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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. If a factor of a number is prime - it is called a
Members of Elements of the Set
rectangular coordinates
Second Axiom of Equality
Prime Factor
2. The Arabic numerals from 0 through 9 are called
Second Axiom of Equality
base-ten number
Digits
addition
3. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Odd Number
Complex numbers
addition
4. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
an equation in two variables defines
magnitude
a curve - a surface or some other such object in n-dimensional space
5. A form of coding in which the value of each digit of a number depends upon its position in relation to the other digits of the number. The convention used in our number system is that each digit has a higher place value than those digits to the right
Positional notation (place value)
Analytic number theory
Complex numbers
algebraic number
6. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
expression
16(5+R)
Factor of the given number
positive
7. 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).
7
T+9
difference
8. Implies a collection or grouping of similar - objects or symbols.
subtraction
Prime Factor
Set
Composite Number
9. Quotient
Commutative Law of Multiplication
Set
division
magnitude
10. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
quadratic field
Associative Law of Addition
Inversive geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
11. A number that has factors other than itself and 1 is a
magnitude
addition
Place Value Concept
Composite Number
12. Product of 16 and the sum of 5 and number R
Prime Number
multiplication
repeated elements
16(5+R)
13. 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
Base of the number system
Definition of genus
Odd Number
Positional notation (place value)
14. 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.
Associative Law of Addition
quadratic field
Composite Number
an equation in two variables defines
15. Does not have an equal sign (3x+5) (2a+9b)
magnitude and direction
expression
Q-16
the number formed by the two right-hand digits is divisible by 4
16. As shown earlier - c - di is the complex conjugate of the denominator c + di.
division
subtraction
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
17. 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
T+9
Algebraic number theory
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.
Downward
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.
Associative Law of Multiplication
expression
Commutative Law of Addition
algebraic number
19. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
the genus of the curve
multiplication
constant
20. Any number that la a multiple of 2 is an
Even Number
Natural Numbers
Base of the number system
complex number
21. 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.
Set
The numbers are conventionally plotted using the real part
quadratic field
polynomial
22. 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
Equal
7
Factor of the given number
constructing a parallelogram
23. Product
Downward
Positional notation (place value)
multiplication
The numbers are conventionally plotted using the real part
24. Total
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
addition
Factor of the given number
25. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
subtraction
addition
Number fields
26. A curve in the plane
a complex number is real if and only if it equals its conjugate.
an equation in two variables defines
(x-12)/40
polynomial
27. 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.
constructing a parallelogram
In Diophantine geometry
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
a complex number is real if and only if it equals its conjugate.
28. LAWS FOR COMBINING NUMBERS
the number formed by the two right-hand digits is divisible by 4
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
magnitude and direction
29. A number is divisible by 5 if its
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
righthand digit is 0 or 5
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).
Analytic number theory
30. An equation - or system of equations - in two or more variables defines
Prime Number
division
even and the sum of its digits is divisible by 3
a curve - a surface or some other such object in n-dimensional space
31. The real and imaginary parts of a complex number can be extracted using the conjugate:
division
multiplication
Commutative Law of Multiplication
a complex number is real if and only if it equals its conjugate.
32. A number is divisible by 9 if
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.
a curve - a surface or some other such object in n-dimensional space
addition
33. Decreased by
subtraction
repeated elements
Prime Factor
magnitude
34. 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
The multiplication of two complex numbers is defined by the following formula:
The real number a of the complex number z = a + bi
subtraction
(x-12)/40
35. 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
Q-16
Members of Elements of the Set
In Diophantine geometry
rectangular coordinates
36. Increased by
variable
addition
Complex numbers
the sum of its digits is divisible by 9
37. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Associative Law of Addition
righthand digit is 0 or 5
counterclockwise through 90
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
38. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Commutative Law of Multiplication
rectangular coordinates
difference
counterclockwise through 90
39. 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.
Commutative Law of Addition
Members of Elements of the Set
constructing a parallelogram
expression
40. Plus
Downward
its the sum of its digits is divisible by 3
solutions
addition
41. 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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42. 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
Associative Law of Addition
subtraction
monomial
base-ten number
43. 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.
magnitude and direction
Second Axiom of Equality
Digits
Even Number
44. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
(x-12)/40
Distributive Law
addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
45. The number touching the variable (in the case of 5x - would be 5)
coefficient
Associative Law of Addition
Commutative Law of Multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
46. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Forth Axiom of Equality
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
repeated elements
Factor of the given number
47. A number is divisible by 3 if
In Diophantine geometry
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).
Second Axiom of Equality
its the sum of its digits is divisible by 3
48. One term (5x or 4)
Commutative Law of Addition
monomial
multiplication
subtraction
49. Any number that can be divided lnto a given number without a remainder is a
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Commutative Law of Multiplication
Factor of the given number
16(5+R)
50. 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.
magnitude and direction
Forth Axiom of Equality
Associative Law of Addition
the genus of the curve