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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. A number is divisible by 2 if
16(5+R)
Complex numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
right-hand digit is even
2. 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
Algebraic number theory
Even Number
Commutative Law of Addition
3. The greatest of 3 consecutive whole numbers - the smallest of which is F
F - F+1 - F+2.......answer is F+2
solutions
addition
Commutative Law of Multiplication
4. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
To separate a number into prime factors
Inversive geometry
order of operations
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
5. 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.
counterclockwise through 90
constructing a parallelogram
6. 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.
polynomial
Second Axiom of Equality
F - F+1 - F+2.......answer is F+2
a complex number is real if and only if it equals its conjugate.
7. 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
C or
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Numerals
8. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
monomial
its the sum of its digits is divisible by 3
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
rectangular coordinates
9. 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.
Commutative Law of Addition
algebraic number
polynomial
Positional notation (place value)
10. A curve in the plane
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
an equation in two variables defines
Prime Number
Natural Numbers
11. A number is divisible by 8 if
the number formed by the three right-hand digits is divisible by 8
Second Axiom of Equality
In Diophantine geometry
Members of Elements of the Set
12. The real and imaginary parts of a complex number can be extracted using the conjugate:
equation
Factor of the given number
rectangular coordinates
a complex number is real if and only if it equals its conjugate.
13. Are used to indicate sets
its the sum of its digits is divisible by 3
quadratic field
coefficient
Braces
14. The numbers which are used for counting in our number system are sometimes called
Natural Numbers
the number formed by the three right-hand digits is divisible by 8
constructing a parallelogram
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
15. Plus
addition
(x-12)/40
the number formed by the two right-hand digits is divisible by 4
In Diophantine geometry
16. 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
Prime Factor
order of operations
quadratic field
17. The central problem of Diophantine geometry is to determine when a Diophantine equation has
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
the number formed by the three right-hand digits is divisible by 8
solutions
upward
18. 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
variable
Associative Law of Addition
base-ten number
rectangular coordinates
19. Remainder
rectangular coordinates
subtraction
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
its the sum of its digits is divisible by 3
20. If a factor of a number is prime - it is called a
coefficient
magnitude
Prime Factor
righthand digit is 0 or 5
21. A number is divisible by 6 if it is
magnitude
Analytic number theory
even and the sum of its digits is divisible by 3
Third Axiom of Equality
22. The defining characteristic of a position vector is that it has
constructing a parallelogram
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
magnitude and direction
Forth Axiom of Equality
23. Less than
upward
constant
subtraction
order of operations
24. As shown earlier - c - di is the complex conjugate of the denominator c + di.
Base of the number system
7
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Analytic number theory
25. A number is divisible by 5 if its
difference
Complex numbers
algebraic number
righthand digit is 0 or 5
26. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
Downward
algebraic number
repeated elements
the sum of its digits is divisible by 9
27. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
quadratic field
positive
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Commutative Law of Multiplication
28. 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.
equation
difference
Commutative Law of Addition
order of operations
29. Any number that can be divided lnto a given number without a remainder is a
Factor of the given number
Number fields
In Diophantine geometry
addition
30. The relative greatness of positive and negative numbers
negative
K+6 - K+5 - K+4 K+3.........answer is K+3
magnitude
In Diophantine geometry
31. 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 curve - a surface or some other such object in n-dimensional space
In Diophantine geometry
constructing a parallelogram
magnitude and direction
32. Increased by
the number formed by the two right-hand digits is divisible by 4
Commutative Law of Addition
Analytic number theory
addition
33. Number X decreased by 12 divided by forty
Third Axiom of Equality
(x-12)/40
difference
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
34. A number is divisible by 4 if
the number formed by the two right-hand digits is divisible by 4
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
In Diophantine geometry
The multiplication of two complex numbers is defined by the following formula:
35. Has an equal sign (3x+5 = 14)
Inversive geometry
equation
expression
negative
36. No short method has been found for determining whether a number is divisible by
difference
7
Digits
Absolute value and argument
37. Integers greater than zero and less than 5 form a set - as follows:
Analytic number theory
Equal
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
38. The objects in a set have at least
Multiple of the given number
one characteristic in common such as similarity of appearance or purpose
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.
Associative Law of Addition
39. The set of all complex numbers is denoted by
a curve - a surface or some other such object in n-dimensional space
C or
right-hand digit is even
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
40. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
Numerals
Distributive Law
a complex number is real if and only if it equals its conjugate.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
41. 2 -3 -4 -5 -6
Numerals
equation
consecutive whole numbers
Commutative Law of Addition
42. The number without a variable (5m+2). In this case - 2
constant
subtraction
Prime Number
Algebraic number theory
43. The Arabic numerals from 0 through 9 are called
Digits
In Diophantine geometry
Number fields
righthand digit is 0 or 5
44. 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.
polynomial
order of operations
7
quadratic field
45. 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
addition
expression
The multiplication of two complex numbers is defined by the following formula:
The numbers are conventionally plotted using the real part
46. 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
addition
Absolute value and argument
righthand digit is 0 or 5
the number formed by the two right-hand digits is divisible by 4
47. Total
rectangular coordinates
Odd Number
Second Axiom of Equality
addition
48. A number that has factors other than itself and 1 is a
Multiple of the given number
Q-16
algebraic number
Composite Number
49. 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
Algebraic number theory
Definition of genus
repeated elements
the sum of its digits is divisible by 9
50. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
counterclockwise through 90
one characteristic in common such as similarity of appearance or purpose
Composite Number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.