Algebra Flashcards
(134 cards)
1
Q
The part of theorem which is assumed to be true
a. corollary
b. postulate
c. hypothesis
d. conclusion
A
Hypothesis
2
Q
A statement of truth which follows with little or no proof from the theorem
a. corollary
b. postulate
c. axiom
d. conclusion
A
Corollary
3
Q
A statement of which is admitted without proof
a. axiom
b. postulate
c. theorem
d. conclusion
A
axiom
4
Q
Refers to the construction of drawing lines and figures the possibility of which is admitted without proof
corollary
postulate
theorem
hypothesis
A
postulate
5
Q
a proved proposition which is useful mainly as a preliminary to the proof a theorem.
lemma
postulate
hypothesis
corollary
A
lemma
6
Q
a mathematical statement which has neither been proved nor denied by counterexamples
fallacy
theorem
conjecture
paradox
A
conjecture
7
Q
statements that are accepted without discussion or proof are called axioms. the word “axiom” comes from the greek “axioma” which means
worth
correct
true
perfect
A
worth
8
Q
In mathematical and other fields of logical reasoning, axioms are used as a basis for the formulation of statements called:
lemma
hypothesis
postulate
theorem
A
hypothesis
9
Q
“the product of two or more number is the same in whatever order they are multiplied.” this refers to
Associative law of addition
Associative law of multiplication
commutative law of multiplication
distributive law of multiplication
A
commutative law of multiplication
10
Q
if a = b, then b can replace a in any equation. this illustrates what law of identity?
Reflexive law
transitive law
law of symmetry
substitution law
A
substitution law
11
Q
if a = a, then it illustrates what law of identity
Reflexive law
transitive law
law of symmetry
substitution law
A
Reflexive law
12
Q
if a = b, and b = c, then a = c. this illustrates:
Reflexive law
transitive law
law of symmetry
substitution law
A
transitive law
13
Q
the axiom which relates addition and multiplication is the ______ law.
Commutative
distributive
associative
none of the above
A
distributive
14
Q
any combination of symbols and numbers related by the fundamental operation of algebra is called a/an:
equation
term
algebraic expression
algebraic sum
A
algebraic expression
15
Q
the algebraic expression consisting a sum of any number of terms is called a:
multinomial
binomial
summation
monomial
A
multinomial
16
Q
an equation which is satisfied by all values of the variable for which the members of the equation defined is known as
linear equation
conditional equation
rational equation
irrational equation
A
rational equation
17
Q
an equation in which some or all of the known quantities are represented by letters is called:
redundant equation
linear equation
literal equation
defective equation
A
literal equation
18
Q
equation in which the variable appear under the radical symbol
irradical equation
quadratic equation
irrational equation
linear equation
A
irrational equation
19
Q
an equation which, because of some mathematical process, has required an extra root is sometimes called as:
redundant equation
linear equation
literal equation
defective equation
A
redundant equation
20
Q
an algebraic expression consisting of one term
monomial
linear
binomial
monomode
A
monomial
21
Q
in algebra, this consist of products and quotients of ordinary numbers and letter which represent number
expression
equation
term
coefficient
A
term
22
Q
an expression of two terms is called
polynomial
binomial
duomial
all of the above
A
binomial
23
Q
the degree of a polynomial or equation is the:
maximum exponent
exponent of the first variable
maximum sum of exponents
maximum exponent of x
A
maximum sum of exponents
24
Q
any fraction which contains one or more fraction in wither numerator or denominator, or both is called:
compound fraction
complex fraction
composite fraction
all of the above
A
complex fraction
25
a number that consist of an integer part(which may be zero) and a decimal part less than unity that follows the decimal marker, which may be a point or a comma
proper fraction
decimal fraction
improper fraction
mixed fraction
decimal fraction
26
considered as the " counting number"
integers
irrational numbers
rational numbers
natural numbers
natural numbers
27
a number represented by a non-terminating, non- repeating decimal
irrational number
natural number
rational number
integer
irrational number
28
the completeness axiom proved that the real number system has numbers other than:
irrational number
natural number
rational number
integer
rational number
29
venn diagram for sets was introduced by:
venn weierstrass
darbooux venn
venn euler
john venn
john venn
30
two integer numbers are said to be ________ if each is the sum of all possible divisors of the other
perfect number
amicable number
defective number
fermat's number
amicable number
31
what is another name for amicable numbers?
