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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. 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.
Commutative Law of Addition
Associative Law of Multiplication
Odd Number
repeated elements
2. Remainder
constant
variable
subtraction
Commutative Law of Addition
3. 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
(x-12)/40
Equal
its the sum of its digits is divisible by 3
Associative Law of Multiplication
4. Sixteen less than number Q
quadratic field
Commutative Law of Addition
Q-16
righthand digit is 0 or 5
5. 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
The multiplication of two complex numbers is defined by the following formula:
Members of Elements of the Set
variable
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
Composite Number
addition
Absolute value and argument
polynomial
7. A number is divisible by 9 if
addition
rectangular coordinates
the sum of its digits is divisible by 9
magnitude and direction
8. 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.
Number fields
magnitude
quadratic field
Analytic number theory
9. Any number that la a multiple of 2 is an
Even Number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
rectangular coordinates
Set
10. Has an equal sign (3x+5 = 14)
upward
algebraic number
equation
In Diophantine geometry
11. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Positional notation (place value)
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
polynomial
12. 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.
Braces
Third Axiom of Equality
solutions
Commutative Law of Addition
13. No short method has been found for determining whether a number is divisible by
Third Axiom of Equality
Base of the number system
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
7
14. Product
multiplication
addition
Number fields
Associative Law of Addition
15. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
quadratic field
expression
monomial
16. Less than
subtraction
constant
Q-16
Commutative Law of Addition
17. If a factor of a number is prime - it is called a
Digits
division
counterclockwise through 90
Prime Factor
18. The greatest of 3 consecutive whole numbers - the smallest of which is F
Inversive geometry
F - F+1 - F+2.......answer is F+2
the number formed by the three right-hand digits is divisible by 8
monomial
19. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Base of the number system
Inversive geometry
Number fields
repeated elements
20. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
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.
algebraic number
21. 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.
positive
magnitude
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Digits
22. LAWS FOR COMBINING NUMBERS
Even Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Digits
Multiple of the given number
23. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
difference
16(5+R)
Downward
the number formed by the three right-hand digits is divisible by 8
24. A number that has factors other than itself and 1 is a
rectangular coordinates
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
16(5+R)
Composite Number
25. 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
Factor of the given number
even and the sum of its digits is divisible by 3
Digits
base-ten number
26. Does not have an equal sign (3x+5) (2a+9b)
Members of Elements of the Set
expression
addition
repeated elements
27. 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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28. Addition of two complex numbers can be done geometrically by
Downward
constant
Factor of the given number
constructing a parallelogram
29. Any number that can be divided lnto a given number without a remainder is a
algebraic number
Factor of the given number
quadratic field
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).
30. 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
subtraction
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
In Diophantine geometry
31. One term (5x or 4)
Distributive Law
Third Axiom of Equality
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
monomial
32. 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
To separate a number into prime factors
Definition of genus
magnitude and direction
K+6 - K+5 - K+4 K+3.........answer is K+3
33. Subtraction
difference
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Base of the number system
Natural Numbers
34. 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.
Equal
the sum of its digits is divisible by 9
Second Axiom of Equality
its the sum of its digits is divisible by 3
35. The finiteness or not of the number of rational or integer points on an algebraic curve
complex number
order of operations
the genus of the curve
magnitude
36. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Numerals
a curve - a surface or some other such object in n-dimensional space
Multiple of the given number
counterclockwise through 90
37. 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.
F - F+1 - F+2.......answer is F+2
complex number
difference
Associative Law of Addition
38. A number that has no factors except itself and 1 is a
Prime Number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
difference
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
39. 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
consecutive whole numbers
Positional notation (place value)
constant
40. The place value which corresponds to a given position in a number is determined by the
the genus of the curve
subtraction
Base of the number system
Multiple of the given number
41. 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:
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
order of operations
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
42. 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
Odd Number
magnitude
To separate a number into prime factors
43. Quotient
Base of the number system
division
counterclockwise through 90
magnitude
44. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
negative
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
its the sum of its digits is divisible by 3
Definition of genus
45. 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.
Composite Number
Forth Axiom of Equality
Third Axiom of Equality
addition
46. 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.
Digits
(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).
Complex numbers
47. Product of 16 and the sum of 5 and number R
equation
subtraction
magnitude
16(5+R)
48. A curve in the plane
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
an equation in two variables defines
Prime Factor
quadratic field
49. A number is divisible by 6 if it is
Third Axiom of Equality
even and the sum of its digits is divisible by 3
expression
16(5+R)
50. Number X decreased by 12 divided by forty
Second Axiom of Equality
(x-12)/40
Factor of the given number
counterclockwise through 90