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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. A letter tat represents a number that is unknown (usually X or Y)
K+6 - K+5 - K+4 K+3.........answer is K+3
a complex number is real if and only if it equals its conjugate.
variable
polynomial
2. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Commutative Law of Multiplication
Complex numbers
addition
3. Number T increased by 9
its the sum of its digits is divisible by 3
T+9
subtraction
Second Axiom of Equality
4. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Positional notation (place value)
Prime Number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
the sum of its digits is divisible by 9
5. Decreased by
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
subtraction
constant
6. Number X decreased by 12 divided by forty
equation
(x-12)/40
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
7. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Commutative Law of Multiplication
Odd Number
repeated elements
Commutative Law of Addition
8. Any number that is not a multiple of 2 is an
Odd Number
solutions
upward
Multiple of the given number
9. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
multiplication
Prime Factor
Associative Law of Addition
10. 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 real number a of the complex number z = a + bi
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Multiplication
Place Value Concept
11. The objects in a set have at least
addition
Forth Axiom of Equality
Braces
one characteristic in common such as similarity of appearance or purpose
12. The set of all complex numbers is denoted by
Q-16
upward
C or
right-hand digit is even
13. More than
Commutative Law of Addition
addition
complex number
quadratic field
14. The greatest of 3 consecutive whole numbers - the smallest of which is F
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Second Axiom of Equality
right-hand digit is even
F - F+1 - F+2.......answer is F+2
15. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
polynomial
upward
Members of Elements of the Set
negative
16. Subtraction
subtraction
difference
constant
the number formed by the three right-hand digits is divisible by 8
17. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Prime Factor
negative
magnitude and direction
the number formed by the three right-hand digits is divisible by 8
18. More than one term (5x+4 contains two)
Members of Elements of the Set
Inversive geometry
Set
polynomial
19. Does not have an equal sign (3x+5) (2a+9b)
constructing a parallelogram
counterclockwise through 90
expression
F - F+1 - F+2.......answer is F+2
20. 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
Place Value Concept
polynomial
Base of the number system
In Diophantine geometry
21. 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
7
order of operations
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
22. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
consecutive whole numbers
order of operations
Downward
Positional notation (place value)
23. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
equation
K+6 - K+5 - K+4 K+3.........answer is K+3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
24. 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
negative
Equal
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
addition
25. 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.
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.
even and the sum of its digits is divisible by 3
Equal
Commutative Law of Addition
26. Addition of two complex numbers can be done geometrically by
constructing a parallelogram
Prime Number
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
a complex number is real if and only if it equals its conjugate.
27. One term (5x or 4)
monomial
Number fields
magnitude
Associative Law of Addition
28. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
The numbers are conventionally plotted using the real part
a curve - a surface or some other such object in n-dimensional space
difference
29. Any number that is exactly divisible by a given number is a
Even Number
Multiple of the given number
Positional notation (place value)
Distributive Law
30. The number touching the variable (in the case of 5x - would be 5)
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
coefficient
complex number
Equal
31. The Arabic numerals from 0 through 9 are called
Digits
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Associative Law of Multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
32. 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.
a curve - a surface or some other such object in n-dimensional space
Associative Law of Addition
The real number a of the complex number z = a + bi
polynomial
33. A number is divisible by 9 if
the sum of its digits is divisible by 9
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.
Associative Law of Multiplication
34. Quotient
division
Algebraic number theory
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
In Diophantine geometry
35. The real and imaginary parts of a complex number can be extracted using the conjugate:
an equation in two variables defines
Commutative Law of Addition
a complex number is real if and only if it equals its conjugate.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
36. A number is divisible by 3 if
its the sum of its digits is divisible by 3
expression
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).
Distributive Law
37. 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
expression
complex number
Absolute value and argument
solutions
38. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
its the sum of its digits is divisible by 3
K+6 - K+5 - K+4 K+3.........answer is K+3
the sum of its digits is divisible by 9
39. Are used to indicate sets
coefficient
Braces
Distributive Law
The numbers are conventionally plotted using the real part
40. A number is divisible by 5 if its
righthand digit is 0 or 5
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
solutions
Third Axiom of Equality
41. 2 -3 -4 -5 -6
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.
Equal
Analytic number theory
consecutive whole numbers
42. Is a number that can be expressed in the form where a and b are real numbers and i is the imaginary unit - satisfying i2 = -1. For example - -3.5 + 2i is a complex number. It is common to write a for a + 0i and bi for 0 + bi. Moreover - when the imag
Factor of the given number
complex number
base-ten number
Downward
43. The number without a variable (5m+2). In this case - 2
constant
one characteristic in common such as similarity of appearance or purpose
polynomial
solutions
44. Less than
T+9
subtraction
F - F+1 - F+2.......answer is F+2
The multiplication of two complex numbers is defined by the following formula:
45. 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.
The multiplication of two complex numbers is defined by the following formula:
subtraction
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
expression
46. 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)
In Diophantine geometry
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
47. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
algebraic number
difference
quadratic field
48. Begin by taking out the smallest factor If the number is even - take out all the 2's first - then try 3 as a factor
Inversive geometry
To separate a number into prime factors
addition
complex number
49. 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.
solutions
Forth Axiom of Equality
To separate a number into prime factors
Factor of the given number
50. 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
Associative Law of Multiplication
The multiplication of two complex numbers is defined by the following formula:
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
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