ALEGBRA ELEMENTS Flashcards
for a give function, it is found that f(t) = f(-t). what type of symmetry does f(t) have?
a. odd symmetry
b. even symmetry
c. rotational symmetry
d. quarter-wave symmetry
even symmetry
which number has four significant figures?
a. 0.0014
b. 0.01414
c. 0.141
d. 1.4140
0.01414
naperian logarithm have a base closest to which number?
a. 2.17
b. 2.72
c. 3.14
d. 10
2.72
if the 2nd derivative of the eq. of a curve is equal to the negative of the eq. of that same curve, the curve is
a. an exponential
b. a sinusoid
c. a tangent
d. a parabola
a sinusoid
to find the angle of a triangle, given only the lengths of the sides, one would use
a. the law of cosines
b. the law of sines
c. the law of tangents
d. the inverse-square law
the law of cosines
which is true regarding the signs of the natural functions for angles between 90 and 180?
a. the tangent is positive
b. the cotangent is positive
c. the cosine is negative
d. the sine is negative
the cosine is negative
what is the inverse natural function of the cosecant?
a. secant
b. sine
c. cosine
d. cotangent
sine
the graphical presentation of a cumulative frequency distribution in a set of a statistical data is called
a. histogram
b. kurtosis
c. lepticurtic
d. ogive
Ogive
a statement of truth of which follows with little or no proof from a theorem.
a. axiom
b. hypothesis
c. corollary
d. conclusion
corollary
it is a sequence of numbers such that the successive terms differ by a constant.
a. arithmetic progression
b. infinite progression
c. geometric progression
d. harmonic progression
arithmetic progression
a frequency curve which is composed of series of rectangles constructed with the steps as the base and the frequency as the height.
a. histogram
b. ogive
c. frequency distribution
d. bar graph
histogram
if the roots of an equation are zero, then they are classified as
a. hyperbolic solution
b. zeros of function
c. extraneous roots
d. trivial solution
trivial solution
convergent series is a sequence of decreasing number or when the succeeding term is_______ the preceding term.
a. greater than
b. equal to
c. lesser than
d. none of the above
lesser than
if a=b then b=a. this illustrates what axiom in algebra?
a. symmetric axiom
b. reflexive axiom
c. transitive axiom
d. replacement axiom
symmetric axiom
A and B are independent events. the probability 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?
a. Pa-Pab
b. Pb-Pab
c. Pa x Pb
d. Pab/Pa
Pab/Pa
two or more eq. are equal if and only if they have the same
a. solution set
b. degree
c. order
d. variable set
solution set
in any square matrix, when the elements of any two rows are exactly the same, the determinant is
a. zero
b. positive integer
c. negative integer
d. unity
zero
the ratio or product of two expressions in direct or inverse relation with each other is called
a. ratio and proportion
b. means
c. extremes
d. constant of variation
constant of variation
is a sequence of terms whose reciprocals form an arithmetic progression
a. geometric progression
b. harmonic progression
c. algebraic progression
d. ratio and proportion
harmonic progression
an array of m x n quantities which represent a single number system composed of elements in rows and columns is known as
a. transposed matrix
b. cofactor of a matrix
c. matrix
d. determinant
matrix
binary number system is a system of notation for real number that uses the place value method with 2 as the base. what us another name of the binary number system?
a. binary digits
b. binumber system
c. dyadic number system
d. bits
dyadic number system
the number 0.123123123… is a/an.
a. irrational number
b. surd
c. rational number
d. transcendental
rational number
MCMXCIV is the Roman numeral equivalent to
a. 1974
b. 1984
c. 1994
d. 2994
1994
a sequence of numbers where the succeeding term is greater than the preceding term is called
a. dissonant series
b. convergent series
c. divergent series
d. isometric series
divergent series
terms that differs only in numeric coefficients are known as
a. unlike terms
b. unequal terms
c. like terms
d. similar equations
like terms
in complex algebra, we use diagram to represent complex plane commonly called
a. argand diagram
b. venn diagram
c. maxwell diagram
d. cartesian diagram
argand diagram
7+0i is
a. an irrational number
b. real number
c. imaginary number
d. a variable
real number
the number of successful outcomes divided by the number of possible outcome is
a. odd
b. combination
c. permutation
d. probability
probability
if a two digit number has x for its unit digit and y for its tens digit, the number is represented as
a. x+y
b. y-x
c. 10y+x
d. 10x-y
10y+x
a statement of truth which is admitted without proof.
a. axiom
b. theorem
c. postulate
d. corollary
axiom
the part o theorem which is assumed to be true.
a. corollary
b. hypothesis
c. postulate
d. conclusion
hypothesis
a statement of truth which follows with little or no proof from the theorem
a. corollary
b. axiom
c. postulate
d. conclusion
corollary
refers to the construction of drawing of lines and figures the possibility of which is admitted without proof.
a. corollary
b. theorem
c. postulate
d. hypothesis
postulate
a mathematical statement which has neither been proved nor denied by counterexamples.
a. fallacy
b. conjecture
c. theorem
d. paradox
conjecture
a proved proposition which is useful mainly as a preliminary to the proof of a theorem.
a. lemma
b. hypothesis
c. postulate
d. corollary
lemma
axioms are propositions of a general logical nature (about equal or unequal) while _____ are propositions concerning objects and constructions.
