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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. Subtraction
right-hand digit is even
upward
consecutive whole numbers
difference
2. A number that has no factors except itself and 1 is a
addition
To separate a number into prime factors
Prime Number
righthand digit is 0 or 5
3. 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
Third Axiom of Equality
The real number a of the complex number z = a + bi
quadratic field
4. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
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).
F - F+1 - F+2.......answer is F+2
Equal
5. Number symbols
Numerals
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
consecutive whole numbers
6. The numbers which are used for counting in our number system are sometimes called
an equation in two variables defines
positive
Natural Numbers
repeated elements
7. Total
Braces
addition
division
one characteristic in common such as similarity of appearance or purpose
8. Does not have an equal sign (3x+5) (2a+9b)
complex number
Associative Law of Multiplication
expression
constructing a parallelogram
9. A number is divisible by 9 if
the sum of its digits is divisible by 9
Equal
Set
Commutative Law of Addition
10. The set of all complex numbers is denoted by
Factor of the given number
Odd Number
C or
magnitude and direction
11. A number is divisible by 6 if it is
a complex number is real if and only if it equals its conjugate.
righthand digit is 0 or 5
polynomial
even and the sum of its digits is divisible by 3
12. 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
Composite Number
Prime Factor
Analytic number theory
13. The Arabic numerals from 0 through 9 are called
Digits
the number formed by the three right-hand digits is divisible by 8
Absolute value and argument
Commutative Law of Addition
14. Product
multiplication
right-hand digit is even
one characteristic in common such as similarity of appearance or purpose
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.
15. 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.)
the genus of the curve
rectangular coordinates
Natural Numbers
Number fields
16. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
subtraction
repeated elements
division
17. 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.
complex number
Forth Axiom of Equality
magnitude and direction
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
18. A number is divisible by 4 if
the genus of the curve
the number formed by the two right-hand digits is divisible by 4
addition
right-hand digit is even
19. One term (5x or 4)
the number formed by the two right-hand digits is divisible by 4
Second Axiom of Equality
monomial
subtraction
20. A number is divisible by 8 if
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.
the number formed by the three right-hand digits is divisible by 8
division
21. A number is divisible by 2 if
subtraction
right-hand digit is even
The real number a of the complex number z = a + bi
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
22. Any number that is not a multiple of 2 is an
The numbers are conventionally plotted using the real part
Odd Number
quadratic field
the number formed by the three right-hand digits is divisible by 8
23. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
the number formed by the two right-hand digits is divisible by 4
counterclockwise through 90
upward
Factor of the given number
24. More than one term (5x+4 contains two)
polynomial
negative
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
variable
25. 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.
Associative Law of Multiplication
upward
Absolute value and argument
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
26. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
equation
T+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.
Inversive geometry
27. A curve in the plane
Braces
its the sum of its digits is divisible by 3
K+6 - K+5 - K+4 K+3.........answer is K+3
an equation in two variables defines
28. The central problem of Diophantine geometry is to determine when a Diophantine equation has
order of operations
Numerals
Place Value Concept
solutions
29. 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.
Factor of the given number
Forth Axiom of Equality
Digits
Multiple of the given number
30. 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
base-ten number
Multiple of the given number
Composite Number
magnitude and direction
31. Number X decreased by 12 divided by forty
Number fields
constructing a parallelogram
(x-12)/40
positive
32. Sixteen less than number Q
right-hand digit is even
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Q-16
difference
33. No short method has been found for determining whether a number is divisible by
consecutive whole numbers
7
Second Axiom of Equality
solutions
34. 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}
algebraic number
multiplication
the number formed by the two right-hand digits is divisible by 4
35. 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.
The numbers are conventionally plotted using the real part
algebraic 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.
Q-16
36. 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
Prime Number
The real number a of the complex number z = a + bi
righthand digit is 0 or 5
Commutative Law of Addition
37. 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
quadratic field
The real number a of the complex number z = a + bi
repeated elements
In Diophantine geometry
38. A letter tat represents a number that is unknown (usually X or Y)
Algebraic number theory
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
complex number
variable
39. More than
Base of the number system
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
algebraic number
40. 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
addition
counterclockwise through 90
Equal
the number formed by the two right-hand digits is divisible by 4
41. A number is divisible by 3 if
constructing a parallelogram
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
its the sum of its digits is divisible by 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.
42. Has an equal sign (3x+5 = 14)
Prime Factor
solutions
Commutative Law of Multiplication
equation
43. 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.
Associative Law of Addition
constructing a parallelogram
In Diophantine geometry
right-hand digit is even
44. 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
Place Value Concept
subtraction
16(5+R)
variable
45. Number T increased by 9
magnitude
algebraic number
Commutative Law of Addition
T+9
46. If a factor of a number is prime - it is called a
Prime Factor
Associative Law of Addition
complex number
the number formed by the three right-hand digits is divisible by 8
47. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
7
Associative Law of Multiplication
rectangular coordinates
Definition of genus
48. An equation - or system of equations - in two or more variables defines
Complex numbers
quadratic field
subtraction
a curve - a surface or some other such object in n-dimensional space
49. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Prime Number
consecutive whole numbers
upward
a curve - a surface or some other such object in n-dimensional space
50. 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
Composite Number
The real number a of the complex number z = a + bi
In Diophantine geometry
The numbers are conventionally plotted using the real part