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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.
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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. The Arabic numerals from 0 through 9 are called
difference
Distributive Law
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Digits
2. 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}
order of operations
Associative Law of Addition
negative
3. Implies a collection or grouping of similar - objects or symbols.
Absolute value and argument
righthand digit is 0 or 5
one characteristic in common such as similarity of appearance or purpose
Set
4. A number is divisible by 2 if
right-hand digit is even
subtraction
its the sum of its digits is divisible by 3
Analytic number theory
5. A number is divisible by 9 if
K+6 - K+5 - K+4 K+3.........answer is K+3
a curve - a surface or some other such object in n-dimensional space
the sum of its digits is divisible by 9
positive
6. 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
Base of the number system
Multiple of the given number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Absolute value and argument
7. 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
subtraction
Associative Law of Addition
8. A number that has factors other than itself and 1 is a
constructing a parallelogram
the genus of the curve
Composite Number
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.
9. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
the number formed by the two right-hand digits is divisible by 4
constructing a parallelogram
The real number a of the complex number z = a + bi
Distributive Law
10. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
positive
Numerals
negative
magnitude and direction
11. 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.
Forth Axiom of Equality
Distributive Law
Associative Law of Addition
quadratic field
12. 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
polynomial
variable
complex number
subtraction
13. More than
one characteristic in common such as similarity of appearance or purpose
(x-12)/40
addition
Place Value Concept
14. A letter tat represents a number that is unknown (usually X or Y)
variable
Associative Law of Multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
T+9
15. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
solutions
polynomial
repeated elements
16. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
The numbers are conventionally plotted using the real part
a curve - a surface or some other such object in n-dimensional space
rectangular coordinates
16(5+R)
17. Any number that is not a multiple of 2 is an
Odd Number
upward
consecutive whole numbers
Numerals
18. The numbers which are used for counting in our number system are sometimes called
addition
The real number a of the complex number z = a + bi
Natural Numbers
Place Value Concept
19. 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:
constant
Even Number
addition
20. 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
division
rectangular coordinates
To separate a number into prime factors
In Diophantine geometry
21. Number T increased by 9
Second Axiom of Equality
variable
Number fields
T+9
22. The real and imaginary parts of a complex number can be extracted using the conjugate:
quadratic field
negative
a complex number is real if and only if it equals its conjugate.
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).
23. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Associative Law of Multiplication
Complex numbers
negative
24. 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
subtraction
Place Value Concept
Numerals
25. Total
polynomial
division
addition
Multiple of the given number
26. Any number that can be divided lnto a given number without a remainder is a
Prime Number
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Factor of the given number
27. The place value which corresponds to a given position in a number is determined by the
Base of the number system
division
Digits
addition
28. 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.
Third Axiom of Equality
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).
even and the sum of its digits is divisible by 3
subtraction
29. 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
the number formed by the three right-hand digits is divisible by 8
the number formed by the two right-hand digits is divisible by 4
Analytic number theory
30. Has an equal sign (3x+5 = 14)
equation
constant
Algebraic number theory
Commutative Law of Multiplication
31. Remainder
subtraction
magnitude
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
an equation in two variables defines
32. 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)
addition
expression
(x-12)/40
33. Does not have an equal sign (3x+5) (2a+9b)
expression
magnitude
Associative Law of Addition
subtraction
34. Subtraction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
difference
a complex number is real if and only if it equals its conjugate.
Third Axiom of Equality
35. 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
Equal
even and the sum of its digits is divisible by 3
Complex numbers
36. A number that has no factors except itself and 1 is a
addition
Factor of the given number
Prime Number
Members of Elements of the Set
37. A number is divisible by 6 if it is
Associative Law of Addition
positive
addition
even and the sum of its digits is divisible by 3
38. The objects or symbols in a set are called Numerals - Lines - or Points
Number fields
T+9
Members of Elements of the Set
quadratic field
39. 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
Prime Factor
Algebraic number theory
constructing a parallelogram
subtraction
40. Product of 16 and the sum of 5 and number R
its the sum of its digits is divisible by 3
Associative Law of Addition
16(5+R)
expression
41. The number without a variable (5m+2). In this case - 2
solutions
Prime Factor
constant
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
42. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
quadratic field
repeated elements
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
43. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
16(5+R)
Commutative Law of Addition
division
positive
44. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
repeated elements
Number fields
counterclockwise through 90
45. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Commutative Law of Multiplication
order of operations
Prime Factor
46. 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
(x-12)/40
Downward
The real number a of the complex number z = a + bi
multiplication
47. Decreased by
Third Axiom of Equality
subtraction
the sum of its digits is divisible by 9
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.
48. 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
coefficient
Number fields
algebraic number
equation
49. 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
expression
T+9
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Place Value Concept
50. Any number that is exactly divisible by a given number is a
monomial
complex number
equation
Multiple of the given number
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