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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. Decreased by
subtraction
monomial
even and the sum of its digits is divisible by 3
equation
2. 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.
multiplication
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Place Value Concept
consecutive whole numbers
3. A number is divisible by 3 if
Number fields
Prime Factor
its the sum of its digits is divisible by 3
7
4. Any number that is not a multiple of 2 is an
K+6 - K+5 - K+4 K+3.........answer is K+3
Base of the number system
Absolute value and argument
Odd Number
5. The defining characteristic of a position vector is that it has
positive
magnitude
the sum of its digits is divisible by 9
magnitude and direction
6. 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.
the number formed by the three right-hand digits is divisible by 8
Forth Axiom of Equality
Members of Elements of the Set
upward
7. 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
Downward
magnitude
8. The number touching the variable (in the case of 5x - would be 5)
Inversive geometry
magnitude
coefficient
the number formed by the two right-hand digits is divisible by 4
9. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
addition
upward
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
10. 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
Composite Number
base-ten number
one characteristic in common such as similarity of appearance or purpose
K+6 - K+5 - K+4 K+3.........answer is K+3
11. The place value which corresponds to a given position in a number is determined by the
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Composite Number
base-ten number
Base of the number system
12. 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.
F - F+1 - F+2.......answer is F+2
Commutative Law of Multiplication
Commutative Law of Addition
In Diophantine geometry
13. 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
Commutative Law of Addition
a complex number is real if and only if it equals its conjugate.
polynomial
Definition of genus
14. A curve in the plane
an equation in two variables defines
its the sum of its digits is divisible by 3
order of operations
addition
15. LAWS FOR COMBINING NUMBERS
Downward
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
To separate a number into prime factors
Definition of genus
16. 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
Even Number
Positional notation (place value)
Associative Law of Addition
Place Value Concept
17. Any number that can be divided lnto a given number without a remainder is a
order of operations
The real number a of the complex number z = a + bi
Factor of the given number
equation
18. 2 -3 -4 -5 -6
variable
Second Axiom of Equality
monomial
consecutive whole numbers
19. Any number that is exactly divisible by a given number is a
Complex numbers
Forth Axiom of Equality
Multiple of the given number
Associative Law of Addition
20. Implies a collection or grouping of similar - objects or symbols.
Set
Braces
Composite Number
algebraic number
21. 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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22. 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.
addition
upward
Associative Law of Multiplication
Associative Law of Addition
23. 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
one characteristic in common such as similarity of appearance or purpose
Number fields
In Diophantine geometry
Prime Number
24. Total
addition
expression
even and the sum of its digits is divisible by 3
Associative Law of Addition
25. Subtraction
difference
addition
even and the sum of its digits is divisible by 3
Odd Number
26. Increased by
Algebraic number theory
addition
Natural Numbers
Analytic number theory
27. The set of all complex numbers is denoted by
C or
consecutive whole numbers
subtraction
Number fields
28. 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 -
(x-12)/40
K+6 - K+5 - K+4 K+3.........answer is K+3
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
solutions
29. 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
right-hand digit is even
K+6 - K+5 - K+4 K+3.........answer is K+3
F - F+1 - F+2.......answer is F+2
complex number
30. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
counterclockwise through 90
a complex number is real if and only if it equals its conjugate.
In Diophantine geometry
Associative Law of Addition
31. Number symbols
Digits
Numerals
rectangular coordinates
Associative Law of Multiplication
32. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
Inversive geometry
equation
Members of Elements of the Set
Commutative Law of Addition
33. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Numerals
addition
Commutative Law of Multiplication
34. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
upward
Associative Law of Multiplication
magnitude
Complex numbers
35. A letter tat represents a number that is unknown (usually X or Y)
variable
Analytic number theory
Prime Number
expression
36. A number is divisible by 8 if
solutions
the number formed by the three right-hand digits is divisible by 8
Positional notation (place value)
addition
37. Does not have an equal sign (3x+5) (2a+9b)
solutions
Numerals
Algebraic number theory
expression
38. The central problem of Diophantine geometry is to determine when a Diophantine equation has
the sum of its digits is divisible by 9
solutions
Digits
Number fields
39. No short method has been found for determining whether a number is divisible by
the sum of its digits is divisible by 9
Odd Number
7
consecutive whole numbers
40. 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.
a complex number is real if and only if it equals its conjugate.
Second Axiom of Equality
magnitude and direction
Even Number
41. 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
righthand digit is 0 or 5
The real number a of the complex number z = a + bi
Downward
42. One term (5x or 4)
a curve - a surface or some other such object in n-dimensional space
even and the sum of its digits is divisible by 3
right-hand digit is even
monomial
43. More than one term (5x+4 contains two)
Factor of the given number
addition
algebraic number
polynomial
44. 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
Numerals
a curve - a surface or some other such object in n-dimensional space
magnitude
45. Remainder
quadratic field
K+6 - K+5 - K+4 K+3.........answer is K+3
subtraction
solutions
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
Inversive geometry
To separate a number into prime factors
Positional notation (place value)
subtraction
47. A number is divisible by 2 if
Forth Axiom of Equality
right-hand digit is even
Braces
Q-16
48. 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
counterclockwise through 90
Second Axiom of Equality
The multiplication of two complex numbers is defined by the following formula:
constant
49. 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
the sum of its digits is divisible by 9
Associative Law of Multiplication
expression
50. 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.
constant
the genus of the curve
Analytic number theory
magnitude