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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. An equation - or system of equations - in two or more variables defines
Digits
Definition of genus
Braces
a curve - a surface or some other such object in n-dimensional space
2. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Prime Number
Composite Number
negative
Number fields
3. A number that has no factors except itself and 1 is a
Definition of genus
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Prime Number
4. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
consecutive whole numbers
solutions
5. 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
Number fields
Even Number
Complex numbers
Equal
6. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
Odd Number
subtraction
The real number a of the complex number z = a + bi
7. 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
Definition of genus
the number formed by the three right-hand digits is divisible by 8
magnitude
8. Plus
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
addition
constant
7
9. Implies a collection or grouping of similar - objects or symbols.
polynomial
magnitude and direction
coefficient
Set
10. No short method has been found for determining whether a number is divisible by
The real number a of the complex number z = a + bi
Prime Number
7
Number fields
11. Product of 16 and the sum of 5 and number R
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
polynomial
16(5+R)
a curve - a surface or some other such object in n-dimensional space
12. Number X decreased by 12 divided by forty
(x-12)/40
Third Axiom of Equality
Numerals
Commutative Law of Multiplication
13. 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
Inversive geometry
base-ten number
Positional notation (place value)
14. The numbers which are used for counting in our number system are sometimes called
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Absolute value and argument
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Natural Numbers
15. 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.
even and the sum of its digits is divisible by 3
Distributive Law
complex number
16. 2 -3 -4 -5 -6
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
In Diophantine geometry
counterclockwise through 90
consecutive whole numbers
17. More than one term (5x+4 contains two)
Analytic number theory
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
polynomial
Inversive geometry
18. 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.
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.
Associative Law of Multiplication
Commutative Law of Addition
the number formed by the two right-hand digits is divisible by 4
19. The place value which corresponds to a given position in a number is determined by the
Numerals
Associative Law of Addition
Base of the number system
equation
20. 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 -
Set
positive
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
21. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
constructing a parallelogram
In Diophantine geometry
order of operations
The numbers are conventionally plotted using the real part
22. The number touching the variable (in the case of 5x - would be 5)
its the sum of its digits is divisible by 3
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
coefficient
a complex number is real if and only if it equals its conjugate.
23. The set of all complex numbers is denoted by
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.
C or
Associative Law of Multiplication
subtraction
24. The number without a variable (5m+2). In this case - 2
subtraction
variable
Forth Axiom of Equality
constant
25. A number is divisible by 4 if
addition
constructing a parallelogram
upward
the number formed by the two right-hand digits is divisible by 4
26. The defining characteristic of a position vector is that it has
addition
Complex numbers
an equation in two variables defines
magnitude and direction
27. 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.
subtraction
quadratic field
algebraic number
expression
28. Does not have an equal sign (3x+5) (2a+9b)
the genus of the curve
expression
addition
negative
29. 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
algebraic number
positive
T+9
right-hand digit is even
30. Any number that is not a multiple of 2 is an
Distributive Law
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Odd Number
K+6 - K+5 - K+4 K+3.........answer is K+3
31. 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
Forth Axiom of Equality
Absolute value and argument
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Prime Factor
32. Number T increased by 9
Associative Law of Addition
constant
magnitude
T+9
33. 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.
Factor of the given number
The numbers are conventionally plotted using the real part
Q-16
the number formed by the three right-hand digits is divisible by 8
34. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Associative Law of Multiplication
Set
quadratic field
upward
35. Any number that can be divided lnto a given number without a remainder is a
subtraction
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Factor of the given number
36. 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.
Definition of genus
Place Value Concept
Prime Factor
Commutative Law of Addition
37. 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:
Set
solutions
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).
To separate a number into prime factors
38. A number is divisible by 2 if
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
counterclockwise through 90
complex number
right-hand digit is even
39. 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.
quadratic field
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
a complex number is real if and only if it equals its conjugate.
Q-16
40. Less than
complex number
Braces
subtraction
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
41. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
counterclockwise through 90
The real number a of the complex number z = a + bi
quadratic field
42. 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.
Second Axiom of Equality
an equation in two variables defines
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
43. Sixteen less than number Q
algebraic number
Composite Number
The real number a of the complex number z = a + bi
Q-16
44. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
45. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
consecutive whole numbers
Inversive geometry
order of operations
Commutative Law of Addition
46. Are used to indicate sets
Place Value Concept
In Diophantine geometry
Associative Law of Multiplication
Braces
47. Decreased by
positive
subtraction
Multiple of the given number
addition
48. Quotient
variable
consecutive whole numbers
division
Commutative Law of Multiplication
49. More than
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
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.
addition
Third Axiom of Equality
50. 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.
Associative Law of Addition
Positional notation (place value)
a complex number is real if and only if it equals its conjugate.
Analytic number theory