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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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Subjects
:
clep
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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. 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
Definition of genus
Third Axiom of Equality
The real number a of the complex number z = a + bi
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.
Associative Law of Addition
Factor of the given number
division
Commutative Law of Addition
3. Quotient
7
division
In Diophantine geometry
Analytic number theory
4. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Place Value Concept
magnitude and direction
difference
negative
5. The place value which corresponds to a given position in a number is determined by the
addition
The real number a of the complex number z = a + bi
Base of the number system
K+6 - K+5 - K+4 K+3.........answer is K+3
6. Integers greater than zero and less than 5 form a set - as follows:
Number fields
a curve - a surface or some other such object in n-dimensional space
Set
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
7. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
upward
The real number a of the complex number z = a + bi
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.
counterclockwise through 90
8. 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
Definition of genus
Braces
variable
solutions
9. A number is divisible by 8 if
Definition of genus
one characteristic in common such as similarity of appearance or purpose
the number formed by the three right-hand digits is divisible by 8
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.
10. 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
Forth Axiom of Equality
equation
Equal
righthand digit is 0 or 5
11. A number is divisible by 5 if its
the number formed by the two right-hand digits is divisible by 4
Positional notation (place value)
righthand digit is 0 or 5
Inversive geometry
12. A number is divisible by 4 if
equation
addition
the number formed by the two right-hand digits is divisible by 4
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
13. 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 number
Complex numbers
solutions
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).
14. The real and imaginary parts of a complex number can be extracted using the conjugate:
coefficient
Analytic number theory
a complex number is real if and only if it equals its conjugate.
16(5+R)
15. 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
To separate a number into prime factors
positive
In Diophantine geometry
polynomial
16. Remainder
consecutive whole numbers
subtraction
even and the sum of its digits is divisible by 3
positive
17. 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
Positional notation (place value)
addition
addition
algebraic number
18. Decreased by
quadratic field
subtraction
addition
Associative Law of Addition
19. A number is divisible by 9 if
the sum of its digits is divisible by 9
addition
Equal
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
20. 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.)
Number fields
Base of the number system
Associative Law of Multiplication
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
21. 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
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Forth Axiom of Equality
consecutive whole numbers
Absolute value and argument
22. A number that has no factors except itself and 1 is a
subtraction
Prime Number
base-ten number
Absolute value and argument
23. A number is divisible by 6 if it is
even and the sum of its digits is divisible by 3
magnitude
positive
Even Number
24. The number without a variable (5m+2). In this case - 2
C or
Complex numbers
constant
complex number
25. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
K+6 - K+5 - K+4 K+3.........answer is K+3
a complex number is real if and only if it equals its conjugate.
an equation in two variables defines
addition
26. Number symbols
Members of Elements of the Set
Prime Number
subtraction
Numerals
27. 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.
quadratic field
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Complex numbers
Forth Axiom of Equality
28. A number that has factors other than itself and 1 is a
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
a curve - a surface or some other such object in n-dimensional space
Composite Number
The real number a of the complex number z = a + bi
29. Are used to indicate sets
Associative Law of Multiplication
Q-16
(x-12)/40
Braces
30. 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.
Absolute value and argument
solutions
the number formed by the two right-hand digits is divisible by 4
Associative Law of Addition
31. 2 -3 -4 -5 -6
consecutive whole numbers
The numbers are conventionally plotted using the real part
expression
addition
32. 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.
positive
monomial
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Forth Axiom of Equality
33. Plus
the number formed by the two right-hand digits is divisible by 4
Set
Factor of the given number
addition
34. 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
(x-12)/40
In Diophantine geometry
addition
16(5+R)
35. The relative greatness of positive and negative numbers
the genus of the curve
magnitude
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
base-ten number
36. Any number that la a multiple of 2 is an
16(5+R)
solutions
Even Number
addition
37. 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.
Definition of genus
Factor of the given number
Associative Law of Multiplication
addition
38. Number T increased by 9
T+9
the sum of its digits is divisible by 9
Prime Factor
division
39. Has an equal sign (3x+5 = 14)
Prime Number
To separate a number into prime factors
equation
Commutative Law of Addition
40. 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
the genus of the curve
repeated elements
16(5+R)
Place Value Concept
41. Less than
Absolute value and argument
Associative Law of Addition
subtraction
repeated elements
42. 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
coefficient
In Diophantine geometry
Base of the number system
algebraic number
43. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
rectangular coordinates
The real number a of the complex number z = a + bi
Inversive geometry
Downward
44. If a factor of a number is prime - it is called a
Prime Factor
Place Value Concept
multiplication
Associative Law of Addition
45. 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.
Downward
Second Axiom of Equality
(x-12)/40
7
46. 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.
Prime Number
Place Value Concept
Commutative Law of Multiplication
order of operations
47. The finiteness or not of the number of rational or integer points on an algebraic curve
T+9
Odd Number
the genus of the curve
algebraic number
48. The number touching the variable (in the case of 5x - would be 5)
coefficient
the genus of the curve
Braces
In Diophantine geometry
49. An equation - or system of equations - in two or more variables defines
a curve - a surface or some other such object in n-dimensional space
rectangular coordinates
addition
consecutive whole numbers
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
Complex numbers
division
C or
complex number