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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. 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.
Prime Factor
quadratic field
Absolute value and argument
the genus of the curve
2. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
rectangular coordinates
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.
a curve - a surface or some other such object in n-dimensional space
subtraction
3. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Multiple of the given number
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
righthand digit is 0 or 5
addition
4. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
complex number
To separate a number into prime factors
Associative Law of Multiplication
5. 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.
the sum of its digits is divisible by 9
its the sum of its digits is divisible by 3
Downward
6. The greatest of 3 consecutive whole numbers - the smallest of which is F
7
To separate a number into prime factors
F - F+1 - F+2.......answer is F+2
Positional notation (place value)
7. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
magnitude and direction
Even Number
variable
8. A number that has factors other than itself and 1 is a
Composite Number
an equation in two variables defines
addition
Digits
9. 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 absolute value (or modulus or magnitude) of a complex number z = x + yi is
Associative Law of Addition
Equal
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
10. 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.
Associative Law of Multiplication
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.
Q-16
subtraction
11. The place value which corresponds to a given position in a number is determined by the
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
subtraction
base-ten number
Base of the number system
12. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
addition
Absolute value and argument
variable
repeated elements
13. A number is divisible by 3 if
Multiple of the given number
its the sum of its digits is divisible by 3
Braces
Associative Law of Multiplication
14. Number T increased by 9
coefficient
T+9
addition
Analytic number theory
15. 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
T+9
In Diophantine geometry
the genus of the curve
constant
16. Are used to indicate sets
T+9
Braces
rectangular coordinates
polynomial
17. 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
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
magnitude
Prime Number
18. The objects in a set have at least
one characteristic in common such as similarity of appearance or purpose
right-hand digit is even
Associative Law of Addition
constant
19. 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.
algebraic number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
7
Distributive Law
20. A number is divisible by 9 if
Analytic number theory
its the sum of its digits is divisible by 3
the number formed by the three right-hand digits is divisible by 8
the sum of its digits is divisible by 9
21. Plus
addition
consecutive whole numbers
magnitude
upward
22. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
division
Forth Axiom of Equality
Associative Law of Multiplication
counterclockwise through 90
23. 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.
Prime Number
Prime Factor
Third Axiom of Equality
Commutative Law of Addition
24. Addition of two complex numbers can be done geometrically by
Commutative Law of Addition
constructing a parallelogram
Associative Law of Addition
the number formed by the three right-hand digits is divisible by 8
25. The defining characteristic of a position vector is that it has
order of operations
magnitude and direction
T+9
Q-16
26. If two equal quantities are multiplied by the same quantity - the resulting products are equal. If equals are multiplied by equals - the products are equal.
Third Axiom of Equality
Digits
Set
The real number a of the complex number z = a + bi
27. The number without a variable (5m+2). In this case - 2
upward
constant
subtraction
base-ten number
28. Number X decreased by 12 divided by forty
Set
positive
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
(x-12)/40
29. The numbers which are used for counting in our number system are sometimes called
difference
Natural Numbers
addition
algebraic number
30. 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
addition
base-ten number
coefficient
Definition of genus
31. 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.
Equal
constructing a parallelogram
Commutative Law of Multiplication
Commutative Law of Addition
32. Number symbols
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).
Numerals
Associative Law of Addition
Prime Number
33. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
In Diophantine geometry
constructing a parallelogram
Braces
34. 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
Associative Law of Multiplication
Odd Number
Positional notation (place value)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
35. 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:
Third Axiom of Equality
The real number a of the complex number z = a + bi
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).
an equation in two variables defines
36. 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
multiplication
Digits
In Diophantine geometry
37. 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
In Diophantine geometry
magnitude and direction
an equation in two variables defines
base-ten number
38. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
order of operations
Braces
'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
39. Sum
addition
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude and direction
Base of the number system
40. The relative greatness of positive and negative numbers
multiplication
Commutative Law of Addition
magnitude
Third Axiom of Equality
41. Product of 16 and the sum of 5 and number R
complex number
16(5+R)
addition
polynomial
42. A number is divisible by 4 if
Equal
the number formed by the two right-hand digits is divisible by 4
quadratic field
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
43. Any number that is not a multiple of 2 is an
Downward
Odd Number
F - F+1 - F+2.......answer is F+2
constructing a parallelogram
44. Any number that la a multiple of 2 is an
righthand digit is 0 or 5
Even Number
Commutative Law of Addition
Natural Numbers
45. 2 -3 -4 -5 -6
the sum of its digits is divisible by 9
Factor of the given number
its the sum of its digits is divisible by 3
consecutive whole numbers
46. Increased by
The numbers are conventionally plotted using the real part
addition
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
subtraction
47. If a factor of a number is prime - it is called a
positive
a curve - a surface or some other such object in n-dimensional space
Inversive geometry
Prime Factor
48. 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
In Diophantine geometry
Prime Factor
Factor of the given number
49. The Arabic numerals from 0 through 9 are called
solutions
Digits
negative
the genus of the curve
50. One term (5x or 4)
Q-16
monomial
constructing a parallelogram
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.