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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 defining characteristic of a position vector is that it has
magnitude and direction
Commutative Law of Multiplication
Distributive Law
equation
2. Remainder
subtraction
right-hand digit is even
Factor of the given number
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
3. Less than
Downward
subtraction
Algebraic number theory
coefficient
4. More than one term (5x+4 contains two)
Factor of the given number
16(5+R)
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
polynomial
5. A number is divisible by 3 if
To separate a number into prime factors
Equal
its the sum of its digits is divisible by 3
subtraction
6. Product of 16 and the sum of 5 and number R
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).
repeated elements
Forth Axiom of Equality
16(5+R)
7. 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.
Distributive Law
the genus of the curve
The multiplication of two complex numbers is defined by the following formula:
Forth Axiom of Equality
8. Subtraction
subtraction
difference
C or
Prime Number
9. 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.
Analytic number theory
Inversive geometry
even and the sum of its digits is divisible by 3
Third Axiom of Equality
10. Decreased by
Set
To separate a number into prime factors
Equal
subtraction
11. The set of all complex numbers is denoted by
Base of the number system
Commutative Law of Multiplication
the number formed by the two right-hand digits is divisible by 4
C or
12. 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.
quadratic field
(x-12)/40
the number formed by the three right-hand digits is divisible by 8
Set
13. No short method has been found for determining whether a number is divisible by
7
Commutative Law of Addition
Definition of genus
Braces
14. Total
the sum of its digits is divisible by 9
addition
the number formed by the two right-hand digits is divisible by 4
The elements of a mathematical set are usually symbols - such as {1 - 2 - 3 - 4}
15. 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.
variable
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
the genus of the curve
16. LAWS FOR COMBINING NUMBERS
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.
Members of Elements of the Set
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
Prime Factor
17. The real and imaginary parts of a complex number can be extracted using the conjugate:
a complex number is real if and only if it equals its conjugate.
Set
Factor of the given number
Associative Law of Addition
18. A branch of geometry studying more general reflections than ones about a line - can also be expressed in terms of complex numbers.
In Diophantine geometry
Inversive geometry
the number formed by the two right-hand digits is divisible by 4
magnitude and direction
19. If a factor of a number is prime - it is called a
equation
Commutative Law of Addition
Second Axiom of Equality
Prime Factor
20. Addition of two complex numbers can be done geometrically by
Associative Law of Addition
constructing a parallelogram
monomial
Commutative Law of Addition
21. 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.
C or
Complex numbers
addition
coefficient
22. An equation - or system of equations - in two or more variables defines
subtraction
Members of Elements of the Set
a curve - a surface or some other such object in n-dimensional space
quadratic field
23. 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.
Even Number
order of operations
Analytic number theory
magnitude and direction
24. 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.
Even Number
Associative Law of Multiplication
one characteristic in common such as similarity of appearance or purpose
Base of the number system
25. Plus
Base of the number system
addition
Q-16
negative
26. A number is divisible by 8 if
monomial
the number formed by the three right-hand digits is divisible by 8
Even Number
16(5+R)
27. A number is divisible by 2 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).
right-hand digit is even
quadratic field
The absolute value (or modulus or magnitude) of a complex number z = x + yi is
28. 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
subtraction
base-ten number
Members of Elements of the Set
Absolute value and argument
29. 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.
K+6 - K+5 - K+4 K+3.........answer is K+3
Commutative Law of Addition
a curve - a surface or some other such object in n-dimensional space
Numerals
30. Are used to indicate sets
Distributive Law
Prime Factor
Forth Axiom of Equality
Braces
31. The place value which corresponds to a given position in a number is determined by the
To separate a number into prime factors
its the sum of its digits is divisible by 3
Base of the number system
the number formed by the three right-hand digits is divisible by 8
32. 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 -
even and the sum of its digits is divisible by 3
which shows that with complex numbers - a solution exists to every polynomial equation of degree one or higher.
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
Base of the number system
33. Sum
addition
Associative Law of Addition
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
34. The finiteness or not of the number of rational or integer points on an algebraic curve
Digits
the genus of the curve
consecutive whole numbers
difference
35. Implies a collection or grouping of similar - objects or symbols.
Factor of the given number
multiplication
negative
Set
36. 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
Number fields
In Diophantine geometry
an equation in two variables defines
consecutive whole numbers
37. 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).
consecutive whole numbers
Commutative Law of Addition
Equal
38. 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
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
To separate a number into prime factors
the sum of its digits is divisible by 9
subtraction
39. 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
Associative Law of Addition
The real number a of the complex number z = a + bi
Complex numbers
40. 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
subtraction
its the sum of its digits is divisible by 3
an equation in two variables defines
Positional notation (place value)
41. 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
constant
righthand digit is 0 or 5
negative
In Diophantine geometry
42. Product
consecutive whole numbers
negative
multiplication
Digits
43. A number that has factors other than itself and 1 is a
addition
Composite Number
algebraic 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.
44. 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.
subtraction
addition
Associative Law of Addition
Algebraic number theory
45. Increased by
Algebraic number theory
addition
the genus of the curve
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
46. 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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47. Number T increased by 9
Commutative Law of Addition
C or
T+9
16(5+R)
48. A letter tat represents a number that is unknown (usually X or Y)
Definition of genus
variable
Using the visualization of complex numbers in the complex plane - the addition has the following geometric interpretation:
1. The associative laws of addition and multiplication. 2. The commutative laws of addition and multiplication. 3. The distributive law.
49. Sixteen less than number Q
subtraction
Q-16
Place Value Concept
division
50. The number touching the variable (in the case of 5x - would be 5)
Composite Number
coefficient
Positional notation (place value)
Numerals