compatible
fermats
friendly
inconsistent
friendly numbers
32
prime numbers that appear in pair and differs by 2 are called:
mersenne primes
twin primes
prime number theorem
pseudo primes
twin primes
33
a succession of numbers in which one number is designated as first, another as 2nd, another as 3rd so on is called:
series
arrangement
sequence
sequence
34
an indicated sum a1 + a2 +a3 +.... is called
series
arrangement
sequence
partial sum
series
35
a progression whose reciprocal forms an arithmetic progression:
arithmetic mean
geometric progression
harmonic means
harmonic progression
harmonic progression
36
the number between two geometric terms
means
geometric means
arithmetic means
median
geometric meanst
37
he sum of the first n terms of a series is called the nth
sum
arrangement
sequence
partial sum
partial sum
38
the sum of the terms of an arithmetic progression
arithmetic means
arithmetic series
arithmetic sequence
all of these
arithmetic series
39
are number which can be drawn as dots and arranged in triangular shape
triangular number
pentagonal numbers
square numbers
tetrahedral numbers
triangular number
39
a figure numbers which can be drawn as dots and arranged in square shape
cubic number
pyramid numbers
square numbers
pentagon numbers
square numbers
40
the fundamental principle of counting states that if one thing can be done in "m" different ways and another thing can be done in "n" different ways, then the two things can be done in ________ different ways
m+n
mxn
m!+n!
mn
mxn
41
is the arrangement of the objects in specific order
permutation
probability
combination
all of the above
permutation
42
a sequence of numbers where the succeeding terms is greater than the preceding term.
isometric series
dissonant series
divergent series
convergent series
divergent series
43
the process of reasoning where in a final conclusion is obtained by experimental method.
Mathematical deduction
Mathematical conversion
Mathematical opposition
Mathematical induction
Mathematical deduction
44
the set of all subsets of a given set, containing the empty set and the original set.
intersection
proper subset
power set
improper subset
power set
45
an integer number that is equal to the sum of all its possible divisor except the number itself is called:
amicable number
defective number
perfect number
redundant number
perfect number
46
an integer the sum of all its possible divisors except the number itself is greater than the integer is called:
amicable number
defective number
perfect number
abundant number
abundant number
47
an integer the sum of all its possible divisors except the number itself is less than the integer is called:
amicable number
defective number
friendly number
abundant number
defective number
48
a statement of truth which is admitted without proof
axiom
postulate
theorem
corollary
axiom
49
a sequence 1,5 ,12 ,22 ,35 ,.... is known as
oblong numbers
cubic numbers
pentagonal numbers
pyramid numbers
pentagonal numbers
50
the part of theorem which is assumed to be true
hypothesis
postulate
conclusion
corollary
hypothesis
51
a statement containing one or more variables and having the property that it becomes either true or false when the variables are given specific values from their domains
solution
open sentence
problem
worded problem
open sentence
52
a number which can be expressed as a quotient of two integers (division of zero excluded) is called
irrational number
imaginary
rational
real
rational
53
a prime number has exactly how many divisor
1
2
3
4
2
54
a prime number is an integer greater than 1 which has
-1 as its only positive divisor
-itself as its only divisor
-1 and itself as its only positive divisor
-1 and it additive inverse as its only positive divisor
1 and itself as its only positive divisor
55
a composite number has at least _______ divisor
1
2
3
4
3
56
two natural numbers a and b are ______. if their greatest common divisor is 1.
relatively prime
equal
relative composite
reciprocal
relatively prime
57
numbers used to count the objects or ideas in a given collection
cardinal
ordinal
irrational
numerals
cardinal
58
what is the smallest perfect number possible
1
6
12
8
6
59
all perfect numbers are
even
prime
composite
odd
even
60
what is the smallest pair of friendly number
180 and 190
200 and 120
220 and 284
220 and 264
220 and 284
61
" every even integer greater than 2 can be written as the sum of two primes" this is known as :
fermat's last theorem
prime number theorem
goldbach conjecture
mersenne primes
goldbach conjecture
62
" every sufficiently large off number can be expressed as a sum of three prime numbers" this is known as :
Goldbach conjecture
Pascal's law
Vinogradov's theorem
Mersenne'e theorem
Vinogradov's theorem
63
the term " ratio" comes from latin verb "ratus" meaning
to divide
to get the mean
to estimate
to make a proportion
to estimate
64
the second term of a ratio is called
antecedent
mean
consequent
extreme
consequent
65
if the mean of proportion are equal, their common value is called
mean
mean proportional
extreme
extreme proportional
mean proportional
66
the theorem that in every arithmetic progression a, a + d,a + 2d, ....., where a and b are relatively prime.
