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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. Decreased by
subtraction
The real number a of the complex number z = a + bi
consecutive whole numbers
division
2. 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
In Diophantine geometry
addition
T+9
Base of the number system
3. 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:
Digits
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Forth 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).
4. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
subtraction
repeated elements
Natural Numbers
5. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
repeated elements
base-ten number
complex number
6. The place value which corresponds to a given position in a number is determined by the
Associative Law of Addition
The numbers are conventionally plotted using the real part
In Diophantine geometry
Base of the number system
7. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
the sum of its digits is divisible by 9
Forth Axiom of Equality
an equation in two variables defines
8. The objects in a set have at least
Prime Number
constant
one characteristic in common such as similarity of appearance or purpose
Factor of the given number
9. Total
addition
Multiple of the given number
Positional notation (place value)
Composite Number
10. Remainder
subtraction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Odd Number
Algebraic number theory
11. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
The numbers are conventionally plotted using the real part
addition
Distributive Law
12. The Arabic numerals from 0 through 9 are called
Digits
addition
right-hand digit is even
Braces
13. Implies a collection or grouping of similar - objects or symbols.
(x-12)/40
Commutative Law of Addition
Set
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
14. One term (5x or 4)
addition
algebraic number
(x-12)/40
monomial
15. The number without a variable (5m+2). In this case - 2
constant
addition
a complex number is real if and only if it equals its conjugate.
subtraction
16. 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
Inversive geometry
Natural Numbers
To separate a number into prime factors
In Diophantine geometry
17. The set of all complex numbers is denoted by
Members of Elements of the Set
C or
subtraction
the number formed by the three right-hand digits is divisible by 8
18. A curve in the plane
F - F+1 - F+2.......answer is F+2
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
an equation in two variables defines
a curve - a surface or some other such object in n-dimensional space
19. A number is divisible by 9 if
Associative Law of Addition
Q-16
the sum of its digits is divisible by 9
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
20. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Commutative Law of Multiplication
K+6 - K+5 - K+4 K+3.........answer is K+3
positive
Second Axiom of Equality
21. The number touching the variable (in the case of 5x - would be 5)
coefficient
repeated elements
Associative Law of Multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
22. Number symbols
a curve - a surface or some other such object in n-dimensional space
Definition of genus
Numerals
one characteristic in common such as similarity of appearance or purpose
23. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
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.
Commutative Law of Addition
Distributive Law
To separate a number into prime factors
24. Any number that la a multiple of 2 is an
Third Axiom of Equality
addition
Even Number
(x-12)/40
25. More than one term (5x+4 contains two)
In Diophantine geometry
polynomial
addition
difference
26. 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
The multiplication of two complex numbers is defined by the following formula:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
Definition of genus
27. Product
Equal
multiplication
the number formed by the two right-hand digits is divisible by 4
Set
28. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
(x-12)/40
Third Axiom of Equality
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
29. 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
C or
Commutative Law of Multiplication
an equation in two variables defines
30. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
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
Inversive geometry
addition
31. A number is divisible by 4 if
K+6 - K+5 - K+4 K+3.........answer is K+3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
polynomial
the number formed by the two right-hand digits is divisible by 4
32. If the same quantity is subtracted from each of two equal quantities - the resulting quantities are equal. If equals are subtracted from equals - the results are equal.
Members of Elements of the Set
Second Axiom of Equality
Distributive Law
Multiple of the given number
33. 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.)
Downward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Number fields
addition
34. 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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35. Number T increased by 9
Third Axiom of Equality
righthand digit is 0 or 5
the number formed by the two right-hand digits is divisible by 4
T+9
36. 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
Definition of genus
addition
polynomial
The real number a of the complex number z = a + bi
37. 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.
Associative Law of Addition
The real number a of the complex number z = a + bi
Place Value Concept
Commutative Law of Addition
38. Addition of two complex numbers can be done geometrically by
Members of Elements of the Set
To separate a number into prime factors
constructing a parallelogram
solutions
39. 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
The numbers are conventionally plotted using the real part
order of operations
40. 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.
Positional notation (place value)
Definition of genus
division
Commutative Law of Multiplication
41. Does not have an equal sign (3x+5) (2a+9b)
complex number
C or
expression
Prime Factor
42. A number that has no factors except itself and 1 is a
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Factor of the given number
Prime Number
magnitude and direction
43. 2 -3 -4 -5 -6
Commutative Law of Addition
rectangular coordinates
consecutive whole numbers
Associative Law of Multiplication
44. Are used to indicate sets
Braces
Commutative Law of Addition
subtraction
addition
45. No short method has been found for determining whether a number is divisible by
repeated elements
an equation in two variables defines
7
The real number a of the complex number z = a + bi
46. As shown earlier - c - di is the complex conjugate of the denominator c + di.
magnitude and direction
Base of the number system
Number fields
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
47. Any number that can be divided lnto a given number without a remainder is a
Forth Axiom of Equality
Factor of the given number
Multiple of the given number
Complex numbers
48. The relative greatness of positive and negative numbers
magnitude
The multiplication of two complex numbers is defined by the following formula:
Multiple of the given number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
49. 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
Distributive Law
Absolute value and argument
addition
base-ten number
50. 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.
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.
difference
its the sum of its digits is divisible by 3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.