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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. 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.
Composite Number
Third Axiom of Equality
Even Number
Associative Law of Addition
2. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Commutative Law of Addition
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.
7
3. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
7
subtraction
an equation in two variables defines
4. 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.
counterclockwise through 90
constructing a parallelogram
Associative Law of Multiplication
variable
5. The Arabic numerals from 0 through 9 are called
Digits
the genus of the curve
Members of Elements of the Set
monomial
6. As the horizontal component - and imaginary part as vertical These two values used to identify a given complex number are therefore called its Cartesian - rectangular - or algebraic form.
Multiple of the given number
K+6 - K+5 - K+4 K+3.........answer is K+3
The numbers are conventionally plotted using the real part
division
7. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
16(5+R)
Composite Number
8. Product of 16 and the sum of 5 and number R
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
16(5+R)
Prime Number
expression
9. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
base-ten number
algebraic number
Distributive Law
positive
10. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
The real number a of the complex number z = a + bi
counterclockwise through 90
Set
C or
11. The number without a variable (5m+2). In this case - 2
addition
Downward
constant
Number fields
12. More than one term (5x+4 contains two)
Associative Law of Addition
Numerals
polynomial
addition
13. 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)
the genus of the curve
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
14. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
T+9
righthand digit is 0 or 5
Associative Law of Addition
15. The set of all complex numbers is denoted by
magnitude
Analytic number theory
Base of the number system
C or
16. 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 real number a of the complex number z = a + bi
coefficient
base-ten number
subtraction
17. Decreased by
Associative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
subtraction
polynomial
18. The defining characteristic of a position vector is that it has
Even Number
magnitude and direction
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Set
19. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
quadratic field
Associative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
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.
20. Number symbols
Even Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Numerals
F - F+1 - F+2.......answer is F+2
21. The real and imaginary parts of a complex number can be extracted using the conjugate:
C or
Inversive geometry
a complex number is real if and only if it equals its conjugate.
Positional notation (place value)
22. 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.
C or
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
constant
Composite Number
23. 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 -
F - F+1 - F+2.......answer is F+2
The multiplication of two complex numbers is defined by the following formula:
the genus of the curve
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
24. A number that has no factors except itself and 1 is a
Commutative Law of Addition
Members of Elements of the Set
Prime Number
counterclockwise through 90
25. As shown earlier - c - di is the complex conjugate of the denominator c + di.
polynomial
Inversive geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
26. The number touching the variable (in the case of 5x - would be 5)
Digits
coefficient
addition
Prime Number
27. This law states that the sum of three or more addends is the same regardless of the manner in which they are grouped. suggests association or grouping.
Associative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
variable
Natural Numbers
28. An equation - or system of equations - in two or more variables defines
the genus of the curve
a curve - a surface or some other such object in n-dimensional space
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Place Value Concept
29. Integers greater than zero and less than 5 form a set - as follows:
constructing a parallelogram
even and the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
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).
30. More than
addition
the genus of the curve
magnitude and direction
T+9
31. 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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
To separate a number into prime factors
Commutative Law of Addition
The real number a of the complex number z = a + bi
32. Increased by
Set
one characteristic in common such as similarity of appearance or purpose
addition
Even Number
33. A letter tat represents a number that is unknown (usually X or Y)
subtraction
Complex numbers
Second Axiom of Equality
variable
34. If z is a real number (i.e. - y = 0) - then r = |x|. In general - by Pythagoras' theorem - r is the distance of the point P representing the complex number z to the origin.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
even and the sum of its digits is divisible by 3
35. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
K+6 - K+5 - K+4 K+3.........answer is K+3
a complex number is real if and only if it equals its conjugate.
36. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.
subtraction
In Diophantine geometry
Analytic number theory
coefficient
37. 2 -3 -4 -5 -6
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).
The real number a of the complex number z = a + bi
consecutive whole numbers
38. A number is divisible by 6 if it is
Commutative Law of Multiplication
even and the sum of its digits is divisible by 3
Second Axiom of Equality
Equal
39. Addition of two complex numbers can be done geometrically by
addition
consecutive whole numbers
expression
constructing a parallelogram
40. 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
addition
To separate a number into prime factors
Forth Axiom of Equality
the number formed by the three right-hand digits is divisible by 8
41. 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
coefficient
Absolute value and argument
Commutative Law of Multiplication
subtraction
42. The relative greatness of positive and negative numbers
Downward
addition
Set
magnitude
43. 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.
Odd Number
Complex numbers
subtraction
Prime Number
44. No short method has been found for determining whether a number is divisible by
7
Multiple of the given number
its the sum of its digits is divisible by 3
right-hand digit is even
45. A number that has factors other than itself and 1 is a
righthand digit is 0 or 5
Composite Number
The numbers are conventionally plotted using the real part
Inversive geometry
46. 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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47. Plus
(x-12)/40
subtraction
addition
Commutative Law of Addition
48. A number is divisible by 5 if its
Numerals
Digits
righthand digit is 0 or 5
algebraic number
49. Are used to indicate sets
Multiple of the given number
magnitude and direction
Analytic number theory
Braces
50. 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
Distributive Law
addition
Equal
Digits
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