Fibonacci theorem
lejeune theorem
gauss theorem
dirichlet theorem
dirichlet theorem
67
if the same number is added to both sides of an inequality, the inequality is
becomes negative
is reversed
becomes positive
is preserved
is preserved
68
an inequality is preserved if both sides are multiplied by
0
positive number
-1
negative number
positive number
69
an inequality is reserved if both sides are multiplied by
0
positive number
-1
negative number
positive number
70
division of a population or same into two groups based either on measurable variables or on attributes
decomposition
deviance
denomination
dichotomy
dichotomy
71
an irrational number which is a root of a positive integer of fraction is called
radical
radix
surd
radicant
surd
72
the rules of combining radicals follows the rules for
signed numbers
fractional exponents
logarithms
factoring
fractional exponents
73
when the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is
one
indeterminate
infinite
zero
zero
74
an array of MxN quantites which represent a single number and is composed of elements in rows and columns is known as
transpose of a matrix
co-factor of a matrix
determinant
matrix
matrix
75
to eliminate a surd, multiply it by its
square
cube
reciprocal
conjugate
conjugate
76
A radical which is equivalent to a non-terminating and non-repeating decimal
irrational number
surd
natural number
transcendental number
surd
77
what determines the nature of the roots of a quadratic equation
coefficient
factors
discriminant
all of the above
discriminant
78
if the discriminant of a quadratic equation is less than zero, the equation has
no real roots
two real roots
one root only
none of the above
no real roots
79
when can we say that two roots of a quadratic equation are equal
when the discriminant is zero
80
a sequence 1, 4, 10,20, 35, 56 .... is known as
pyramid numbers
tetrahedral numbers
cubic numbers
square numbers
tetrahedral numbers
81
a sequece of numbers where that number is equal to the sum of the two preceding numbers such as 1, 1, 2, 3, 5, 8, 13, 21 ... is called
fermat's numbers
gaussian numbers
fibonacci numbers
archimedean numbers
fibonacci numbers
82
all real numbers have additive inverse, commonly called
reciprocals
opposites
addends
equivalent
opposites
83
all real numbers except 0 have multiplicative inverses, commonly called
equivalents
factors
opposites
reciprocals
reciprocals
84
the number zero has no
multiplicative inverse
85
if the sign between the terms of the binomial is negative, its expansion will have signs which are
all positive
alternate starting with positive
all negative
alternate starting with negative
alternate starting with positive
86
when the factors of a product are equal, the product is called a/an ________ of the repeated factor
coefficient
identity
power
algebraic sum
power
87
a symbol holding a place for an unspecifies constant is called
arbitrary constant
variable
parameter
all of the above
all of the above
88
the sum of any point number and its reciprocal is
always less than 2
always equal to 2
always greater than 2
always equal to the number's additive inverse
always greater than 2
89
what is the absolute value of a number less than one but greater than negative one raised to exponent infinity
infinity
zero
one
indeterminate
zero
90
the absolute value of a non-zero number is
always zero
always positive
always negative
sometimes zero and sometimes positive
always positive
91
a polynomial which is exactly divisible by two or more polynomials is called
least common denominator
factors
common multiple
binomial
common multiple
92
a polynomial with real coefficient can be factored into real linear factors and irreducible _____________ factors.
linear
quadratic
cubic
repeated
quadratic
93
if the degree of the numerator is one more than the degree of the denominator, the quotient is a _________ polynomial
linear
quadratic
cubic
quartic
linear
94
for every law of addition and subtraction, there is a parallel law for multiplication and division, except division by
negative values
zero
one
positive values
zero
95
refers to the numbers which are not the roots of any algebraic equation
irrational numbers
imaginary numbers
transcendental numbers
composite
transcendental numbers
96
all number multiplied by ____ equals unity
negative of the number
conjugate
one
its reciprocal
its reciprocal
97
when the absolute error is divided by the true value, the quotient is called as
relative error
residue
gradient
slope
relative error
98
a set of numbers arrange in a definite order.
permutation
combination
progression
mathematical sequence
permutation
99
if the roots of an equation are zero then, how do you classify the solutions?
extranous solutions
conditional solutions
trivial solutions
ambiguous solutions
trivial solutions
100
a value not exact but might be accurate enough for some specific consideration
interpolation
assumption
eigen value
approximation
approximation
101
how do you call the opposite of the prefix of nano
peta
tera
giga
hexa
giga
102
the ____ of the permutation is the number of elements in the collection belong permuted.
index
sequence
order
degree
degree
103
this is the measure of central tendency defined as the most frequent score. how do you call this measure of central tendency
median
mode
mean
deviation
mode
104
the number of permutations of n different things taken n at a time is:
(n-1)!
