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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. Has an equal sign (3x+5 = 14)
consecutive whole numbers
equation
Forth Axiom of Equality
positive
2. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
3. 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.
Factor of the given number
variable
K+6 - K+5 - K+4 K+3.........answer is K+3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
4. Less than
monomial
Third Axiom of Equality
subtraction
Even Number
5. 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 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}
the number formed by the two right-hand digits is divisible by 4
In Diophantine geometry
6. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Commutative Law of Addition
coefficient
repeated elements
7. A number that has no factors except itself and 1 is a
Prime Number
negative
a complex number is real if and only if it equals its conjugate.
Digits
8. The Arabic numerals from 0 through 9 are called
Factor of the given number
The numbers are conventionally plotted using the real part
Digits
The real number a of the complex number z = a + bi
9. No short method has been found for determining whether a number is divisible by
Forth Axiom of Equality
base-ten number
7
Factor of the given number
10. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
C or
solutions
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Inversive geometry
11. 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
negative
upward
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
In Diophantine geometry
12. Any number that is not a multiple of 2 is an
Odd Number
(x-12)/40
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).
Algebraic number theory
13. Sixteen less than number Q
Q-16
Prime Number
Equal
the sum of its digits is divisible by 9
14. The place value which corresponds to a given position in a number is determined by the
Complex numbers
Members of Elements of the Set
polynomial
Base of the number system
15. 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.
the number formed by the three right-hand digits is divisible by 8
Commutative Law of Addition
(x-12)/40
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).
16. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Definition of genus
even and the sum of its digits is divisible by 3
Associative Law of Addition
repeated elements
17. Sum
polynomial
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Downward
18. The defining characteristic of a position vector is that it has
Absolute value and argument
magnitude and direction
C or
Analytic number theory
19. Subtraction
difference
Numerals
multiplication
Inversive geometry
20. 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.
Second Axiom of Equality
Associative Law of Multiplication
right-hand digit is even
21. 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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
algebraic number
Multiple of the given number
expression
22. 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.
Complex numbers
Downward
Forth Axiom of Equality
the sum of its digits is divisible by 9
23. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Definition of genus
Equal
right-hand digit is even
24. Does not have an equal sign (3x+5) (2a+9b)
The real number a of the complex number z = a + bi
(x-12)/40
expression
K+6 - K+5 - K+4 K+3.........answer is K+3
25. 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
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
counterclockwise through 90
addition
26. Any number that is exactly divisible by a given number is a
Natural Numbers
Analytic number theory
7
Multiple of the given number
27. The relative greatness of positive and negative numbers
K+6 - K+5 - K+4 K+3.........answer is K+3
Distributive Law
equation
magnitude
28. 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.
16(5+R)
Commutative Law of Multiplication
Second Axiom of Equality
In Diophantine geometry
29. 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:
constant
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).
a curve - a surface or some other such object in n-dimensional space
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.
30. LAWS FOR COMBINING NUMBERS
magnitude
(x-12)/40
repeated elements
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
31. Integers greater than zero and less than 5 form a set - as follows:
expression
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
order of operations
Place Value Concept
32. Plus
addition
monomial
C or
complex number
33. Remainder
the number formed by the three right-hand digits is divisible by 8
subtraction
the genus of the curve
righthand digit is 0 or 5
34. A letter tat represents a number that is unknown (usually X or Y)
the number formed by the two right-hand digits is divisible by 4
the genus of the curve
division
variable
35. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Set
right-hand digit is even
polynomial
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
36. More than one term (5x+4 contains two)
polynomial
Absolute value and argument
subtraction
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
37. 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
rectangular coordinates
7
The multiplication of two complex numbers is defined by the following formula:
consecutive whole numbers
38. Number T increased by 9
variable
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).
T+9
C or
39. 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
constant
Number fields
a complex number is real if and only if it equals its conjugate.
Positional notation (place value)
40. Decreased by
The numbers are conventionally plotted using the real part
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
7
subtraction
41. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Complex numbers
addition
In Diophantine geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
42. The central problem of Diophantine geometry is to determine when a Diophantine equation has
counterclockwise through 90
base-ten number
addition
solutions
43. A number is divisible by 9 if
righthand digit is 0 or 5
In Diophantine geometry
Associative Law of Addition
the sum of its digits is divisible by 9
44. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
Second Axiom of Equality
Commutative Law of Multiplication
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
45. The number without a variable (5m+2). In this case - 2
7
constant
Downward
Natural Numbers
46. Quotient
the number formed by the two right-hand digits is divisible by 4
division
Commutative Law of Addition
Complex numbers
47. 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
righthand digit is 0 or 5
To separate a number into prime factors
Digits
negative
48. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
coefficient
Commutative Law of Addition
Associative Law of Addition
49. The number touching the variable (in the case of 5x - would be 5)
C or
solutions
monomial
coefficient
50. 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
Place Value Concept
variable
The multiplication of two complex numbers is defined by the following formula:
difference