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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. Any number that is not a multiple of 2 is an
Odd Number
an equation in two variables defines
even and the sum of its digits is divisible by 3
Factor of the given number
2. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
expression
a complex number is real if and only if it equals its conjugate.
Associative Law of Addition
3. 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
Commutative Law of Multiplication
base-ten number
Odd Number
Commutative Law of Addition
4. Sum
negative
Commutative Law of Addition
Absolute value and argument
addition
5. 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
Absolute value and argument
Set
Commutative Law of Addition
order of operations
6. 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.
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.
Q-16
Commutative Law of Addition
rectangular coordinates
7. The place value which corresponds to a given position in a number is determined by the
Base of the number system
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Place Value Concept
Digits
8. The set of all complex numbers is denoted by
C or
subtraction
Downward
Composite Number
9. Integers greater than zero and less than 5 form a set - as follows:
The numbers are conventionally plotted using the real part
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude and direction
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
10. 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
To separate a number into prime factors
the number formed by the two right-hand digits is divisible by 4
Associative Law of Multiplication
11. 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
Absolute value and argument
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
algebraic number
the sum of its digits is divisible by 9
12. 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
Associative Law of Addition
Prime Factor
a complex number is real if and only if it equals its conjugate.
Positional notation (place value)
13. 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.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Composite Number
Commutative Law of Addition
solutions
14. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
Commutative Law of Addition
magnitude and direction
Complex numbers
15. An equation - or system of equations - in two or more variables defines
addition
K+6 - K+5 - K+4 K+3.........answer is K+3
rectangular coordinates
a curve - a surface or some other such object in n-dimensional space
16. 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.
variable
Forth Axiom of Equality
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
16(5+R)
17. A number is divisible by 3 if
Q-16
Commutative Law of Addition
F - F+1 - F+2.......answer is F+2
its the sum of its digits is divisible by 3
18. No short method has been found for determining whether a number is divisible by
algebraic number
Braces
7
Associative Law of Multiplication
19. 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.
The real number a of the complex number z = a + bi
multiplication
Forth Axiom of Equality
20. A number is divisible by 6 if it is
addition
even and the sum of its digits is divisible by 3
the genus of the curve
In Diophantine geometry
21. In particular - the square of the imaginary unit is -1: The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit. Indeed - if i is treated as a number so that di mean
Members of Elements of the Set
The multiplication of two complex numbers is defined by the following formula:
Multiple of the given number
the genus of the curve
22. 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:
Second 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).
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
23. More than
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Place Value Concept
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
24. The real and imaginary parts of a complex number can be extracted using the conjugate:
Set
a complex number is real if and only if it equals its conjugate.
Distributive Law
equation
25. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
consecutive whole numbers
Place Value Concept
26. 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
Algebraic number theory
Equal
Even Number
In Diophantine geometry
27. 2 -3 -4 -5 -6
Number fields
consecutive whole numbers
an equation in two variables defines
Set
28. 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
addition
Place Value Concept
negative
In Diophantine geometry
29. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Digits
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
order of operations
Forth Axiom of Equality
30. A number that has no factors except itself and 1 is a
Prime Number
Third Axiom of Equality
subtraction
order of operations
31. First axiom of equality
Definition of genus
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.
Absolute value and argument
repeated elements
32. Quotient
Associative Law of Addition
Commutative Law of Addition
division
subtraction
33. 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.
Associative Law of Addition
Second Axiom of Equality
In Diophantine geometry
C or
34. 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
Associative Law of Addition
Definition of genus
repeated elements
To separate a number into prime factors
35. Number T increased by 9
T+9
Braces
even and the sum of its digits is divisible by 3
right-hand digit is even
36. 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 -
Downward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
7
Equal
37. Does not have an equal sign (3x+5) (2a+9b)
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
expression
coefficient
C or
38. A number is divisible by 9 if
complex number
subtraction
the sum of its digits is divisible by 9
Complex numbers
39. The relative greatness of positive and negative numbers
Set
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
magnitude
Positional notation (place value)
40. Plus
Distributive Law
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).
The multiplication of two complex numbers is defined by the following formula:
addition
41. A number is divisible by 8 if
Distributive Law
T+9
the number formed by the three right-hand digits is divisible by 8
addition
42. Any number that la a multiple of 2 is an
order of operations
K+6 - K+5 - K+4 K+3.........answer is K+3
Distributive Law
Even Number
43. 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.
quadratic field
Composite Number
monomial
negative
44. Product of 16 and the sum of 5 and number R
Analytic number theory
16(5+R)
In Diophantine geometry
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
45. Product
multiplication
polynomial
the genus of the curve
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
46. 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.
Complex numbers
(x-12)/40
addition
16(5+R)
47. A number is divisible by 2 if
Forth Axiom of Equality
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
magnitude
right-hand digit is even
48. If a factor of a number is prime - it is called a
Numerals
Prime Factor
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
49. Increased by
In Diophantine geometry
variable
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.
addition
50. 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.
division
repeated elements
The numbers are conventionally plotted using the real part
T+9