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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. Total
To separate a number into prime factors
(x-12)/40
Digits
addition
2. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Algebraic number theory
monomial
Q-16
Inversive geometry
3. 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.
Braces
Commutative Law of Multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
magnitude
4. 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}
To separate a number into prime factors
righthand digit is 0 or 5
polynomial
5. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
multiplication
base-ten number
T+9
6. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
even and the sum of its digits is divisible by 3
Absolute value and argument
monomial
7. Implies a collection or grouping of similar - objects or symbols.
Set
Inversive geometry
Even Number
multiplication
8. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Natural Numbers
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
one characteristic in common such as similarity of appearance or purpose
a complex number is real if and only if it equals its conjugate.
9. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
algebraic number
subtraction
The real number a of the complex number z = a + bi
10. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
the genus of the curve
To separate a number into prime factors
coefficient
11. 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 absolute value (or modulus or magnitude) of a complex number z = x + yi is
Analytic number theory
Digits
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).
12. A number is divisible by 9 if
Factor of the given number
Analytic number theory
the sum of its digits is divisible by 9
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
13. 2 -3 -4 -5 -6
consecutive whole numbers
multiplication
Multiple of the given number
expression
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
upward
Numerals
To separate a number into prime factors
15. 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 -
difference
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
the number formed by the three right-hand digits is divisible by 8
Braces
16. More than
addition
7
complex number
a curve - a surface or some other such object in n-dimensional space
17. An equation - or system of equations - in two or more variables defines
addition
Associative Law of Addition
a curve - a surface or some other such object in n-dimensional space
Downward
18. Number T increased by 9
solutions
T+9
division
constructing a parallelogram
19. A letter tat represents a number that is unknown (usually X or Y)
coefficient
upward
variable
addition
20. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
(x-12)/40
rectangular coordinates
Place Value Concept
division
21. First axiom of equality
addition
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
Absolute value and argument
22. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
addition
upward
Analytic number theory
Forth Axiom of Equality
23. 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
Place Value Concept
Complex numbers
Braces
24. If a factor of a number is prime - it is called a
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
division
Equal
Prime Factor
25. 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
The numbers are conventionally plotted using the real part
The real number a of the complex number z = a + bi
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
26. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Complex numbers
Downward
righthand digit is 0 or 5
Inversive geometry
27. 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)
Odd Number
expression
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
28. 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
the genus of the curve
complex number
In Diophantine geometry
subtraction
29. 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.
Numerals
Complex numbers
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Base of the number system
30. 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.
Second Axiom of Equality
addition
Prime Factor
consecutive whole numbers
31. 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
equation
In Diophantine geometry
To separate a number into prime factors
Base of the number system
32. A number that has no factors except itself and 1 is a
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
positive
Prime Number
Even Number
33. Has an equal sign (3x+5 = 14)
The real number a of the complex number z = a + bi
complex number
equation
variable
34. Plus
Second Axiom of Equality
Q-16
addition
Equal
35. The real and imaginary parts of a complex number can be extracted using the conjugate:
addition
Commutative Law of Addition
a complex number is real if and only if it equals its conjugate.
K+6 - K+5 - K+4 K+3.........answer is K+3
36. Product
multiplication
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula:
Definition of genus
37. Product of 16 and the sum of 5 and number R
Number fields
C or
The multiplication of two complex numbers is defined by the following formula:
16(5+R)
38. 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
complex number
Definition of genus
Absolute value and argument
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
39. Any number that is exactly divisible by a given number is a
an equation in two variables defines
Multiple of the given number
coefficient
the genus of the curve
40. 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.)
rectangular coordinates
Number fields
addition
Complex numbers
41. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Forth Axiom of Equality
Digits
Members of Elements of the Set
K+6 - K+5 - K+4 K+3.........answer is K+3
42. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Associative Law of Addition
magnitude and direction
43. Sixteen less than number Q
Q-16
polynomial
the sum of its digits is divisible by 9
Commutative Law of Multiplication
44. The set of all complex numbers is denoted by
addition
C or
Second Axiom of Equality
Algebraic number theory
45. Addition of two complex numbers can be done geometrically by
its the sum of its digits is divisible by 3
the number formed by the three right-hand digits is divisible by 8
constructing a parallelogram
Prime Factor
46. One term (5x or 4)
monomial
subtraction
one characteristic in common such as similarity of appearance or purpose
T+9
47. Less than
equation
subtraction
addition
Members of Elements of the Set
48. The number touching the variable (in the case of 5x - would be 5)
Inversive geometry
coefficient
Prime Factor
Multiple of the given number
49. A number is divisible by 5 if its
Equal
Positional notation (place value)
righthand digit is 0 or 5
Definition of genus
50. More than one term (5x+4 contains two)
positive
Braces
polynomial
subtraction