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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. Less than
subtraction
a curve - a surface or some other such object in n-dimensional space
addition
Second Axiom of Equality
2. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
The numbers are conventionally plotted using the real part
Downward
Second Axiom of Equality
3. 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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4. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
7
The real number a of the complex number z = a + bi
an equation in two variables defines
5. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
solutions
Positional notation (place value)
magnitude and direction
6. 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
Equal
Place Value Concept
Distributive Law
C or
7. Number T increased by 9
coefficient
T+9
C or
magnitude and direction
8. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Set
righthand digit is 0 or 5
positive
complex number
9. More than
the number formed by the three right-hand digits is divisible by 8
Downward
addition
Inversive geometry
10. A number is divisible by 3 if
its the sum of its digits is divisible by 3
coefficient
Q-16
addition
11. If a factor of a number is prime - it is called a
coefficient
Prime Factor
Commutative Law of Addition
Second Axiom of Equality
12. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
solutions
Associative Law of Addition
13. 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 elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
In Diophantine geometry
Numerals
subtraction
14. A number is divisible by 2 if
right-hand digit is even
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Definition of genus
C or
15. 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 -
Analytic number theory
Number fields
counterclockwise through 90
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
16. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Number fields
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Commutative Law of Addition
17. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
the sum of its digits is divisible by 9
Associative Law of Addition
Multiple of the given number
18. Increased by
solutions
addition
Numerals
Analytic number theory
19. Subtraction
Set
Place Value Concept
difference
Downward
20. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
T+9
K+6 - K+5 - K+4 K+3.........answer is K+3
Associative Law of Addition
Odd Number
21. 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
K+6 - K+5 - K+4 K+3.........answer is K+3
Composite Number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
algebraic number
22. Number symbols
one characteristic in common such as similarity of appearance or purpose
Numerals
Base of the number system
T+9
23. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
its the sum of its digits is divisible by 3
Third Axiom of Equality
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Base of the number system
24. 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
order of operations
the number formed by the two right-hand digits is divisible by 4
magnitude and direction
The multiplication of two complex numbers is defined by the following formula:
25. A number is divisible by 9 if
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Commutative Law of Addition
multiplication
the sum of its digits is divisible by 9
26. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
an equation in two variables defines
order of operations
The real number a of the complex number z = a + bi
To separate a number into prime factors
27. 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
negative
Algebraic number theory
base-ten number
Positional notation (place value)
28. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
Complex numbers
repeated elements
Associative Law of Addition
29. 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.
one characteristic in common such as similarity of appearance or purpose
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
counterclockwise through 90
Composite Number
30. 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.)
the number formed by the three right-hand digits is divisible by 8
Number fields
coefficient
repeated elements
31. The set of all complex numbers is denoted by
C or
addition
the number formed by the two right-hand digits is divisible by 4
Multiple of the given number
32. LAWS FOR COMBINING NUMBERS
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
C or
the sum of its digits is divisible by 9
33. 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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
the sum of its digits is divisible by 9
difference
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).
34. 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
consecutive whole numbers
F - F+1 - F+2.......answer is F+2
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).
35. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Commutative Law of Multiplication
To separate a number into prime factors
Associative Law of Addition
36. 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.
The real number a of the complex number z = a + bi
Commutative Law of Multiplication
addition
multiplication
37. Any number that is exactly divisible by a given number is a
To separate a number into prime factors
repeated elements
Multiple of the given number
F - F+1 - F+2.......answer is F+2
38. First axiom of equality
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.
variable
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Prime Number
39. Any number that la a multiple of 2 is an
counterclockwise through 90
Analytic number theory
Even Number
the number formed by the three right-hand digits is divisible by 8
40. No short method has been found for determining whether a number is divisible by
7
quadratic field
Set
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
41. The place value which corresponds to a given position in a number is determined by the
Numerals
negative
an equation in two variables defines
Base of the number system
42. 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:
solutions
Odd Number
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).
Positional notation (place value)
43. A number is divisible by 6 if it is
Braces
magnitude and direction
repeated elements
even and the sum of its digits is divisible by 3
44. A number that has factors other than itself and 1 is a
To separate a number into prime factors
Composite Number
Commutative Law of Multiplication
Second Axiom of Equality
45. The number touching the variable (in the case of 5x - would be 5)
Complex numbers
Associative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
coefficient
46. One term (5x or 4)
Q-16
The real number a of the complex number z = a + bi
monomial
Complex numbers
47. The defining characteristic of a position vector is that it has
magnitude and direction
Complex numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Numerals
48. The real and imaginary parts of a complex number can be extracted using the conjugate:
Third Axiom of Equality
consecutive whole numbers
complex number
a complex number is real if and only if it equals its conjugate.
49. Number X decreased by 12 divided by forty
Analytic number theory
Prime Number
(x-12)/40
Commutative Law of Addition
50. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Members of Elements of the Set
repeated elements
Prime Number
The multiplication of two complex numbers is defined by the following formula: