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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. 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
order of operations
Braces
Place Value Concept
2. Sixteen less than number Q
Q-16
T+9
Associative Law of Addition
Base of the number system
3. 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
Odd Number
Prime Number
Positional notation (place value)
Prime Factor
4. These are emphasised in a complex number's polar form and it turns out notably that the operations of addition and multiplication take on a very natural geometric character when complex numbers are viewed as position vectors:
subtraction
Complex numbers
Associative Law of Multiplication
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).
5. 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
The real number a of the complex number z = a + bi
equation
T+9
6. Number X decreased by 12 divided by forty
To separate a number into prime factors
(x-12)/40
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
rectangular coordinates
7. Any number that can be divided lnto a given number without a remainder is a
Algebraic number theory
Numerals
Complex numbers
Factor of the given number
8. One term (5x or 4)
multiplication
monomial
coefficient
To separate a number into prime factors
9. 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.
(x-12)/40
Third Axiom of Equality
The real number a of the complex number z = a + bi
Forth Axiom of Equality
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
Base of the number system
Analytic number theory
Equal
right-hand digit is even
11. The place value which corresponds to a given position in a number is determined by the
constructing a parallelogram
Base of the number system
Prime Number
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
12. A number is divisible by 4 if
Downward
righthand digit is 0 or 5
the number formed by the two right-hand digits is divisible by 4
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).
13. Viewed in this way the multiplication of a complex number by i corresponds to rotating a complex number
Composite Number
counterclockwise through 90
right-hand digit is even
expression
14. Less than
The multiplication of two complex numbers is defined by the following formula:
K+6 - K+5 - K+4 K+3.........answer is K+3
subtraction
Inversive geometry
15. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
variable
rectangular coordinates
repeated elements
addition
16. 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.
the number formed by the two right-hand digits is divisible by 4
its the sum of its digits is divisible by 3
division
Associative Law of Addition
17. Product of 16 and the sum of 5 and number R
16(5+R)
multiplication
Distributive Law
T+9
18. An equation - or system of equations - in two or more variables defines
F - F+1 - F+2.......answer is F+2
Distributive Law
a curve - a surface or some other such object in n-dimensional space
Q-16
19. Implies a collection or grouping of similar - objects or symbols.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
consecutive whole numbers
its the sum of its digits is divisible by 3
Set
20. 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.
Complex numbers
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
monomial
Place Value Concept
21. This law combines the operations of addition and multiplication. The distribution of a common multiplier among the terms of an additive expression.
rectangular coordinates
7
Distributive Law
Members of Elements of the Set
22. A number is divisible by 2 if
right-hand digit is even
expression
one characteristic in common such as similarity of appearance or purpose
magnitude and direction
23. A number is divisible by 6 if it is
C or
Complex numbers
7
even and the sum of its digits is divisible by 3
24. Are not necessary. That is - the elements of {2 - 2 - 3 - 4} are simply {2 - 3 - and 4}
repeated elements
multiplication
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
25. Sum
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude
addition
repeated elements
26. The greatest of 3 consecutive whole numbers - the smallest of which is F
Equal
polynomial
F - F+1 - F+2.......answer is F+2
solutions
27. More than one term (5x+4 contains two)
Multiple of the given number
Commutative Law of Addition
negative
polynomial
28. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
Prime Number
Multiple of the given number
negative
rectangular coordinates
29. 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
Absolute value and argument
division
coefficient
addition
30. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
an equation in two variables defines
Inversive geometry
Associative Law of Multiplication
base-ten number
31. Quotient
complex number
an equation in two variables defines
division
Absolute value and argument
32. In the Rectangular Coordinate System - On the vertical line - direction ________ is positive
Multiple of the given number
upward
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Braces
33. More than
Odd Number
addition
variable
Q-16
34. The relative greatness of positive and negative numbers
upward
the number formed by the three right-hand digits is divisible by 8
magnitude
7
35. Remainder
Braces
one characteristic in common such as similarity of appearance or purpose
the genus of the curve
subtraction
36. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
positive
Number fields
the sum of its digits is divisible by 9
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
37. Integers greater than zero and less than 5 form a set - as follows:
magnitude
expression
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Definition of genus
38. 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
In Diophantine geometry
algebraic number
base-ten number
variable
39. Total
Set
Downward
addition
positive
40. Product
multiplication
one characteristic in common such as similarity of appearance or purpose
addition
positive
41. 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.
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
Complex numbers
Commutative Law of Addition
In Diophantine geometry
42. 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
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
The multiplication of two complex numbers is defined by the following formula:
Definition of genus
43. 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.
equation
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
right-hand digit is even
its the sum of its digits is divisible by 3
44. 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
Braces
Prime Factor
Q-16
45. A number is divisible by 3 if
a complex number is real if and only if it equals its conjugate.
its the sum of its digits is divisible by 3
Prime Number
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
46. The Arabic numerals from 0 through 9 are called
The real number a of the complex number z = a + bi
addition
even and the sum of its digits is divisible by 3
Digits
47. The defining characteristic of a position vector is that it has
Prime Factor
constant
magnitude and direction
addition
48. 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 -
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Odd Number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Prime Factor
49. 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.
its the sum of its digits is divisible by 3
division
quadratic field
Equal
50. Number T increased by 9
constant
T+9
Third Axiom of Equality
complex number
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