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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. 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
complex number
To separate a number into prime factors
Absolute value and argument
base-ten number
2. 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 Multiplication
Commutative Law of Addition
addition
Associative Law of Multiplication
3. The set of all complex numbers is denoted by
repeated elements
addition
Braces
C or
4. 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
positive
Associative Law of Addition
complex number
Composite Number
5. 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.
polynomial
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.
Absolute value and argument
6. 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.
Associative Law of Addition
Downward
C or
F - F+1 - F+2.......answer is F+2
7. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
complex number
rectangular coordinates
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).
magnitude and direction
8. 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
division
7
The multiplication of two complex numbers is defined by the following formula:
9. The relative greatness of positive and negative numbers
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
magnitude
Commutative Law of Addition
Commutative Law of Addition
10. Sixteen less than number Q
solutions
Q-16
Positional notation (place value)
Associative Law of Addition
11. 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:
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).
Set
Algebraic number theory
Third Axiom of Equality
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.
Complex numbers
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
F - F+1 - F+2.......answer is F+2
Commutative Law of Addition
13. Any number that can be divided lnto a given number without a remainder is a
the sum of its digits is divisible by 9
Factor of the given number
addition
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
14. Product of 16 and the sum of 5 and number R
16(5+R)
Even Number
Definition of genus
F - F+1 - F+2.......answer is F+2
15. The Arabic numerals from 0 through 9 are called
complex number
Digits
Q-16
Second Axiom of Equality
16. 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}
Analytic number theory
the number formed by the two right-hand digits is divisible by 4
Base of the number system
17. The place value which corresponds to a given position in a number is determined by the
Base of the number system
Even Number
Factor of the given number
Odd Number
18. 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
Commutative Law of Addition
constant
one characteristic in common such as similarity of appearance or purpose
19. A number is divisible by 2 if
Absolute value and argument
right-hand digit is even
Multiple of the given number
Second Axiom of Equality
20. The defining characteristic of a position vector is that it has
magnitude and direction
T+9
Base of the number system
even and the sum of its digits is divisible by 3
21. The central problem of Diophantine geometry is to determine when a Diophantine equation has
constant
K+6 - K+5 - K+4 K+3.........answer is K+3
solutions
constructing a parallelogram
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.
F - F+1 - F+2.......answer is F+2
Associative Law of Addition
Base of the number system
an equation in two variables defines
23. Number X decreased by 12 divided by forty
(x-12)/40
Definition of genus
Algebraic number theory
righthand digit is 0 or 5
24. Sum
constant
Q-16
even and the sum of its digits is divisible by 3
addition
25. No short method has been found for determining whether a number is divisible by
Set
Prime Number
7
polynomial
26. 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.
negative
rectangular coordinates
Second Axiom of Equality
order of operations
27. 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
addition
Equal
Commutative Law of Multiplication
variable
28. Has an equal sign (3x+5 = 14)
complex number
variable
equation
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
29. A number is divisible by 4 if
consecutive whole numbers
the number formed by the three right-hand digits is divisible by 8
Commutative Law of Addition
the number formed by the two right-hand digits is divisible by 4
30. The number touching the variable (in the case of 5x - would be 5)
coefficient
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
variable
upward
31. The finiteness or not of the number of rational or integer points on an algebraic curve
difference
even and the sum of its digits is divisible by 3
the genus of the curve
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.
32. LAWS FOR COMBINING NUMBERS
Equal
magnitude and direction
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
33. As shown earlier - c - di is the complex conjugate of the denominator c + di.
7
polynomial
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
counterclockwise through 90
34. 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
division
Multiple of the given number
In Diophantine geometry
consecutive whole numbers
35. Are used to indicate sets
Equal
Braces
its the sum of its digits is divisible by 3
subtraction
36. 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.
difference
The numbers are conventionally plotted using the real part
F - F+1 - F+2.......answer is F+2
polynomial
37. Less than
F - F+1 - F+2.......answer is F+2
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
subtraction
38. 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
righthand digit is 0 or 5
magnitude
Place Value Concept
K+6 - K+5 - K+4 K+3.........answer is K+3
39. Addition of two complex numbers can be done geometrically by
T+9
rectangular coordinates
constructing a parallelogram
F - F+1 - F+2.......answer is F+2
40. 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.
one characteristic in common such as similarity of appearance or purpose
Complex numbers
upward
To separate a number into prime factors
41. The numbers which are used for counting in our number system are sometimes called
counterclockwise through 90
Natural Numbers
Prime Number
Third Axiom of Equality
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
The multiplication of two complex numbers is defined by the following formula:
a curve - a surface or some other such object in n-dimensional space
Natural Numbers
To separate a number into prime factors
43. 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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44. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Q-16
Braces
negative
positive
45. 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
solutions
the genus of the curve
7
46. The greatest of 3 consecutive whole numbers - the smallest of which is F
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
F - F+1 - F+2.......answer is F+2
solutions
In Diophantine geometry
47. A number is divisible by 9 if
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.
the sum of its digits is divisible by 9
an equation in two variables defines
solutions
48. 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.
a complex number is real if and only if it equals its conjugate.
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
the number formed by the three right-hand digits is divisible by 8
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
49. 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.
Place Value Concept
Third Axiom of Equality
Equal
coefficient
50. A letter tat represents a number that is unknown (usually X or Y)
variable
Commutative Law of Addition
the number formed by the three right-hand digits is divisible by 8
a curve - a surface or some other such object in n-dimensional space