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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 relative greatness of positive and negative numbers
rectangular coordinates
Complex numbers
C or
magnitude
2. Plus
addition
Second Axiom of Equality
the sum of its digits is divisible by 9
Complex numbers
3. In the Rectangular Coordinate System - the direction to the right along the horizontal line is
Base of the number system
F - F+1 - F+2.......answer is F+2
The numbers are conventionally plotted using the real part
positive
4. 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.
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
counterclockwise through 90
Commutative Law of Multiplication
Associative Law of Addition
5. 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.
algebraic number
Commutative Law of Addition
division
complex number
6. A number is divisible by 8 if
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).
In Diophantine geometry
the number formed by the three right-hand digits is divisible by 8
addition
7. Integers greater than zero and less than 5 form a set - as follows:
Braces
Third Axiom of Equality
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
Natural Numbers
8. 2 -3 -4 -5 -6
C or
addition
consecutive whole numbers
expression
9. 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
righthand digit is 0 or 5
Prime Number
The real number a of the complex number z = a + bi
Complex numbers
10. The place value which corresponds to a given position in a number is determined by the
the number formed by the three right-hand digits is divisible by 8
Prime Number
its the sum of its digits is divisible by 3
Base of the number system
11. More than
16(5+R)
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
a curve - a surface or some other such object in n-dimensional space
addition
12. A number is divisible by 3 if
Factor of the given number
its the sum of its digits is divisible by 3
one characteristic in common such as similarity of appearance or purpose
The numbers are conventionally plotted using the real part
13. This formula can be used to compute the multiplicative inverse of a complex number if it is given in
Forth Axiom of Equality
rectangular coordinates
The real number a of the complex number z = a + bi
Place Value Concept
14. Are used to indicate sets
Braces
multiplication
Third Axiom of Equality
Q-16
15. A number is divisible by 9 if
its the sum of its digits is divisible by 3
'reflection' of z about the real axis. In particular - conjugating twice gives the original complex number: .
the sum of its digits is divisible by 9
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
16. The central problem of Diophantine geometry is to determine when a Diophantine equation has
solutions
T+9
F - F+1 - F+2.......answer is F+2
Number fields
17. Number X decreased by 12 divided by forty
(x-12)/40
Numerals
addition
addition
18. If a factor of a number is prime - it is called a
Set
Commutative Law of Addition
Prime Factor
coefficient
19. First axiom of equality
Prime Number
addition
Inversive geometry
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.
20. 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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21. 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.
F - F+1 - F+2.......answer is F+2
Commutative Law of Multiplication
monomial
Number fields
22. Sixteen less than number Q
even and the sum of its digits is divisible by 3
addition
Here is called the modulus of a + bi - and the square root with non-negative real part is called the principal square root.
Q-16
23. In the Rectangular Coordinate System - the direction to the left along the horizontal line is
negative
Prime Factor
coefficient
magnitude
24. A number is divisible by 5 if its
righthand digit is 0 or 5
Natural Numbers
upward
To separate a number into prime factors
25. Any number that can be divided lnto a given number without a remainder is a
Odd Number
T+9
Factor of the given number
addition
26. A number is divisible by 4 if
righthand digit is 0 or 5
expression
the number formed by the two right-hand digits is divisible by 4
one characteristic in common such as similarity of appearance or purpose
27. Product of 16 and the sum of 5 and number R
monomial
coefficient
7
16(5+R)
28. 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:
Algebraic number theory
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.
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).
Complex numbers
29. Implies a collection or grouping of similar - objects or symbols.
addition
right-hand digit is even
Set
addition
30. 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.
variable
Q-16
Complex numbers
addition
31. 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.
Associative Law of Multiplication
coefficient
one characteristic in common such as similarity of appearance or purpose
32. The Arabic numerals from 0 through 9 are called
The numbers are conventionally plotted using the real part
Digits
Associative Law of Addition
Commutative Law of Addition
33. Product
multiplication
Multiple of the given number
Definition of genus
The numbers are conventionally plotted using the real part
34. The number touching the variable (in the case of 5x - would be 5)
coefficient
complex number
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Odd Number
35. An equation - or system of equations - in two or more variables defines
multiplication
a curve - a surface or some other such object in n-dimensional space
repeated elements
Factor of the given number
36. 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.
multiplication
Equal
Associative Law of Multiplication
variable
37. No short method has been found for determining whether a number is divisible by
magnitude
subtraction
7
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.
38. 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
coefficient
addition
Base of the number system
39. The numbers which are used for counting in our number system are sometimes called
righthand digit is 0 or 5
a curve - a surface or some other such object in n-dimensional space
consecutive whole numbers
Natural Numbers
40. The smallest of four sonsecutive whole numbers - the biggest of which is K+6
Definition of genus
K+6 - K+5 - K+4 K+3.........answer is K+3
Commutative Law of Addition
monomial
41. 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.
Commutative Law of Addition
7
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
one characteristic in common such as similarity of appearance or purpose
42. A curve in the plane
Odd Number
subtraction
an equation in two variables defines
7
43. The objects or symbols in a set are called Numerals - Lines - or Points
Members of Elements of the Set
base-ten number
subtraction
a complex number is real if and only if it equals its conjugate.
44. The set of all complex numbers is denoted by
Commutative Law of Multiplication
C or
In Diophantine geometry
The real part c and the imaginary part d of the denominator must not both be zero for division to be defined.
45. Increased by
(x-12)/40
addition
difference
equation
46. Is any complex number that is a solution to some polynomial equation with rational coefficients; for example - every solution x of (say) is an algebraic number. Fields of algebraic numbers are also called algebraic number fields - or shortly number f
algebraic number
In Diophantine geometry
Number fields
expression
47. A letter tat represents a number that is unknown (usually X or Y)
variable
its the sum of its digits is divisible by 3
algebraic number
Commutative Law of Multiplication
48. 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.
Associative Law of Addition
consecutive whole numbers
(x-12)/40
constant
49. Number T increased by 9
positive
T+9
The real number a of the complex number z = a + bi
Downward
50. 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.
Multiple of the given number
algebraic number
Natural Numbers
Third Axiom of Equality