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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 the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
C or
The numbers are conventionally plotted using the real part
one characteristic in common such as similarity of appearance or purpose
2. Sixteen less than number Q
complex number
Inversive geometry
upward
Q-16
3. 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.
the number formed by the two right-hand digits is divisible by 4
order of operations
the sum of its digits is divisible by 9
Associative Law of Addition
4. Increased by
variable
a complex number is real if and only if it equals its conjugate.
addition
coefficient
5. 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
The real number a of the complex number z = a + bi
7
Prime Number
counterclockwise through 90
6. The relative greatness of positive and negative numbers
In Diophantine geometry
magnitude
In Diophantine geometry
Algebraic number theory
7. Product of 16 and the sum of 5 and number R
Absolute value and argument
the genus of the curve
16(5+R)
The multiplication of two complex numbers is defined by the following formula:
8. The numbers which are used for counting in our number system are sometimes called
Absolute value and argument
Place Value Concept
Numerals
Natural Numbers
9. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
subtraction
Natural Numbers
positive
Q-16
10. The set of all complex numbers is denoted by
algebraic number
C or
subtraction
The real number a of the complex number z = a + bi
11. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
In Diophantine geometry
Associative Law of Addition
(x-12)/40
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
12. Number T increased by 9
multiplication
The numbers are conventionally plotted using the real part
T+9
To separate a number into prime factors
13. Quotient
the number formed by the two right-hand digits is divisible by 4
addition
division
Third Axiom of Equality
14. No short method has been found for determining whether a number is divisible by
7
monomial
The real number a of the complex number z = a + bi
Complex numbers
15. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Place Value Concept
K+6 - K+5 - K+4 K+3.........answer is K+3
repeated elements
counterclockwise through 90
16. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
C or
coefficient
order of operations
17. 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
16(5+R)
The multiplication of two complex numbers is defined by the following formula:
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
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).
18. A number is divisible by 6 if it is
T+9
the number formed by the three right-hand digits is divisible by 8
negative
even and the sum of its digits is divisible by 3
19. One term (5x or 4)
monomial
polynomial
Multiple of the given number
Digits
20. A number that has factors other than itself and 1 is a
rectangular coordinates
Positional notation (place value)
even and the sum of its digits is divisible by 3
Composite Number
21. The number without a variable (5m+2). In this case - 2
constant
subtraction
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
complex number
22. Decreased by
magnitude
Place Value Concept
Second Axiom of Equality
subtraction
23. A number is divisible by 8 if
division
Odd Number
Members of Elements of the Set
the number formed by the three right-hand digits is divisible by 8
24. 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:
Equal
counterclockwise through 90
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).
consecutive whole numbers
25. A number is divisible by 5 if its
righthand digit is 0 or 5
algebraic number
quadratic field
Third Axiom of Equality
26. Does not have an equal sign (3x+5) (2a+9b)
multiplication
an equation in two variables defines
expression
quadratic field
27. 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
K+6 - K+5 - K+4 K+3.........answer is K+3
Algebraic number theory
Digits
expression
28. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
subtraction
the number formed by the two right-hand digits is divisible by 4
Distributive Law
29. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Definition of genus
The multiplication of two complex numbers is defined by the following formula:
K+6 - K+5 - K+4 K+3.........answer is K+3
the number formed by the two right-hand digits is divisible by 4
30. 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.
its the sum of its digits is divisible by 3
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
quadratic field
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
31. 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
algebraic number
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.
constructing a parallelogram
Place Value Concept
32. Plus
Multiple of the given number
addition
Equal
Natural Numbers
33. An equation - or system of equations - in two or more variables defines
algebraic number
Digits
consecutive whole numbers
a curve - a surface or some other such object in n-dimensional space
34. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
base-ten number
quadratic field
Absolute value and argument
Inversive geometry
35. 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 -
a complex number is real if and only if it equals its conjugate.
Commutative Law of Addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
magnitude and direction
36. The Arabic numerals from 0 through 9 are called
Forth Axiom of Equality
Digits
the sum of its digits is divisible by 9
Q-16
37. The defining characteristic of a position vector is that it has
polynomial
The multiplication of two complex numbers is defined by the following formula:
magnitude and direction
Distributive Law
38. Are used to indicate sets
coefficient
(x-12)/40
Braces
a curve - a surface or some other such object in n-dimensional space
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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
multiplication
division
In Diophantine geometry
40. More than one term (5x+4 contains two)
Complex numbers
righthand digit is 0 or 5
polynomial
rectangular coordinates
41. A curve in the plane
Digits
Positional notation (place value)
7
an equation in two variables defines
42. The objects or symbols in a set are called Numerals - Lines - or Points
order of operations
Q-16
even and the sum of its digits is divisible by 3
Members of Elements of the Set
43. The real and imaginary parts of a complex number can be extracted using the conjugate:
Analytic number theory
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
16(5+R)
a complex number is real if and only if it equals its conjugate.
44. 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.
Base of the number system
Second Axiom of Equality
Set
F - F+1 - F+2.......answer is F+2
45. 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
In Diophantine geometry
algebraic number
counterclockwise through 90
Absolute value and argument
46. 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
equation
Odd Number
Definition of genus
righthand digit is 0 or 5
47. 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
Number fields
In Diophantine geometry
Second Axiom of Equality
48. 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
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
To separate a number into prime factors
magnitude and direction
righthand digit is 0 or 5
49. Any number that can be divided lnto a given number without a remainder is a
constructing a parallelogram
Factor of the given number
a curve - a surface or some other such object in n-dimensional space
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
50. 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
quadratic field
complex number
Factor of the given number
addition