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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 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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
7
base-ten number
2. Quotient
its the sum of its digits is divisible by 3
Associative Law of Addition
division
an equation in two variables defines
3. 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.
quadratic field
consecutive whole numbers
the number formed by the three right-hand digits is divisible by 8
solutions
4. 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:
expression
K+6 - K+5 - K+4 K+3.........answer is K+3
(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).
5. 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.
Commutative Law of Addition
Second Axiom of Equality
Complex numbers
Base of the number system
6. The real and imaginary parts of a complex number can be extracted using the conjugate:
Digits
Place Value Concept
algebraic number
a complex number is real if and only if it equals its conjugate.
7. 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
Braces
In Diophantine geometry
(x-12)/40
subtraction
8. Number symbols
division
Numerals
Complex numbers
16(5+R)
9. A number is divisible by 4 if
positive
(x-12)/40
the number formed by the two right-hand digits is divisible by 4
addition
10. Less than
Natural Numbers
subtraction
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.
11. The defining characteristic of a position vector is that it has
subtraction
magnitude and direction
coefficient
addition
12. Any number that la a multiple of 2 is an
Distributive Law
positive
Even Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
13. Any number that can be divided lnto a given number without a remainder is a
Multiple of the given number
Factor of the given number
C or
Associative Law of Addition
14. The finiteness or not of the number of rational or integer points on an algebraic curve
addition
the genus of the curve
Algebraic number theory
Commutative Law of Addition
15. The numbers which are used for counting in our number system are sometimes called
an equation in two variables defines
Multiple of the given number
Associative Law of Multiplication
Natural Numbers
16. 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 -
Place Value Concept
monomial
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
equation
17. The number without a variable (5m+2). In this case - 2
Members of Elements of the Set
Factor of the given number
C or
constant
18. Decreased by
a curve - a surface or some other such object in n-dimensional space
7
subtraction
its the sum of its digits is divisible by 3
19. The greatest of 3 consecutive whole numbers - the smallest of which is F
Inversive geometry
F - F+1 - F+2.......answer is F+2
Positional notation (place value)
Place Value Concept
20. A number that has no factors except itself and 1 is a
Members of Elements of the Set
multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Prime Number
21. One term (5x or 4)
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
monomial
the sum of its digits is divisible by 9
addition
22. 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
7
Absolute value and argument
The multiplication of two complex numbers is defined by the following formula:
Inversive geometry
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
Definition of genus
addition
coefficient
Equal
24. Integers greater than zero and less than 5 form a set - as follows:
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.
a complex number is real if and only if it equals its conjugate.
Commutative Law of Addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
25. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
quadratic field
order of operations
F - F+1 - F+2.......answer is F+2
Multiple of the given number
26. Any number that is not a multiple of 2 is an
Odd Number
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).
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.
27. LAWS FOR COMBINING NUMBERS
Prime Number
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
K+6 - K+5 - K+4 K+3.........answer is K+3
28. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Associative Law of Addition
counterclockwise through 90
repeated elements
Distributive Law
29. No short method has been found for determining whether a number is divisible by
Even Number
Second Axiom of Equality
7
K+6 - K+5 - K+4 K+3.........answer is K+3
30. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Factor of the given number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
difference
31. 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.
T+9
Numerals
Forth Axiom of Equality
In Diophantine geometry
32. Are used to indicate sets
Braces
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
difference
division
33. 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
Third Axiom of Equality
addition
The real number a of the complex number z = a + bi
Commutative Law of Multiplication
34. Remainder
subtraction
negative
difference
In Diophantine geometry
35. 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.
order of operations
Prime Number
Definition of genus
Associative Law of Addition
36. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Composite Number
positive
Base of the number system
Inversive geometry
37. A number is divisible by 6 if it is
In Diophantine geometry
consecutive whole numbers
In Diophantine geometry
even and the sum of its digits is divisible by 3
38. The Arabic numerals from 0 through 9 are called
addition
In Diophantine geometry
order of operations
Digits
39. More than one term (5x+4 contains two)
polynomial
Third Axiom of Equality
Prime Number
the genus of the curve
40. A number is divisible by 2 if
righthand digit is 0 or 5
right-hand digit is even
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Associative Law of Multiplication
41. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Natural Numbers
Associative Law of Addition
division
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
42. Has an equal sign (3x+5 = 14)
Base of the number system
Commutative Law of Multiplication
subtraction
equation
43. 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.
Commutative Law of Addition
Even Number
a curve - a surface or some other such object in n-dimensional space
The numbers are conventionally plotted using the real part
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
order of operations
base-ten number
Composite Number
45. 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.
an equation in two variables defines
magnitude and direction
Braces
Associative Law of Addition
46. A letter tat represents a number that is unknown (usually X or Y)
Positional notation (place value)
variable
Downward
constructing a parallelogram
47. A number is divisible by 3 if
Absolute value and argument
its the sum of its digits is divisible by 3
base-ten number
Associative Law of Addition
48. 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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49. 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.
the sum of its digits is divisible by 9
Third Axiom of Equality
algebraic number
division
50. 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
F - F+1 - F+2.......answer is F+2
base-ten number
In Diophantine geometry
Definition of genus
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