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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. Any number that la a multiple of 2 is an
The numbers are conventionally plotted using the real part
Even Number
even and the sum of its digits is divisible by 3
algebraic number
2. 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.
Prime Number
Associative Law of Addition
addition
constant
3. 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
Algebraic number theory
Place Value Concept
The real number a of the complex number z = a + bi
In Diophantine geometry
4. Product of 16 and the sum of 5 and number R
Natural Numbers
Numerals
Complex numbers
16(5+R)
5. Increased by
addition
the genus of the curve
Downward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
6. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Prime Factor
multiplication
Commutative Law of Addition
positive
7. A number is divisible by 6 if it is
In Diophantine geometry
Members of Elements of the Set
even and the sum of its digits is divisible by 3
In Diophantine geometry
8. Total
Factor of the given number
addition
a complex number is real if and only if it equals its conjugate.
(x-12)/40
9. 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
the number formed by the three right-hand digits is divisible by 8
Equal
10. 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.
Algebraic number theory
Number fields
The real number a of the complex number z = a + bi
Complex numbers
11. 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.
Positional notation (place value)
polynomial
Associative Law of Addition
addition
12. A number is divisible by 3 if
polynomial
F - F+1 - F+2.......answer is F+2
complex number
its the sum of its digits is divisible by 3
13. 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.
algebraic number
Composite Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
14. Less than
Inversive geometry
In Diophantine geometry
variable
subtraction
15. 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
its the sum of its digits is divisible by 3
positive
In Diophantine geometry
16. Number T increased by 9
the sum of its digits is divisible by 9
T+9
To separate a number into prime factors
Absolute value and argument
17. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
rectangular coordinates
repeated elements
Factor of the given number
an equation in two variables defines
18. 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 -
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Number
Second Axiom of Equality
19. The number without a variable (5m+2). In this case - 2
Equal
negative
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
constant
20. Quotient
Absolute value and argument
Even Number
division
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
21. Implies a collection or grouping of similar - objects or symbols.
constant
Set
The real number a of the complex number z = a + bi
right-hand digit is even
22. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
difference
solutions
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Definition of genus
23. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Complex numbers
Third Axiom of Equality
Distributive Law
The multiplication of two complex numbers is defined by the following formula:
24. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Complex numbers
K+6 - K+5 - K+4 K+3.........answer is K+3
the genus of the curve
upward
25. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
the sum of its digits is divisible by 9
addition
Definition of genus
26. Sixteen less than number Q
Q-16
rectangular coordinates
constant
In Diophantine geometry
27. More than one term (5x+4 contains two)
constructing a parallelogram
constant
the number formed by the three right-hand digits is divisible by 8
polynomial
28. If a factor of a number is prime - it is called a
Digits
Prime Factor
In Diophantine geometry
Forth Axiom of Equality
29. 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
repeated elements
Algebraic number theory
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.
30. Product
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
constructing a parallelogram
Commutative Law of Addition
multiplication
31. 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:
base-ten 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).
C or
polynomial
32. 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
7
the number formed by the three right-hand digits is divisible by 8
Members of Elements of the Set
33. Any number that is not a multiple of 2 is an
The multiplication of two complex numbers is defined by the following formula:
an equation in two variables defines
Odd Number
The real number a of the complex number z = a + bi
34. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Base of the number system
order of operations
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
K+6 - K+5 - K+4 K+3.........answer is K+3
35. The set of all complex numbers is denoted by
Forth Axiom of Equality
quadratic field
C or
right-hand digit is even
36. The central problem of Diophantine geometry is to determine when a Diophantine equation has
the number formed by the three right-hand digits is divisible by 8
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Members of Elements of the Set
solutions
37. The finiteness or not of the number of rational or integer points on an algebraic curve
Absolute value and argument
the genus of the curve
Numerals
(x-12)/40
38. Since the elements of the set {2 - 4 - e} are the same as the elements of{4 - 2 - e} - these two sets are said to be
multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
constructing a parallelogram
Equal
39. 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
Distributive Law
In Diophantine geometry
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Numerals
40. 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
In Diophantine geometry
expression
Definition of genus
the number formed by the two right-hand digits is divisible by 4
41. 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.
even and the sum of its digits is divisible by 3
Composite Number
quadratic field
In Diophantine geometry
42. 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.
quadratic field
the genus of the curve
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Second Axiom of Equality
43. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
Downward
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Base of the number system
44. The objects in a set have at least
counterclockwise through 90
addition
the sum of its digits is divisible by 9
one characteristic in common such as similarity of appearance or purpose
45. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
Algebraic number theory
subtraction
Commutative Law of Addition
46. 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
Commutative Law of Addition
K+6 - K+5 - K+4 K+3.........answer is K+3
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
The real number a of the complex number z = a + bi
47. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The multiplication of two complex numbers is defined by the following formula:
one characteristic in common such as similarity of appearance or purpose
equation
48. 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
Second Axiom of Equality
algebraic number
base-ten number
order of operations
49. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
order of operations
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Definition of genus
50. 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.
Commutative Law of Multiplication
addition
T+9
Numerals