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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. Implies a collection or grouping of similar - objects or symbols.
the sum of its digits is divisible by 9
Place Value Concept
Natural Numbers
Set
2. 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.
magnitude
Even Number
Associative Law of Addition
Composite Number
3. The objects or symbols in a set are called Numerals - Lines - or Points
Absolute value and argument
Members of Elements of the Set
Distributive Law
counterclockwise through 90
4. 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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5. Subtraction
one characteristic in common such as similarity of appearance or purpose
Digits
difference
upward
6. Total
variable
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
upward
7. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
repeated elements
constant
8. 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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Absolute value and argument
counterclockwise through 90
Equal
9. No short method has been found for determining whether a number is divisible by
quadratic field
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).
rectangular coordinates
7
10. 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.
Commutative Law of Addition
solutions
The real number a of the complex number z = a + bi
Factor of the given number
11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
addition
Equal
K+6 - K+5 - K+4 K+3.........answer is K+3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
12. 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
Natural Numbers
righthand digit is 0 or 5
To separate a number into prime factors
constructing a parallelogram
13. The number touching the variable (in the case of 5x - would be 5)
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.
equation
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).
coefficient
14. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Algebraic number theory
addition
Associative Law of Addition
15. 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
its the sum of its digits is divisible by 3
Numerals
Definition of genus
Associative Law of Addition
16. More than
Even Number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
addition
monomial
17. Sum
a curve - a surface or some other such object in n-dimensional space
addition
subtraction
Multiple of the given number
18. Any number that can be divided lnto a given number without a remainder is a
Absolute value and argument
magnitude
Factor of the given number
repeated elements
19. 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.)
To separate a number into prime factors
Definition of genus
Number fields
subtraction
20. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Second Axiom of Equality
Third Axiom of Equality
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
In Diophantine geometry
21. 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
solutions
order of operations
multiplication
22. 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 -
Prime Number
expression
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Forth Axiom of Equality
23. A number is divisible by 9 if
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
In Diophantine geometry
the sum of its digits is divisible by 9
24. A number is divisible by 4 if
positive
Positional notation (place value)
the number formed by the two right-hand digits is divisible by 4
Definition of genus
25. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
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 three right-hand digits is divisible by 8
upward
26. Number X decreased by 12 divided by forty
In Diophantine geometry
(x-12)/40
positive
the sum of its digits is divisible by 9
27. 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
Commutative Law of Addition
subtraction
Equal
The multiplication of two complex numbers is defined by the following formula:
28. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Commutative Law of Addition
the sum of its digits is divisible by 9
righthand digit is 0 or 5
Inversive geometry
29. 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
Second Axiom of Equality
complex number
Complex numbers
Even Number
30. One term (5x or 4)
Second Axiom of Equality
monomial
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).
one characteristic in common such as similarity of appearance or purpose
31. A number is divisible by 6 if it is
Commutative Law of Multiplication
Digits
difference
even and the sum of its digits is divisible by 3
32. Number symbols
Commutative Law of Multiplication
division
Numerals
monomial
33. 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
Factor of the given number
Number fields
addition
34. Any number that is not a multiple of 2 is an
Algebraic number theory
K+6 - K+5 - K+4 K+3.........answer is K+3
Odd Number
negative
35. Integers greater than zero and less than 5 form a set - as follows:
F - F+1 - F+2.......answer is F+2
equation
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
36. A curve in the plane
an equation in two variables defines
The multiplication of two complex numbers is defined by the following formula:
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
37. The numbers which are used for counting in our number system are sometimes called
one characteristic in common such as similarity of appearance or purpose
Natural Numbers
variable
the number formed by the three right-hand digits is divisible by 8
38. The relative greatness of positive and negative numbers
Digits
magnitude
magnitude and direction
Commutative Law of Addition
39. First axiom of equality
right-hand digit is even
Associative Law of 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.
Natural Numbers
40. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
the sum of its digits is divisible by 9
Commutative Law of Addition
Prime Number
Distributive Law
41. 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
its the sum of its digits is divisible by 3
the sum of its digits is divisible by 9
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
42. 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
The real number a of the complex number z = a + bi
In Diophantine geometry
Analytic number theory
Positional notation (place value)
43. 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
algebraic number
In Diophantine geometry
Commutative Law of Addition
Positional notation (place value)
44. The central problem of Diophantine geometry is to determine when a Diophantine equation has
positive
C or
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
solutions
45. 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.
16(5+R)
quadratic field
Associative Law of Addition
its the sum of its digits is divisible by 3
46. Less than
Absolute value and argument
subtraction
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).
magnitude
47. The set of all complex numbers is denoted by
multiplication
equation
C or
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).
48. The finiteness or not of the number of rational or integer points on an algebraic curve
the sum of its digits is divisible by 9
the genus of the curve
difference
right-hand digit is even
49. Product
one characteristic in common such as similarity of appearance or purpose
T+9
multiplication
addition
50. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Positional notation (place value)
Downward
consecutive whole numbers
difference