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WorksheetsYellow Book - Algebra A
Total questions: 100
Worksheet time: 50mins
For a given function, it is found that f(t) = f(-t). What type of symmetry does f(t) have?
Odd symmetry
Even symmetry
Rotational symmetry
Quarter-wave symmetry
Which number has four significant figures?
0.0014
0.01414
0.141
1.4140
Naperian logarithm have a base closest to which number?
2.17
2.72
3.14
10
If the second derivative of the equation of a curve is equal to the negative of the equation of that same curve, the curve is
An exponential
A sinusoid
A tangent
A parabola
To find the angle of triangle, given only the lengths of the sides, one would use
The law of cosines
The law of sines
The law of tangents
The inverse-square law
Which us true regarding the signs of the natural functions for angles between 90 deg to 180 deg?
The tangent is positive
The cotangent is positive
The cosine is negative
The sine is negative
What is the inverse natural function of the cosecant?
secant
sine
cosine
cotangent
The graphical presentation of a cumulative frequency distribution in a set of statistical data is called ____
histogram
kurtosis
lepticurtic
ogive
A statement of truth of which follows with little or no proof from a theorem
axiom
hypothesis
corollary
conclusion
It is a sequence of numbers such that the successive terms differ by a constant.
arithmetic progression
infinite progression
geometric progression
harmonic progression
A frequency curve which is composed of series of rectangles constructed with the steps as the base and the frequency as the height.
histogram
ogive
frequency of distribution
bar graph
If the roots of an equation are zero, then they are classified as
hyperbolic solution
zeros of function
extraneous roots
trivial roots
Convergent series is a sequence of decreasing number or when the succeeding term is ____ the preceding term.
greater than
equal to
lesser than
none of the above
If a = b then b = a. This illustrates what axiom in algebra?
symmetric axiom
reflexive axiom
transitive axiom
replacement axiom
A and B are independent events. The probabilty that event A will occur is Pa and the probability that A and B will occur is Pab. From these two statements, what is the probability that event B will occur?
Pa - Pb
Pb - Pab
Pa x Pb
Pab/Pa
Two or more equation are equal if and only if they have the same
solution set
degree
order
variable set
In any square matrix, when the elements of any two rows are exactly the same, the determinant is
zero
positive integer
negative integer
unity
The ratio or product of two expressions in direct or inverse relation with each other is called
ratio and proportion
means
extremes
constant of variation
Is a sequence of terms whose reciprocals form an arithmetic progression?
geometric progression
harmonic progression
algebraic progression
ratio and proportion
An array m x n quantities which represent a single number system composed of elements in rows and columns is known as
transposed matrix
cofactor of a matrix
matrix
determinant
Binary number system is a system of notation for real number that uses the place method with 2 as the base, what is another name of binary number system
binary digits
binumber system
dyadic number system
bits
The number 0.123123123…. is a/an
irrational number
surd
rational number
transcendental
MCMXCIV is the roman numeral equivalent to
1974
1984
1994
2994
A sequence of numbers where the succeeding term is greater than the preceding term is called
dissonant series
convergent series
divergent series
isometric series
Terms that differs only in numeric coefficients are known as
unlike terms
unequal terms
like terms
similar equations
In complex algebra, we use diagram to represent complex plane commonly called
Argand diagram
Venn diagram
Maxwell diagram
Cartesian diagram
7 + 0i is?
an irrational number
real number
imaginary number
a variable
The number of successful outcomes divided by the number of possible outcomes is
odd
combination
permutation
probability
If a two digit number has x for its unit digit and y for its tens digit, the number is represented as
x + y
y – x
10y + x
10x – y
A statement of truth which is admitted without proof
axiom
theorem
postulate
corollary
The part of theorem which is assumed to be true
corollary
hypothesis
postulate
conclusion
A statement of truth which follows with little or no proof from the theorem
corollary
axiom
postulate
conclusion
Refers to the construction of drawing of lines and figures the possibility of which is admitted without proof
corollary
theorem
postulate
hypothesis
A mathematical statement which has neither been proved nor denied by counterexamples
fallacy
conjecture
theorem
paradox
A proved proposition which is useful mainly as preliminary to the proof of a theorem
lemma
hypothesis
postulate
corollary
Axioms are propositions of a general logical nature (about equal or unequal ) while ______ are propositions concerning objects and constructions.
theorems
corollaries
conclusions
postulates
A ______ is an ancillary theorem whose results is not for the proof
postulate
lemma
hypothesis
conclusion
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
In mathematical and other fields of logical reasoning, axioms are used as basis for the formulation of statements called
lemma
hypothesis
postulate
theorem
“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
If a = b, then b can replace a in any equation. This illustrates what law of identity?
reflexive law
law of symmetry
transitive law
substitution law
If a = a , then it illustrates what law of identity?
reflexive law
law of symmetry
transitive law
substitution law
If a = b and b = c , then a = c this illustrates
reflexive law
law of symmetry
transitive law
substitution law
The axiom which related addition and multiplication is the ______ law
commutative
associative
distributive
none of the above
Any combination of symbols and numbers related by the fundamental operation of algebra is called a/an
equation
algebraic expression
term
algebraic sum
The algebraic expression consisting of a sum of any number of terms is called a
multinomial
summation
binomial
monomial
An equation which is satisfied by all values of the variables for which the members of equation defined is known as
linear equation
rational equation
conditional equation
irrational equation
An equation in which some or all of the known quantities are represented by letters is called
redundant equation
literal equation
linear equation
irrational equation
An equation in which the variable appear under the radical symbol
irradical equation
irrational equation
quadratic equation
linear equation
An equation which, because of some mathematical process, has required an extra root is sometimes called as
redundant equation
literal equation
linear equation
defective equation
Any equation which, because of some mathematical process, has fewer roots than its original is sometimes called as
redundant equation
literal equation
linear equation
defective equation
An algebraic expression which can be represented as a quotient of two polynomials
irrational algebraic equation
reduced algebraic expression
rational algebraic equation
complex algebraic equation
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
problem
open sentence
worded problem
Any algebraic term is a/an __________ term in certain representing numbers if it consists of the products of possible integral powers of these numbers and a factor not containing them.
