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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. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Q-16
repeated elements
Third Axiom of Equality
Associative Law of Addition
2. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
solutions
Associative Law of Multiplication
Distributive Law
3. Any number that is not a multiple of 2 is an
Odd Number
coefficient
Number fields
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
4. 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
complex number
positive
multiplication
In Diophantine geometry
5. Plus
variable
addition
expression
Natural Numbers
6. 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.
subtraction
Associative Law of Multiplication
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
F - F+1 - F+2.......answer is F+2
7. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
monomial
quadratic field
order of operations
8. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
rectangular coordinates
righthand digit is 0 or 5
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
9. More than
addition
Inversive geometry
Commutative Law of Addition
consecutive whole numbers
10. Product of 16 and the sum of 5 and number R
Prime Factor
Q-16
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.
16(5+R)
11. One term (5x or 4)
Base of the number system
Even Number
monomial
one characteristic in common such as similarity of appearance or purpose
12. Remainder
subtraction
counterclockwise through 90
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
division
13. Number symbols
variable
The real number a of the complex number z = a + bi
the genus of the curve
Numerals
14. A number is divisible by 5 if its
In Diophantine geometry
righthand digit is 0 or 5
rectangular coordinates
Prime Number
15. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
K+6 - K+5 - K+4 K+3.........answer is K+3
Set
F - F+1 - F+2.......answer is F+2
16. 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
Members of Elements of the Set
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
order of operations
17. The objects in a set have at least
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.
Algebraic number theory
a complex number is real if and only if it equals its conjugate.
one characteristic in common such as similarity of appearance or purpose
18. The defining characteristic of a position vector is that it has
magnitude and direction
the sum of its digits is divisible by 9
Positional notation (place value)
algebraic number
19. 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
multiplication
Inversive geometry
In Diophantine geometry
20. 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
Members of Elements of the Set
To separate a number into prime factors
quadratic field
rectangular coordinates
21. Sum
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Prime Number
22. An equation - or system of equations - in two or more variables defines
Composite Number
a curve - a surface or some other such object in n-dimensional space
even and the sum of its digits is divisible by 3
Forth Axiom of Equality
23. More than one term (5x+4 contains two)
coefficient
Number fields
In Diophantine geometry
polynomial
24. The relative greatness of positive and negative numbers
Braces
monomial
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude
25. The place value which corresponds to a given position in a number is determined by the
Downward
equation
Natural Numbers
Base of the number system
26. 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.
The multiplication of two complex numbers is defined by the following formula:
magnitude and direction
Second Axiom of Equality
Inversive geometry
27. The real and imaginary parts of a complex number can be extracted using the conjugate:
Composite Number
variable
solutions
a complex number is real if and only if it equals its conjugate.
28. A number that has factors other than itself and 1 is a
Base of the number system
T+9
Composite 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.
29. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
variable
negative
30. 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
Composite Number
Second Axiom of Equality
The real number a of the complex number z = a + bi
Commutative Law of Addition
31. Subtraction
base-ten number
difference
a curve - a surface or some other such object in n-dimensional space
monomial
32. Implies a collection or grouping of similar - objects or symbols.
Analytic number theory
the number formed by the three right-hand digits is divisible by 8
Downward
Set
33. Any number that can be divided lnto a given number without a remainder is a
negative
the number formed by the two right-hand digits is divisible by 4
a curve - a surface or some other such object in n-dimensional space
Factor of the given number
34. The set of all complex numbers is denoted by
C or
Multiple of the given number
Numerals
division
35. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Natural Numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
order of operations
addition
36. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
one characteristic in common such as similarity of appearance or purpose
righthand digit is 0 or 5
Members of Elements of the Set
37. A number is divisible by 3 if
Associative Law of Multiplication
Inversive geometry
C or
its the sum of its digits is divisible by 3
38. A number that has no factors except itself and 1 is a
Absolute value and argument
subtraction
Prime Number
positive
39. The number touching the variable (in the case of 5x - would be 5)
upward
Multiple of the given number
coefficient
Base of the number system
40. The finiteness or not of the number of rational or integer points on an algebraic curve
the number formed by the two right-hand digits is divisible by 4
the genus of the curve
The numbers are conventionally plotted using the real part
Commutative Law of Multiplication
41. Decreased by
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
even and the sum of its digits is divisible by 3
subtraction
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).
42. A number is divisible by 2 if
right-hand digit is even
Composite Number
repeated elements
division
43. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Forth Axiom of Equality
Members of Elements of the Set
Second Axiom of Equality
44. 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
In Diophantine geometry
multiplication
addition
45. 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.
Associative Law of Addition
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.
The numbers are conventionally plotted using the real part
46. 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
Place Value Concept
base-ten number
its the sum of its digits is divisible by 3
righthand digit is 0 or 5
47. The greatest of 3 consecutive whole numbers - the smallest of which is F
Third Axiom of Equality
Associative Law of Multiplication
solutions
F - F+1 - F+2.......answer is F+2
48. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
consecutive whole numbers
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.
a complex number is real if and only if it equals its conjugate.
Downward
49. LAWS FOR COMBINING NUMBERS
constant
the number formed by the three right-hand digits is divisible by 8
Complex numbers
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
50. A number is divisible by 6 if it is
consecutive whole numbers
order of operations
even and the sum of its digits is divisible by 3
Downward