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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. A number that has factors other than itself and 1 is a
Composite Number
the genus of the curve
division
the number formed by the two right-hand digits is divisible by 4
2. 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.
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.
division
righthand digit is 0 or 5
3. A number is divisible by 3 if
The multiplication of two complex numbers is defined by the following formula:
its the sum of its digits is divisible by 3
difference
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
4. 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
magnitude
the number formed by the two right-hand digits is divisible by 4
the number formed by the three right-hand digits is divisible by 8
Positional notation (place value)
5. Product of 16 and the sum of 5 and number R
its the sum of its digits is divisible by 3
Inversive geometry
Commutative Law of Addition
16(5+R)
6. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Algebraic number theory
the number formed by the three right-hand digits is divisible by 8
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
The real number a of the complex number z = a + bi
7. No short method has been found for determining whether a number is divisible by
subtraction
7
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 absolute value (or modulus or magnitude) of a complex number z = x + yi is
8. Total
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
In Diophantine geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
addition
9. 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.
Associative Law of Addition
Commutative Law of Addition
Forth Axiom of Equality
Inversive geometry
10. 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
equation
Associative Law of Addition
complex number
Commutative Law of Multiplication
11. The greatest of 3 consecutive whole numbers - the smallest of which is F
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
magnitude and direction
F - F+1 - F+2.......answer is F+2
Braces
12. The numbers which are used for counting in our number system are sometimes called
right-hand digit is even
Natural Numbers
addition
The real number a of the complex number z = a + bi
13. 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
Even Number
Place Value Concept
Set
the genus of the curve
14. 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
Commutative Law of Multiplication
Commutative Law of Addition
To separate a number into prime factors
upward
15. 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
The multiplication of two complex numbers is defined by the following formula:
In Diophantine geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
constructing a parallelogram
16. Are used to indicate sets
quadratic field
a curve - a surface or some other such object in n-dimensional space
Multiple of the given number
Braces
17. Decreased by
Analytic number theory
multiplication
subtraction
Odd Number
18. Remainder
variable
Analytic number theory
Odd Number
subtraction
19. 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
a complex number is real if and only if it equals its conjugate.
Complex numbers
magnitude and direction
The multiplication of two complex numbers is defined by the following formula:
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 -
upward
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Definition of genus
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
21. Number T increased by 9
addition
T+9
The multiplication of two complex numbers is defined by the following formula:
Numerals
22. 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.
counterclockwise through 90
Associative Law of Multiplication
the number formed by the three right-hand digits is divisible by 8
algebraic number
23. Sixteen less than number Q
F - F+1 - F+2.......answer is F+2
solutions
Q-16
C or
24. Implies a collection or grouping of similar - objects or symbols.
consecutive whole numbers
constructing a parallelogram
Algebraic number theory
Set
25. A number that has no factors except itself and 1 is a
The multiplication of two complex numbers is defined by the following formula:
division
In Diophantine geometry
Prime Number
26. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Commutative Law of Multiplication
Inversive geometry
complex number
27. 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
upward
In Diophantine geometry
16(5+R)
subtraction
28. Subtraction
difference
F - F+1 - F+2.......answer is F+2
negative
Even Number
29. The finiteness or not of the number of rational or integer points on an algebraic curve
Absolute value and argument
Composite Number
the genus of the curve
Distributive Law
30. 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.
righthand digit is 0 or 5
Commutative Law of Addition
The numbers are conventionally plotted using the real part
Analytic number theory
31. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
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.
order of operations
Distributive Law
32. 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:
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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The real number a of the complex number z = a + bi
33. Quotient
16(5+R)
division
positive
Odd Number
34. 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
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.
Algebraic number theory
base-ten number
35. More than
addition
Absolute value and argument
F - F+1 - F+2.......answer is F+2
multiplication
36. 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.)
constructing a parallelogram
(x-12)/40
Number fields
Composite Number
37. The set of all complex numbers is denoted by
Positional notation (place value)
C or
positive
righthand digit is 0 or 5
38. If a factor of a number is prime - it is called a
The numbers are conventionally plotted using the real part
upward
Prime Factor
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
39. 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}
Q-16
16(5+R)
Positional notation (place value)
40. A curve in the plane
an equation in two variables defines
addition
Inversive geometry
In Diophantine geometry
41. 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.
magnitude and direction
Complex numbers
7
division
42. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
Absolute value and argument
Commutative Law of Addition
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
43. As shown earlier - c - di is the complex conjugate of the denominator c + di.
(x-12)/40
addition
even and the sum of its digits is divisible by 3
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
44. Increased by
difference
Commutative Law of Addition
addition
Associative Law of Addition
45. 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
Second Axiom of Equality
Even Number
base-ten number
a complex number is real if and only if it equals its conjugate.
46. 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
upward
algebraic number
Prime Factor
Digits
47. A letter tat represents a number that is unknown (usually X or Y)
variable
Distributive Law
Associative Law of Addition
Algebraic number theory
48. Sum
7
Commutative Law of Addition
addition
magnitude
49. 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
rectangular coordinates
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).
Absolute value and argument
Algebraic number theory
50. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
In Diophantine geometry
even and the sum of its digits is divisible by 3
quadratic field