
even and the sum of its digits is divisible by 3
Associative Law of Addition
15. Subtraction
magnitude and direction
difference
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The multiplication of two complex numbers is defined by the following formula:
16. As shown earlier - c - di is the complex conjugate of the denominator c + di.
coefficient
In Diophantine geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
17. A curve in the plane
an equation in two variables defines
base-ten number
The real number a of the complex number z = a + bi
positive
18. Total
Place Value Concept
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
subtraction
addition
19. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
negative
repeated elements
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
variable
20. 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
Members of Elements of the Set
order of operations
multiplication
21. Number X decreased by 12 divided by forty
(x-12)/40
division
complex number
variable
22. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
monomial
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
counterclockwise through 90
Second Axiom of Equality
23. 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
the number formed by the three right-hand digits is divisible by 8
Digits
Composite Number
base-ten number
24. 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.
Prime Factor
Commutative Law of Addition
negative
T+9
25. A number is divisible by 8 if
coefficient
the number formed by the three right-hand digits is divisible by 8
Algebraic number theory
Composite Number
26. 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:
The real number a of the complex number z = a + bi
Third Axiom of Equality
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).
negative
27. 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
righthand digit is 0 or 5
Natural Numbers
addition
complex number
28. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Base of the number system
Digits
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
solutions
29. 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.
repeated elements
Commutative Law of Addition
Digits
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
30. Less than
subtraction
magnitude and direction
right-hand digit is even
In Diophantine geometry
31. The relative greatness of positive and negative numbers
upward
magnitude
rectangular coordinates
F - F+1 - F+2.......answer is F+2
32. A number is divisible by 4 if
Inversive geometry
subtraction
a curve - a surface or some other such object in n-dimensional space
the number formed by the two right-hand digits is divisible by 4
33. Addition of two complex numbers can be done geometrically by
Braces
constructing a parallelogram
rectangular coordinates
Second Axiom of Equality
34. 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.
addition
Members of Elements of the Set
constructing a parallelogram
Third Axiom of Equality
35. Any number that la a multiple of 2 is an
Even Number
subtraction
Distributive Law
the number formed by the two right-hand digits is divisible by 4
36. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
T+9
Forth Axiom of Equality
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
quadratic field
37. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
repeated elements
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.
division
Distributive Law
38. 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}
Prime Number
the sum of its digits is divisible by 9
subtraction
39. A number that has factors other than itself and 1 is a
K+6 - K+5 - K+4 K+3.........answer is K+3
Associative Law of Addition
Composite Number
Second Axiom of Equality
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.
coefficient
addition
Natural Numbers
Associative Law of Multiplication
41. Any number that is exactly divisible by a given number is a
rectangular coordinates
Multiple of the given number
Distributive Law
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.
42. Sixteen less than number Q
addition
Absolute value and argument
Q-16
Set
43. 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
Algebraic number theory
constant
a curve - a surface or some other such object in n-dimensional space
addition
44. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Commutative Law of Addition
Associative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
45. The numbers which are used for counting in our number system are sometimes called
upward
Definition of genus
Natural Numbers
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
46. 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
Factor of the given number
Absolute value and argument
algebraic number
To separate a number into prime factors
47. Any number that is not a multiple of 2 is an
Downward
Set
Odd Number
Second Axiom of Equality
48. A number that has no factors except itself and 1 is a
Factor of the given number
Prime Number
C or
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
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)
7
Base of the number system
magnitude and direction
50. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
base-ten number
rectangular coordinates
Factor of the given number
subtraction