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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 is divisible by 2 if
right-hand digit is even
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
algebraic number
2. 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.)
Algebraic number theory
Distributive Law
Number fields
positive
3. 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
To separate a number into prime factors
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
negative
addition
4. If a factor of a number is prime - it is called a
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).
Prime Factor
Complex numbers
Associative Law of Addition
5. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
addition
upward
coefficient
6. A number is divisible by 9 if
subtraction
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
C or
the sum of its digits is divisible by 9
7. No short method has been found for determining whether a number is divisible by
Associative Law of Addition
7
expression
The numbers are conventionally plotted using the real part
8. As shown earlier - c - di is the complex conjugate of the denominator c + di.
counterclockwise through 90
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 real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The numbers are conventionally plotted using the real part
9. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
addition
monomial
Distributive Law
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
10. 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.
base-ten number
multiplication
variable
11. An equation - or system of equations - in two or more variables defines
rectangular coordinates
K+6 - K+5 - K+4 K+3.........answer is K+3
a curve - a surface or some other such object in n-dimensional space
the genus of the curve
12. The number of digits in an integer indicates its rank; that is - whether it is 'in the hundreds -' 'in the thousands -' etc. The idea of ranking numbers in terms of tens - hundreds - thousands - etc. - is based on the
its the sum of its digits is divisible by 3
Members of Elements of the Set
addition
Place Value Concept
13. The Arabic numerals from 0 through 9 are called
Digits
complex number
equation
rectangular coordinates
14. Sum
complex number
To separate a number into prime factors
addition
upward
15. 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.
a curve - a surface or some other such object in n-dimensional space
K+6 - K+5 - K+4 K+3.........answer is K+3
Complex numbers
The multiplication of two complex numbers is defined by the following formula:
16. Plus
Absolute value and argument
The multiplication of two complex numbers is defined by the following formula:
addition
solutions
17. This law states that the product of two or more factors is the same regardless of the order in which the factors are arranged. Negative signs require no special treatment in the application of this law.
subtraction
Odd Number
Commutative Law of Multiplication
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
18. Number symbols
upward
Numerals
rectangular coordinates
Associative Law of Addition
19. 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
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
counterclockwise through 90
Positional notation (place value)
Composite Number
20. The greatest of 3 consecutive whole numbers - the smallest of which is F
positive
one characteristic in common such as similarity of appearance or purpose
Inversive geometry
F - F+1 - F+2.......answer is F+2
21. 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
polynomial
constructing a parallelogram
righthand digit is 0 or 5
22. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
Even Number
Associative Law of Multiplication
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
23. 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 -
subtraction
Inversive geometry
counterclockwise through 90
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
24. Number X decreased by 12 divided by forty
variable
T+9
a complex number is real if and only if it equals its conjugate.
(x-12)/40
25. Has an equal sign (3x+5 = 14)
equation
addition
the number formed by the three right-hand digits is divisible by 8
Associative Law of Multiplication
26. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Definition of genus
Commutative Law of Addition
one characteristic in common such as similarity of appearance or purpose
27. The finiteness or not of the number of rational or integer points on an algebraic curve
the genus of the curve
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Third Axiom of Equality
28. Sixteen less than number Q
even and the sum of its digits is divisible by 3
Q-16
right-hand digit is even
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
29. More than one term (5x+4 contains two)
algebraic number
7
Complex numbers
polynomial
30. 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.
The numbers are conventionally plotted using the real part
order of operations
addition
subtraction
31. 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
Natural Numbers
In Diophantine geometry
the sum of its digits is divisible by 9
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
32. Any number that is exactly divisible by a given number is a
Multiple of the given number
Odd Number
Associative Law of Multiplication
variable
33. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
polynomial
Absolute value and argument
magnitude
34. The number touching the variable (in the case of 5x - would be 5)
Digits
coefficient
Associative Law of Addition
subtraction
35. LAWS FOR COMBINING NUMBERS
one characteristic in common such as similarity of appearance or purpose
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Place Value Concept
36. Decreased by
Prime Factor
Definition of genus
T+9
subtraction
37. A number that has no factors except itself and 1 is a
consecutive whole numbers
addition
Prime Number
right-hand digit is even
38. 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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39. Does not have an equal sign (3x+5) (2a+9b)
base-ten number
its the sum of its digits is divisible by 3
expression
Associative Law of Addition
40. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
solutions
counterclockwise through 90
Algebraic number theory
its the sum of its digits is divisible by 3
41. 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
16(5+R)
constructing a parallelogram
complex number
To separate a number into prime factors
42. Number T increased by 9
Distributive Law
solutions
T+9
multiplication
43. Any number that is not a multiple of 2 is an
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Odd Number
variable
C or
44. Total
addition
Place Value Concept
base-ten number
an equation in two variables defines
45. A number is divisible by 5 if its
Positional notation (place value)
quadratic field
righthand digit is 0 or 5
the number formed by the three right-hand digits is divisible by 8
46. A number is divisible by 6 if it is
Prime Number
even and 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: .
Members of Elements of the Set
47. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
The real number a of the complex number z = a + bi
Inversive geometry
addition
(x-12)/40
48. First axiom of equality
Set
C or
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.
Braces
49. Product of 16 and the sum of 5 and number R
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
coefficient
16(5+R)
repeated elements
50. The objects or symbols in a set are called Numerals - Lines - or Points
Distributive Law
Associative Law of Multiplication
right-hand digit is even
Members of Elements of the Set