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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. A number that has factors other than itself and 1 is a
subtraction
Composite Number
The multiplication of two complex numbers is defined by the following formula:
repeated elements
2. 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.
subtraction
algebraic number
Prime Number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
3. 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.
Commutative Law of Addition
upward
16(5+R)
Associative Law of Addition
4. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Odd Number
Even Number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
upward
5. A number that has no factors except itself and 1 is a
Factor of the given number
Number fields
Prime Number
In Diophantine geometry
6. Does not have an equal sign (3x+5) (2a+9b)
The numbers are conventionally plotted using the real part
expression
the number formed by the three right-hand digits is divisible by 8
multiplication
7. Subtraction
Commutative Law of Multiplication
subtraction
difference
(x-12)/40
8. The finiteness or not of the number of rational or integer points on an algebraic curve
In Diophantine geometry
multiplication
the genus of the curve
counterclockwise through 90
9. 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
In Diophantine geometry
division
its the sum of its digits is divisible by 3
Equal
10. The real and imaginary parts of a complex number can be extracted using the conjugate:
Forth Axiom of Equality
Numerals
rectangular coordinates
a complex number is real if and only if it equals its conjugate.
11. The defining characteristic of a position vector is that it has
T+9
Associative Law of Addition
magnitude and direction
The real number a of the complex number z = a + bi
12. 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.
a curve - a surface or some other such object in n-dimensional space
Q-16
Definition of genus
Associative Law of Multiplication
13. Number X decreased by 12 divided by forty
(x-12)/40
Numerals
subtraction
righthand digit is 0 or 5
14. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
The real number a of the complex number z = a + bi
repeated elements
constant
15. Addition of two complex numbers can be done geometrically by
Inversive geometry
the genus of the curve
righthand digit is 0 or 5
constructing a parallelogram
16. Product of 16 and the sum of 5 and number R
In Diophantine geometry
16(5+R)
right-hand digit is even
negative
17. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
constructing a parallelogram
positive
Number fields
a curve - a surface or some other such object in n-dimensional space
18. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Equal
Commutative Law of Addition
algebraic number
order of operations
19. Plus
Definition of genus
monomial
addition
Q-16
20. If a factor of a number is prime - it is called a
quadratic field
constructing a parallelogram
Prime Factor
Definition of genus
21. Studies algebraic properties and algebraic objects of interest in number theory. (Thus - analytic and algebraic number theory can and do overlap: the former is defined by its methods - the latter by its objects of study.) A key topic is that of the a
repeated elements
Distributive Law
counterclockwise through 90
Algebraic number theory
22. A number is divisible by 4 if
Q-16
coefficient
complex number
the number formed by the two right-hand digits is divisible by 4
23. An equation - or system of equations - in two or more variables defines
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
a curve - a surface or some other such object in n-dimensional space
Associative Law of Addition
quadratic field
24. 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.
7
algebraic number
Commutative Law of Addition
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
25. 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
addition
Distributive Law
Definition of genus
division
26. 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:
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).
base-ten number
Natural Numbers
addition
27. 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.
monomial
Associative Law of Addition
Number fields
the sum of its digits is divisible by 9
28. 2 -3 -4 -5 -6
consecutive whole numbers
quadratic field
addition
constructing a parallelogram
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.
Even Number
polynomial
Forth Axiom of Equality
To separate a number into prime factors
30. Increased by
addition
repeated elements
polynomial
its the sum of its digits is divisible by 3
31. More than
addition
Commutative Law of Multiplication
(x-12)/40
coefficient
32. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
repeated elements
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.
righthand digit is 0 or 5
Distributive Law
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.)
Complex numbers
division
Composite Number
Number fields
34. 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.
Base of the number system
Analytic number theory
Definition of genus
Prime Number
35. A letter tat represents a number that is unknown (usually X or Y)
T+9
variable
Prime Number
Q-16
36. 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
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
constant
base-ten 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.
37. 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.
Commutative Law of Addition
C or
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
38. 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
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.
variable
equation
39. Product
division
multiplication
subtraction
the sum of its digits is divisible by 9
40. Any number that can be divided lnto a given number without a remainder is a
Positional notation (place value)
polynomial
The multiplication of two complex numbers is defined by the following formula:
Factor of the given number
41. Total
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Second Axiom of Equality
the genus of the curve
42. The relative greatness of positive and negative numbers
magnitude
polynomial
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
43. A number is divisible by 9 if
righthand digit is 0 or 5
the sum of its digits is divisible by 9
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.
44. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
negative
rectangular coordinates
subtraction
Absolute value and argument
45. Has an equal sign (3x+5 = 14)
Inversive geometry
equation
polynomial
Forth Axiom of Equality
46. 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.
Second Axiom of Equality
base-ten number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
its the sum of its digits is divisible by 3
47. 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.
Third Axiom of Equality
consecutive whole numbers
The real number a of the complex number z = a + bi
a complex number is real if and only if it equals its conjugate.
48. A number is divisible by 3 if
magnitude
multiplication
its the sum of its digits is divisible by 3
order of operations
49. A number is divisible by 5 if its
righthand digit is 0 or 5
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Third 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).
50. Sum
To separate a number into prime factors
repeated elements
addition
T+9