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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
In Diophantine geometry
Positional notation (place value)
Odd Number
addition
2. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
a curve - a surface or some other such object in n-dimensional space
Algebraic number theory
division
3. Any number that is exactly divisible by a given number is a
Multiple of the given number
Prime Number
Q-16
Downward
4. 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.
division
Forth Axiom of Equality
complex number
subtraction
5. 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.
(x-12)/40
solutions
even and the sum of its digits is divisible by 3
Associative Law of Addition
6. Integers greater than zero and less than 5 form a set - as follows:
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
monomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
7. Product of 16 and the sum of 5 and number R
Composite Number
16(5+R)
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
(x-12)/40
8. 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.
The real number a of the complex number z = a + bi
Natural Numbers
Associative Law of Addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
9. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Analytic number theory
C or
Digits
order of operations
10. 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.
Distributive Law
addition
quadratic field
right-hand digit is even
11. First axiom of equality
addition
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 genus of the curve
16(5+R)
12. 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.
Composite Number
Place Value Concept
Commutative Law of Multiplication
magnitude and direction
13. If a factor of a number is prime - it is called a
Prime Factor
right-hand digit is even
order of operations
Commutative Law of Addition
14. A number is divisible by 9 if
addition
16(5+R)
polynomial
the sum of its digits is divisible by 9
15. Number X decreased by 12 divided by forty
(x-12)/40
rectangular coordinates
Multiple of the given number
an equation in two variables defines
16. Quotient
Odd Number
Composite Number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
division
17. The set of all complex numbers is denoted by
addition
C or
Positional notation (place value)
expression
18. Addition of two complex numbers can be done geometrically by
The multiplication of two complex numbers is defined by the following formula:
Even Number
Definition of genus
constructing a parallelogram
19. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
C or
addition
an equation in two variables defines
20. 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
subtraction
variable
Prime Number
21. A number is divisible by 2 if
addition
In Diophantine geometry
right-hand digit is even
an equation in two variables defines
22. A letter tat represents a number that is unknown (usually X or Y)
variable
Base of the number system
right-hand digit is even
Place Value Concept
23. Sixteen less than number Q
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
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).
Commutative Law of Addition
Q-16
24. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
Forth Axiom of Equality
To separate a number into prime factors
The real number a of the complex number z = a + bi
25. A curve in the plane
an equation in two variables defines
K+6 - K+5 - K+4 K+3.........answer is K+3
Positional notation (place value)
magnitude and direction
26. An equation - or system of equations - in two or more variables defines
Equal
Third Axiom of Equality
Commutative Law of Multiplication
a curve - a surface or some other such object in n-dimensional space
27. 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 -
addition
The real number a of the complex number z = a + bi
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
algebraic number
28. The place value which corresponds to a given position in a number is determined by the
Base of the number system
solutions
righthand digit is 0 or 5
Associative Law of Addition
29. 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
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
variable
Definition of genus
Algebraic number theory
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.
rectangular coordinates
difference
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
The numbers are conventionally plotted using the real part
31. Number T increased by 9
magnitude
T+9
quadratic field
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.
32. 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.
a complex number is real if and only if it equals its conjugate.
Third 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.
expression
33. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
34. Less than
subtraction
Forth Axiom of Equality
In Diophantine geometry
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
35. As shown earlier - c - di is the complex conjugate of the denominator c + di.
quadratic field
repeated elements
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
negative
36. Implies a collection or grouping of similar - objects or symbols.
Set
Natural Numbers
subtraction
magnitude
37. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
difference
Prime Number
rectangular coordinates
right-hand digit is even
38. The objects in a set have at least
right-hand digit is even
one characteristic in common such as similarity of appearance or purpose
Prime Number
addition
39. The defining characteristic of a position vector is that it has
Q-16
magnitude and direction
Composite Number
difference
40. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
T+9
subtraction
addition
41. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Distributive Law
right-hand digit is even
Commutative Law of Addition
42. 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
polynomial
Third Axiom of Equality
To separate a number into prime factors
43. The Arabic numerals from 0 through 9 are called
Digits
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the sum of its digits is divisible by 9
polynomial
44. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Commutative Law of Multiplication
Members of Elements of the Set
Commutative Law of Addition
negative
45. More than
addition
equation
positive
Absolute value and argument
46. Increased by
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
addition
Odd Number
consecutive whole numbers
47. The numbers which are used for counting in our number system are sometimes called
monomial
subtraction
To separate a number into prime factors
Natural Numbers
48. In terms of its tools - as the study of the integers by means of tools from real and complex analysis - in terms of its concerns - as the study within number theory of estimates on size and density - as opposed to identities.
16(5+R)
Analytic number theory
addition
Number fields
49. The number touching the variable (in the case of 5x - would be 5)
magnitude
coefficient
C or
Braces
50. 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.
order of operations
solutions
Commutative Law of Addition
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).