(n+1)!
n x n
n!
n!
105
any number expressed in place-value notation with base 12 is known as
duodecimal
deonite
decile
dedekind
duodecimal
106
the number of cyclical permutations of n different things taken at a time is:
(n-1)!
(n+1)!
n x n
n!
(n-1)!
107
a group of all or of any part of the things without regard to the order of the things in this group is:
permutation
combination
progression
induction
combination
108
this is use for expressing wavelengths of light or ultraviolet radiation with a unit or length equal to 10^(-10)metre.
mersenne number
midae
light year
angstrom
angstrom
109
two integer number are said to be ___________ if each is the sum of all possible divisors of the other
perfect numbers
amicable numbers
defective numbers
fermta's number
amicable numbers
110
a prefix denoting a multiple of 10 times any of the physical units of the system international.
deka
nano
hecto
exa
deka
111
this is the case of a solution of an plane triangle where the given data leads to two solutions. how do you call this case?
ambiguous case
extraneous case
quadratic case
conditional case
ambiguous case
112
a series of numbers in which each number or term is derived from the preceding number by adding a constant value to it is know as:
geometric sequence
analytical sequence
arithmetic sequence
differential sequence
arithmetic sequence
113
it is a statement that one mathematical expression is greater than or less than another.
conditional expression
inequality
interval
domain
inequality
114
an algebraic expression having two variables in it. for example, 3x + y is called
boolean algebra
matrix
elementary algebra
laplace
boolean algebra
115
a logarithm having a base of 10 is called
natural logarithm
briggsian logarithm
complex logarithm
naperian logarithm
briggsian logarithm
116
a mathematical method that combines two numbers, quantities, etc., to give a third quantity. an example is the multiplication of two numbers in arithmetic.
binary operation
trinomial
polynomial
sequence
binary operation
117
it is a high-level programming language for the computer used to express mathematical and scientific problems in a manner that resembles. english rather than computer notations
algol
cobol
pascal
aldus
algol
118
it refers to a statistical distribution having two distinct peaks of frequency distribution
bimodal
biaxial
binomial
bilingual
bimodal
119
in complex algebra, we use a diagram to represent a complex plane commonly called as:
venn diagram
argand diagram
histogram
funicular diagram
argand diagram
120
a system of units based on time, length, and mass is called _______.
absolute system
cgs system
gravitational system
mks system
mks system
121
what is the logarithm of a negative number
complex number
irrational number
real number
imaginary number
complex number
122
a sequence of numbers where every term is obtained by adding all the preceding terms a square number series such as 1,5, 14, 30 , 55,91 ....
pyramid number
euler's number
tetrahedral number
triangular number
pyramid number
123
a triangular array numbers forming the coefficient of the expansion of a binomial called
egyptian triangle
pascal's triangle
golden triangle
bermuda triangle
pascal's triangle
124
the set of all subsets of a given set, containing the empty set and original set
intersection
proper subset
power set
improper subset
power set
125
the the number of combinations of the n things r at a time is the same as the number of combination _____ at a time
n+r
nr
n/r
n-r
n-r
126
when the factors of aproduct are equal, the product is called a/an __________ of the repeated factor.
coefficient
identity
power
algebraic sum
power
127
number which cannot be expressed as a quotient of two integers
natural
rational
irrational
surd
irrational
128
what is the absolute name for zero
cipher
none
null
empty
cipher
129
it is a collection of numbers or letters used to represent a number arrange properly in rows and columns
determinant
array
matrix
equation
matrix / array
130
this is a series of sequential method for carrying out a desire procedure to solve problems.
algorithm
hypsogram
logarithm
angstrom
algorithm
131
10 to the negative power of 18 is the value of prefix:
atto
femto
micro
pico
atto
132
the whole is greater than any one of its parts. this statement is known as:
postulate
hypothesis
axiom
theorem
axiom
133
