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Test your basic knowledge |
CLEP General Mathematics: Number Systems And Sets
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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. 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.
Second Axiom of Equality
addition
expression
Odd Number
2. One term (5x or 4)
right-hand digit is even
monomial
Absolute value and argument
In Diophantine geometry
3. Increased by
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
addition
right-hand digit is even
Forth Axiom of Equality
4. The complex conjugate of the complex number z = x + yi is defined to be x - yi. It is denoted or . Geometrically - is the
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5. Does not have an equal sign (3x+5) (2a+9b)
one characteristic in common such as similarity of appearance or purpose
expression
right-hand digit is even
K+6 - K+5 - K+4 K+3.........answer is K+3
6. A number that has no factors except itself and 1 is a
Prime Number
Multiple of the given number
solutions
The real number a of the complex number z = a + bi
7. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
a complex number is real if and only if it equals its conjugate.
The numbers are conventionally plotted using the real part
polynomial
8. Total
Factor of the given number
addition
order of operations
T+9
9. 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
In Diophantine geometry
Factor of the given number
consecutive whole numbers
The real number a of the complex number z = a + bi
10. 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
Associative Law of Addition
Definition of genus
Multiple of the given number
coefficient
11. More than one term (5x+4 contains two)
variable
polynomial
Downward
addition
12. The defining characteristic of a position vector is that it has
Members of Elements of the Set
magnitude and direction
Numerals
Place Value Concept
13. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
subtraction
a curve - a surface or some other such object in n-dimensional space
coefficient
14. A number is divisible by 2 if
right-hand digit is even
counterclockwise through 90
Set
the number formed by the two right-hand digits is divisible by 4
15. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
polynomial
subtraction
16. Has an equal sign (3x+5 = 14)
Braces
expression
a complex number is real if and only if it equals its conjugate.
equation
17. A number is divisible by 3 if
upward
addition
its the sum of its digits is divisible by 3
Commutative Law of Multiplication
18. Plus
Place Value Concept
Numerals
magnitude and direction
addition
19. The set of all complex numbers is denoted by
C or
Numerals
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
Commutative Law of Addition
20. 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.
F - F+1 - F+2.......answer is F+2
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Equal
the sum of its digits is divisible by 9
21. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
variable
a complex number is real if and only if it equals its conjugate.
an equation in two variables defines
positive
22. 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
coefficient
base-ten number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
addition
23. 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 -
expression
complex 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).
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
24. This law states that the sum of two or more addends is the same regardless of the order in which they are arranged. Means to change - substitute or move from place to place.
Commutative Law of Addition
monomial
positive
even and the sum of its digits is divisible by 3
25. Sum
Complex numbers
complex number
Multiple of the given number
addition
26. 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.
righthand digit is 0 or 5
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Commutative Law of Addition
polynomial
27. Integers greater than zero and less than 5 form a set - as follows:
consecutive whole numbers
Third Axiom of Equality
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
a complex number is real if and only if it equals its conjugate.
28. The finiteness or not of the number of rational or integer points on an algebraic curve
Prime Factor
7
Base of the number system
the genus of the curve
29. Product
base-ten number
Distributive Law
Composite Number
multiplication
30. An equation - or system of equations - in two or more variables defines
Composite Number
complex number
the number formed by the two right-hand digits is divisible by 4
a curve - a surface or some other such object in n-dimensional space
31. 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.)
a curve - a surface or some other such object in n-dimensional space
constructing a parallelogram
Members of Elements of the Set
Number fields
32. 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
Commutative Law of Addition
Q-16
Members of Elements of the Set
Algebraic number theory
33. A curve in the plane
an equation in two variables defines
the genus of the curve
repeated elements
7
34. 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.
base-ten number
quadratic field
In Diophantine geometry
Analytic number theory
35. The number without a variable (5m+2). In this case - 2
constant
Digits
The multiplication of two complex numbers is defined by the following formula:
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
36. Number T increased by 9
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Number fields
Associative Law of Multiplication
T+9
37. 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
F - F+1 - F+2.......answer is F+2
monomial
repeated elements
38. In the Rectangular Coordinate System - the direction to the left 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).
negative
algebraic number
Members of Elements of the Set
39. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
Analytic number theory
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).
Distributive Law
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
a complex number is real if and only if it equals its conjugate.
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).
In Diophantine geometry
solutions
41. A number is divisible by 4 if
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Number
the number formed by the two right-hand digits is divisible by 4
Number fields
42. The Arabic numerals from 0 through 9 are called
Digits
Analytic number theory
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Algebraic number theory
43. 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
subtraction
multiplication
In Diophantine geometry
Digits
44. 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.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Third Axiom of Equality
Braces
Second Axiom of Equality
45. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
Forth Axiom of Equality
magnitude and direction
addition
46. 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
constructing a parallelogram
magnitude and direction
To separate a number into prime factors
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
47. 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
The numbers are conventionally plotted using the real part
Positional notation (place value)
K+6 - K+5 - K+4 K+3.........answer is K+3
Third Axiom of Equality
48. Addition of two complex numbers can be done geometrically by
Third Axiom of Equality
The real number a of the complex number z = a + bi
constructing a parallelogram
Commutative Law of Addition
49. The greatest of 3 consecutive whole numbers - the smallest of which is F
Downward
Associative Law of Multiplication
Distributive Law
F - F+1 - F+2.......answer is F+2
50. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
coefficient
division
subtraction
order of operations