integral
rational
irrational
integral rational
An equation in x and y which is not easily solved for y in terms of x is called
explicit
implicit function
discontinuity
quadratic
The number which are represented with letters.
variables
unknowns
literal numbers
terms
Equations whose members are equal only for certain or possibly no value of the unknown.
conditional equations
inequalities
unconditional equations
temporary equations
An algebraic expression consisting one term.
monomial
binomial
linear
monomode
In algebra, this consists of products and quotients of ordinary numbers and letters which represent numbers.
expression
term
equation
coefficient
An expression of two terms is called
polynomial
duomial
binomial
all of the above
The degree of a polynomial or equation is the
maximum exponent
maximum sum of exponents
exponent of the first variable
maximum exponent of x
What is the degree of the polynomial 3x4y + 2x3z3 – 4yz2 ?
6th
5th
4th
3rd
Any fraction which contains one or more fractions in either numerator or denominator, or both is called
compound fraction
composite fraction
complex fraction
all of the above
A common fraction with unity for numerator and a positive integer as denominator
(i.e. 1/n)
ordinary fraction
unit fraction
common fraction
improper fraction
If the absolute value of the numerator of a fraction is smaller than the denominator, it is called
proper fraction
improper fraction
Decimal fraction
mixed number
A number that consists 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
improper fraction
Decimal fraction
mixed number
Considered as the “counting numbers”
integers
rational numbers
irrational numbers
natural numbers
A number represented by a non-terminating, non-repeating decimal.
irrational number
rational number
natural number
integer
The completeness axiom proved that the real number system has numbers other than
integers
rational numbers
natural numbers
irrational numbers
The concept of spread of a random variable or a set of observations.
variance
standard deviation
dispersion
range
A number containing a non-terminating but repeating decimal is a/an
integer
rational number
natural number
irrational number
A positive integer which has no perfect-square factor greater than 1.
radical expression
square integer
square integer
square-free integer
Numbers are used to describe a
magnitude
position
magnitude and position
none of the above
Are symbols or combinations of symbols which describe a number.
numerals
digits
terms
notations
Which of the following is not classified as an integer?
negative numbers
positive numbers
zero
imaginary numbers
When an imaginary number is raised to an even exponent, it
becomes infinite
becomes negative imaginary number
becomes relatively small number
becomes real number
The complex number is in the form of a + bi. If
a = 0, what do you call the resulting number?
absolute value of the complex number
pure imaginary number
argument
irrational number
For a complex number a + bi, the real number
(a2+b2) is __________ of the complex number.absolute value
magnitude
modulus
all of the above
The ________ of two complex number is found by multiplying each term of the one by every term of the other.
sum
difference
product
quotient
A number which can be expressed as a quotient of two integers (division of zero is excluded) is called
irrational number
rational number
imaginary number
real number
A prime number has exactly how many divisors?
3
1
2
4
A prime number is an integer greater than 1 which has
1 as its only positive divisor
itself as only positive divisor
1 and itself as its only positive divisors
1 and its additive inverse as its only positive divisor
An integer which is the product of two integers, both different from 1 and -1 is called
prime number
composite number
rational number
compound number
A composite number has at least ____ divisors.
1
2
3
4
Two natural numbers a and b are ________. If their greatest common divisor is one.
relatively prime
relatively composite
equal
reciprocal
Number used to count the objects or ideas in a given collection.
cardinal numbers
irrational numbers
ordinal numbers
numerals
Numbers which is used to state the position of individual objects in a sequence.
cardinal numbers
irrational numbers
ordinal numbers
numerals
An integer number that is equal to the sum of all its possible divisors except the number itself is called
amicable number
perfect number
defective number
redundant number
An integer the sum of all its possible divisors except the number itself is greater than the integer is called
abundant number
perfect number
defective number
amicable number
An integer the sum of all its possible divisors except the number itself is less than the integer is called
abundant number
amicable number
friendly number
defective number
What is the smallest perfect number possible?
1
6
12
8
All perfect numbers are
even numbers
odd numbers
prime numbers
composite numbers
Two integer numbers are said to be ____ if each is the sum of all possible divisors of the other.
perfect numbers
defective numbers
amicable numbers
Fermat’s numbers
What is another name for amicable numbers?
compatible numbers
friendly numbers
Fermats numbers
Inconsistent numbers
What is the smallest pair of friendly number?
180 and 190
200 and 120
220 and 284
220 and 264
Prime numbers that appear in pair and differ by 2 (e.g. 3 and 5, 11 and 13 etc.) are called
Mersenne primes
prime number theorem
twin primes
pseudo primes
“Every even integer greater than 2 can be written as the sum of two primes”. This is known as
Fermat’s last theorem
Goldbach conjecture
Prime number theory
Mersenne primes
“Every positive integer greater than 1 is a prime or can be expresses as a unique product of primes and powers”. This is known as
Fundamental theorem of arithmetic
Pseudo prime theorem
Prime number theorem
Mersenne’s Theorem
“Every sufficiently large off number can be expresses as a sum of three prime numbers” this is known as
Goldbach conjecture
Vinogradov’s theorem
Pascal’s Law
Mersenne’e theorem
The term “ratio” comes from Latin verb “ratus” meaning
to divide
to estimate
to get the mean
to make a proportion
