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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. The number without a variable (5m+2). In this case - 2
K+6 - K+5 - K+4 K+3.........answer is K+3
order of operations
constant
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
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.
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Composite Number
Analytic number theory
Associative Law of Addition
3. Number symbols
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.
Numerals
Digits
Third Axiom of Equality
4. Has an equal sign (3x+5 = 14)
Inversive geometry
equation
Analytic number theory
order of operations
5. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
In Diophantine geometry
Composite Number
Even Number
6. 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
Downward
To separate a number into prime factors
16(5+R)
Prime Factor
7. G - E - M - A Grouping - Exponents - Multiply/Divide - Add/Subtract
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Odd Number
order of operations
Equal
8. 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.
Forth Axiom of Equality
Analytic number theory
Number fields
Associative Law of Addition
9. A number is divisible by 3 if
Set
In Diophantine geometry
its the sum of its digits is divisible by 3
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
10. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
addition
Associative Law of Addition
a complex number is real if and only if it equals its conjugate.
counterclockwise through 90
11. 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
In Diophantine geometry
addition
monomial
solutions
12. Any number that is exactly divisible by a given number is a
Multiple of the given number
(x-12)/40
Commutative Law of Addition
Factor of the given number
13. 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.)
Second Axiom of Equality
addition
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Number fields
14. 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
the sum of its digits is divisible by 9
one characteristic in common such as similarity of appearance or purpose
Definition of genus
right-hand digit is even
15. 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
In Diophantine geometry
counterclockwise through 90
Natural Numbers
16. As shown earlier - c - di is the complex conjugate of the denominator c + di.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
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).
constant
Place Value Concept
17. The finiteness or not of the number of rational or integer points on an algebraic curve
In Diophantine geometry
addition
Number fields
the genus of the curve
18. Subtraction
Multiple of the given number
negative
16(5+R)
difference
19. Number T increased by 9
equation
Base of the number system
subtraction
T+9
20. 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
repeated elements
Prime Factor
polynomial
21. A number is divisible by 2 if
The real number a of the complex number z = a + bi
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
right-hand digit is even
Set
22. Any number that can be divided lnto a given number without a remainder is a
Equal
magnitude and direction
Factor of the given number
Analytic number theory
23. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
a curve - a surface or some other such object in n-dimensional space
subtraction
Second Axiom of Equality
positive
24. Number X decreased by 12 divided by forty
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
Commutative Law of Multiplication
the number formed by the three right-hand digits is divisible by 8
(x-12)/40
25. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
repeated elements
Analytic number theory
polynomial
26. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
the genus of the curve
The real number a of the complex number z = a + bi
right-hand digit is even
27. First axiom of equality
addition
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
Odd Number
28. A number that has factors other than itself and 1 is a
Composite Number
addition
Odd Number
C or
29. If a factor of a number is prime - it is called a
addition
equation
Prime Factor
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).
30. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
In Diophantine geometry
the genus of the curve
Associative Law of Addition
rectangular coordinates
31. In the Rectangular Coordinate System - On the vertical line - direction _______ is negative
division
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Downward
repeated elements
32. Are used to indicate sets
Absolute value and argument
the sum of its digits is divisible by 9
Braces
Associative Law of Addition
33. 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 multiplication of two complex numbers is defined by the following formula:
Place Value Concept
coefficient
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
34. LAWS FOR COMBINING NUMBERS
monomial
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Downward
Complex numbers
35. Less than
To separate a number into prime factors
subtraction
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
(x-12)/40
36. Product
multiplication
variable
Absolute value and argument
Second Axiom of Equality
37. Integers greater than zero and less than 5 form a set - as follows:
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
repeated elements
Second Axiom of Equality
magnitude
38. Does not have an equal sign (3x+5) (2a+9b)
Composite Number
expression
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).
quadratic field
39. Work on the problem of general polynomials ultimately led to the fundamental theorem of algebra -
Digits
Multiple of the given number
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Composite Number
40. Sum
Commutative Law of Multiplication
addition
Even Number
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.
41. Product of 16 and the sum of 5 and number R
variable
16(5+R)
To separate a number into prime factors
In Diophantine geometry
42. 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.
righthand digit is 0 or 5
Forth Axiom of Equality
variable
Definition of genus
43. The place value which corresponds to a given position in a number is determined by the
7
even and the sum of its digits is divisible by 3
Base of the number system
order of operations
44. 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.
Composite Number
difference
Commutative Law of Addition
subtraction
45. 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
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
The real number a of the complex number z = a + bi
a complex number is real if and only if it equals its conjugate.
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
Analytic number theory
magnitude
Absolute value and argument
Inversive geometry
47. Quotient
order of operations
division
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Factor of the given number
48. 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
Members of Elements of the Set
Associative Law of Addition
The multiplication of two complex numbers is defined by the following formula:
Equal
49. Remainder
subtraction
order of operations
rectangular coordinates
Distributive Law
50. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
right-hand digit is even
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
To separate a number into prime factors