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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. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
Multiple of the given number
Distributive Law
repeated elements
C or
2. A number is divisible by 9 if
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
polynomial
Prime Factor
the sum of its digits is divisible by 9
3. The number without a variable (5m+2). In this case - 2
constant
Digits
Members of Elements of the Set
Second Axiom of Equality
4. 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
Analytic number theory
Third Axiom of Equality
the sum of its digits is divisible by 9
5. Remainder
repeated elements
subtraction
Digits
difference
6. Any number that is exactly divisible by a given number is a
Multiple of the given number
Odd Number
The real number a of the complex number z = a + bi
order of operations
7. The numbers which are used for counting in our number system are sometimes called
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Natural Numbers
a complex number is real if and only if it equals its conjugate.
magnitude and direction
8. The relative greatness of positive and negative numbers
Second Axiom of Equality
Commutative Law of Addition
magnitude
addition
9. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Associative Law of Multiplication
Analytic number theory
Downward
positive
10. The number touching the variable (in the case of 5x - would be 5)
addition
coefficient
negative
polynomial
11. A number is divisible by 6 if it is
division
Numerals
even and the sum of its digits is divisible by 3
the genus of the curve
12. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Second Axiom of Equality
quadratic field
subtraction
rectangular coordinates
13. Are used to indicate sets
In Diophantine geometry
Braces
polynomial
constructing a parallelogram
14. 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.
rectangular coordinates
difference
a complex number is real if and only if it equals its conjugate.
15. 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
Commutative Law of Addition
rectangular coordinates
Place Value Concept
Inversive geometry
16. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Downward
addition
Equal
upward
17. 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
Associative Law of Multiplication
Braces
order of operations
In Diophantine geometry
18. 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
equation
subtraction
19. Product of 16 and the sum of 5 and number R
even and the sum of its digits is divisible by 3
16(5+R)
Forth Axiom of Equality
positive
20. First axiom of equality
Multiple of the given number
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
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.
21. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
variable
Braces
addition
negative
22. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Odd Number
Downward
Algebraic number theory
23. 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.
Natural Numbers
Odd Number
expression
24. 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 -
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:
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
25. 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
Downward
even and the sum of its digits is divisible by 3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
To separate a number into prime factors
26. Total
Forth Axiom of Equality
addition
polynomial
In Diophantine geometry
27. 2 -3 -4 -5 -6
Even Number
In Diophantine geometry
consecutive whole numbers
To separate a number into prime factors
28. More than one term (5x+4 contains two)
Digits
In Diophantine geometry
polynomial
Inversive geometry
29. Subtraction
addition
difference
Downward
Associative Law of Addition
30. More than
division
Factor of the given number
addition
the sum of its digits is divisible by 9
31. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
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).
multiplication
positive
Algebraic number theory
32. No short method has been found for determining whether a number is divisible by
Associative Law of Multiplication
7
an equation in two variables defines
In Diophantine geometry
33. 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).
F - F+1 - F+2.......answer is F+2
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
To separate a number into prime factors
34. A number is divisible by 2 if
Members of Elements of the Set
right-hand digit is even
a complex number is real if and only if it equals its conjugate.
Number fields
35. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Distributive Law
subtraction
righthand digit is 0 or 5
Composite Number
36. Quotient
upward
Number fields
Braces
division
37. Plus
addition
Commutative Law of Addition
Natural Numbers
the genus of the curve
38. Integers greater than zero and less than 5 form a set - as follows:
Distributive Law
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Downward
rectangular coordinates
39. Implies a collection or grouping of similar - objects or symbols.
variable
the sum of its digits is divisible by 9
Set
Definition of genus
40. 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.)
Distributive Law
Factor of the given number
Number fields
Braces
41. 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
the number formed by the three right-hand digits is divisible by 8
base-ten number
consecutive whole numbers
repeated elements
42. A number that has factors other than itself and 1 is a
the sum of its digits is divisible by 9
Composite Number
16(5+R)
one characteristic in common such as similarity of appearance or purpose
43. 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
Commutative Law of Addition
a curve - a surface or some other such object in n-dimensional space
variable
Definition of genus
44. Any number that la a multiple of 2 is an
Associative Law of Addition
Even Number
right-hand digit is even
polynomial
45. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
coefficient
counterclockwise through 90
Downward
Factor of the given number
46. The finiteness or not of the number of rational or integer points on an algebraic curve
K+6 - K+5 - K+4 K+3.........answer is K+3
the genus of the curve
a curve - a surface or some other such object in n-dimensional space
Prime Factor
47. Is called the real part of z - and the real number b is often called the imaginary part. By this convention the imaginary part is a real number - not including the imaginary unit: hence b - not bi - is the imaginary part. (Others - however call bi th
Prime Number
The real number a of the complex number z = a + bi
even and the sum of its digits is divisible by 3
algebraic number
48. Sum
Even Number
addition
an equation in two variables defines
even and the sum of its digits is divisible by 3
49. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
C or
Equal
In Diophantine geometry
K+6 - K+5 - K+4 K+3.........answer is K+3
50. A curve in the plane
an equation in two variables defines
expression
monomial
Multiple of the given number