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