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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. 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.
Digits
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Forth Axiom of Equality
To separate a number into prime factors
2. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
negative
Second Axiom of Equality
3. Product of 16 and the sum of 5 and number R
16(5+R)
order of operations
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.
Composite Number
4. 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
Downward
quadratic field
The real number a of the complex number z = a + bi
5. Integers greater than zero and less than 5 form a set - as follows:
The multiplication of two complex numbers is defined by the following formula:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The numbers are conventionally plotted using the real part
upward
6. Decreased by
base-ten number
Positional notation (place value)
Third Axiom of Equality
subtraction
7. A number is divisible by 8 if
Numerals
Natural Numbers
the number formed by the three right-hand digits is divisible by 8
upward
8. 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.)
Odd Number
The numbers are conventionally plotted using the real part
Number fields
The multiplication of two complex numbers is defined by the following formula:
9. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
magnitude
an equation in two variables defines
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
10. 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.
even and the sum of its digits is divisible by 3
Members of Elements of the Set
Composite Number
Commutative Law of Addition
11. 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
Second Axiom of Equality
Absolute value and argument
In Diophantine geometry
Multiple of the given number
12. LAWS FOR COMBINING NUMBERS
Composite Number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
13. One term (5x or 4)
Equal
addition
monomial
division
14. A number that has no factors except itself and 1 is a
Odd Number
base-ten number
addition
Prime Number
15. A number is divisible by 5 if its
consecutive whole numbers
righthand digit is 0 or 5
the number formed by the three right-hand digits is divisible by 8
subtraction
16. A number is divisible by 9 if
Prime Factor
Algebraic number theory
the sum of its digits is divisible by 9
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
17. No short method has been found for determining whether a number is divisible by
The real number a of the complex number z = a + bi
7
Associative Law of Addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
18. Allow the variables in f(x -y) = 0 to be complex numbers; then f(x -y) = 0 defines a 2-dimensional surface in (projective) 4-dimensional space (since two complex variables can be decomposed into four real variables - i.e. - four dimensions). Count th
righthand digit is 0 or 5
polynomial
Definition of genus
Q-16
19. The objects or symbols in a set are called Numerals - Lines - or Points
the genus of the curve
Members of Elements of the Set
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
coefficient
20. 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 -
C or
solutions
In Diophantine geometry
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
21. 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.
Place Value Concept
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
constant
addition
22. 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 sum of its digits is divisible by 9
Commutative Law of Multiplication
Algebraic number theory
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
23. 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
an equation in two variables defines
Factor of the given number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
24. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
Prime Number
Positional notation (place value)
rectangular coordinates
25. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.
constructing a parallelogram
expression
Positional notation (place value)
Third Axiom of Equality
26. Total
one characteristic in common such as similarity of appearance or purpose
In Diophantine geometry
addition
F - F+1 - F+2.......answer is F+2
27. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
addition
counterclockwise through 90
polynomial
Commutative Law of Multiplication
28. The real and imaginary parts of a complex number can be extracted using the conjugate:
Odd Number
Distributive Law
Associative Law of Multiplication
a complex number is real if and only if it equals its conjugate.
29. A number is divisible by 2 if
Commutative Law of Addition
right-hand digit is even
Definition of genus
constructing a parallelogram
30. Any number that la a multiple of 2 is an
Equal
Definition of genus
Even Number
In Diophantine geometry
31. As shown earlier - c - di is the complex conjugate of the denominator c + di.
coefficient
Members of Elements of the Set
Factor of the given number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
32. 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
even and the sum of its digits is divisible by 3
Q-16
right-hand digit is even
33. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
subtraction
base-ten number
34. A letter tat represents a number that is unknown (usually X or Y)
Distributive Law
Inversive geometry
variable
addition
35. Sixteen less than number Q
Q-16
consecutive whole numbers
Prime Number
its the sum of its digits is divisible by 3
36. Sum
subtraction
In Diophantine geometry
Associative Law of Addition
addition
37. Implies a collection or grouping of similar - objects or symbols.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
multiplication
addition
Set
38. Number T increased by 9
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).
Members of Elements of the Set
the number formed by the two right-hand digits is divisible by 4
T+9
39. Does not have an equal sign (3x+5) (2a+9b)
expression
algebraic number
Associative Law of Addition
quadratic field
40. The defining characteristic of a position vector is that it has
Inversive geometry
Commutative Law of Addition
its the sum of its digits is divisible by 3
magnitude and direction
41. 2 -3 -4 -5 -6
Definition of genus
Digits
consecutive whole numbers
Associative Law of Addition
42. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
7
base-ten number
T+9
43. 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.
the sum of its digits is divisible by 9
Second Axiom of Equality
Multiple of the given number
Complex numbers
44. The central problem of Diophantine geometry is to determine when a Diophantine equation has
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
solutions
order of operations
complex number
45. Any number that can be divided lnto a given number without a remainder is a
a curve - a surface or some other such object in n-dimensional space
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Factor of the given number
consecutive whole numbers
46. Plus
addition
polynomial
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Composite Number
47. 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:
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
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).
Numerals
right-hand digit is even
48. The number touching the variable (in the case of 5x - would be 5)
T+9
F - F+1 - F+2.......answer is F+2
coefficient
polynomial
49. 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
Associative Law of Addition
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Forth Axiom of Equality
50. A curve in the plane
7
monomial
an equation in two variables defines
coefficient