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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. 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.
Analytic number theory
Composite Number
Third Axiom of Equality
solutions
2. The number without a variable (5m+2). In this case - 2
constant
Members of Elements of the Set
variable
rectangular coordinates
3. The place value which corresponds to a given position in a number is determined by the
Base of the number system
its the sum of its digits is divisible by 3
Second Axiom of Equality
Composite Number
4. 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
base-ten number
Numerals
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
constant
5. A number is divisible by 2 if
Analytic number theory
right-hand digit is even
counterclockwise through 90
Odd Number
6. 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
Definition of genus
upward
Complex numbers
Commutative Law of Addition
7. 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.
constructing a parallelogram
Associative Law of Addition
magnitude and direction
Set
8. 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
To separate a number into prime factors
polynomial
expression
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
9. Implies a collection or grouping of similar - objects or symbols.
consecutive whole numbers
Set
quadratic field
Associative Law of Multiplication
10. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
constant
addition
subtraction
Inversive geometry
11. The relative greatness of positive and negative numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
magnitude
Distributive Law
Commutative Law of Multiplication
12. Quotient
division
counterclockwise through 90
upward
one characteristic in common such as similarity of appearance or purpose
13. 2 -3 -4 -5 -6
Members of Elements of the Set
consecutive whole numbers
the number formed by the three right-hand digits is divisible by 8
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).
14. Has an equal sign (3x+5 = 14)
Even Number
equation
the number formed by the two right-hand digits is divisible by 4
Place Value Concept
15. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
one characteristic in common such as similarity of appearance or purpose
the sum of its digits is divisible by 9
16. One term (5x or 4)
Digits
Distributive Law
16(5+R)
monomial
17. A number is divisible by 9 if
the sum of its digits is divisible by 9
Factor of the given number
Commutative Law of Multiplication
Distributive Law
18. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Third Axiom of Equality
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
polynomial
19. 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.
Commutative Law of Addition
16(5+R)
a curve - a surface or some other such object in n-dimensional space
C or
20. Are used to indicate sets
constant
difference
Braces
subtraction
21. Increased by
16(5+R)
Commutative Law of Multiplication
Positional notation (place value)
addition
22. 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
The multiplication of two complex numbers is defined by the following formula:
Associative Law of Addition
addition
division
23. 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
difference
solutions
The real number a of the complex number z = a + bi
Place Value Concept
24. 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
Prime Number
Prime Factor
Definition of genus
25. 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
Commutative Law of Multiplication
addition
Set
In Diophantine geometry
26. 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 -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Number fields
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
negative
27. The number touching the variable (in the case of 5x - would be 5)
coefficient
Positional notation (place value)
subtraction
Associative Law of Multiplication
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
The numbers are conventionally plotted using the real part
Q-16
Inversive geometry
In Diophantine geometry
29. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Number fields
subtraction
Second Axiom of Equality
30. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
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31. Total
right-hand digit is even
Digits
Algebraic number theory
addition
32. Number symbols
coefficient
In Diophantine geometry
The numbers are conventionally plotted using the real part
Numerals
33. 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
Positional notation (place value)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
In Diophantine geometry
the number formed by the two right-hand digits is divisible by 4
34. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
monomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
the number formed by the two right-hand digits is divisible by 4
35. LAWS FOR COMBINING NUMBERS
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).
repeated elements
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Second Axiom of Equality
36. Any number that is exactly divisible by a given number is a
Analytic number theory
Q-16
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Multiple of the given number
37. Product of 16 and the sum of 5 and number R
constructing a parallelogram
Q-16
16(5+R)
an equation in two variables defines
38. 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.
Forth Axiom of Equality
Associative Law of Addition
constant
variable
39. Any number that la a multiple of 2 is an
complex number
Second Axiom of Equality
Q-16
Even Number
40. 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.
addition
Associative Law of Multiplication
difference
The multiplication of two complex numbers is defined by the following formula:
41. Integers greater than zero and less than 5 form a set - as follows:
variable
The real number a of the complex number z = a + bi
equation
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
42. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Prime Factor
multiplication
monomial
positive
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
monomial
subtraction
repeated elements
44. A number that has no factors except itself and 1 is a
a curve - a surface or some other such object in n-dimensional space
Even Number
polynomial
Prime Number
45. 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
addition
complex number
F - F+1 - F+2.......answer is F+2
Odd Number
46. 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.
Commutative Law of Multiplication
monomial
Second Axiom of Equality
even and the sum of its digits is divisible by 3
47. The objects in a set have at least
Place Value Concept
one characteristic in common such as similarity of appearance or purpose
Commutative Law of Multiplication
subtraction
48. Decreased by
Positional notation (place value)
algebraic number
subtraction
rectangular coordinates
49. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
its the sum of its digits is divisible by 3
Number fields
upward
the sum of its digits is divisible by 9
50. Less than
its the sum of its digits is divisible by 3
magnitude and direction
subtraction
positive