a. theorems
b. corollaries
c. conclusions
d. postulates
postulates
a _____ is an ancillary theorem whose result is not target for the proof.
a. postulate
b. lemma
c. hypothesis
d. conclusion
lemma
statement that are accepted without discussion or proof are called axioms. the word “axiom” comes from the Greek “axioma”. which means
a. worth
b. correct
c. true
d. perfect
worth
in mathematical and other fields of logical reasoning, axioms are used as basis for the formulation of statements called
a. lemma
b. hypothesis
c. postulate
d. theorem
hypothesis
“the product of two or more number is the same in whatever order they are multiplied”. this refers to
a. associative law of addition
b. associative law of multiplication
c. commutative law of multiplication
d. distributive law of multiplication
commutative law of multiplication
if a=b, then b can replace a in any equation. this illustrates what law of identify?
a. reflexive law
b. law of symmetry
c. transitive law
d. substitution law
substitution law
if a=a, then it illustrates what law of identity?
a. reflexive law
b. law of symmetry
c. transitive law
d. substitution law
reflexive law
if a=b, and b=c, then a=c. this illustrates
a. reflexive law
b. law of symmetry
c. transitive law
d. substitution law
transitive law
the axiom which relates addition and multiplication is the _____ law.
a. commutative
b. associative
c. distributive
d. none of the above
distributive
any combination of symbols and numbers related by the fundamental operation of algebra is called a/an.
a. equation
b. algebraic expression
c. term
d. algebraic sum
algebraic expression
the algebraic expression consisting a sum of any number of terms is called a
a. multinomial
b. summation
c. binomial
d. monomial
multinomial
an equation which is satisfied by all values of the variable for which the members of the equation defined is known as
a. linear equation
b. rational equation
c. conditional equation
d. irrational equation
rational equation
an equation in which some or all of the known quantities are represented by letters is called
a. redundant equation
b. literal equation
c. linear equation
d. defective equation
literal equation
an equation in which variable appear under the radical symbol
a. irradical equation
b. irrational equation
c. quadratic equation
d. linear equation
irrational equation
an equation which, because of some mathematical process, has required an extra root is sometimes called
a. redundant equation
b. literal equation
c. linear equation
d. defective equation
redundant equation
any equation which, because of some mathematical process, has fewer roots than its original is sometimes called as
a. redundant equation
b. literal equation
c. linear equation
d. defective equation
defective equation
an algebraic expression which can be represented as a quotient of two polynomials
a. irrational algebraic expression
b. reduced algebraic expression
c. rational algebraic expression
d. complex algebraic expression
rational algebraic expression
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.
a. solution
b. problem
c. open sentence
d. worded problem
open sentence
any algebraic term is a/an _____ term in certain representing numbers if it is consists of the product of possible integral powers of these numbers and a factor not containing them.
a. integral
b. rational
c. irrational
d. integral rational
integral rational
an equation in x and y which is not easily solved for y in terms of x is called
a. explicit
b. implicit function
c. discontinuity
d. quadratic
implicit function
the numbers which are represented with letters
a. variables
b. unknowns
c. literal numbers
d. terms
c. literal numbers
Equation whose members are equal only for certain or possibly no value of the unknown
a. conditional equations
b. inequalities
c. unconditional equations
d. temporary equations
a. conditional equations
an algebraic expression consisting of one term
a. monomial
b. binomial
c. linear
d. monomode
a. monomial
in algebra, this consists of products and quotients of ordinary numbers and letters which represent numbers
a. expression
b. term
c. equation
d. coefficient
b. term
an expression of two terms is called
a. polynomial
b. duomial
c. binomial
d. all of the above
c. binomial
the degree of polynomial or equation is the
a. maximum exponent
b. maximum sum of the exponents
c. exponent of the first variable
d. maximum exponent of x
b. maximum sum of the exponents
what is the degree of the polynomial 3x^4 y + 2x^3 z^3 - 4 y z^2
a. 6th
b. 5th
c. 4th
d. 3rd
a. 6th
any fractions which contains one or more fractions in either numerator or denominator, or both is called
a. compound fraction
b. composite fraction
c. complex fraction
d. all of the above
c. complex fraction
a common fraction with unity for numerator and a positive integer as denominator (i.e 1/n)
a. ordinary fraction
b. unit fraction
c. common fraction
d. improper fraction
b. unit fraction
if the absolute value of the numerator of a fraction is smaller than the denominator, it is called
a. proper fraction
b. improper fraction
c. decimal fraction
d. mixed number
a. proper fraction
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
a. proper fraction
b. improper fraction
c. decimal fraction
d. mixed number
c. decimal fraction
considered as the counting numbers
a. integers
b. rational numbers
c. irrational numbers
d. natural numbers
d. natural numbers
a number represented by a non-terminating, non-repeating decimal.
a. irrational number
b. rational number
c. natural number
d. integer
irrational number
the completeness axiom proved that the real number system has numbers other than
a. integers
b. rational numbers
c. natural number
d. irrational numbers
rational numbers
the concept of spread of a random variable or a set of observations
a. variance
b. standard deviation
c. dispersion
d. range
dispersion
a number containing containing a non-terminating but repeating decimal is a/an.
a. integer
b. rational number
c. natural number
d. irrational number
rational number
a positive integer which has no perfect square factor greater than 1.
a. radical expression
b. square integer
c. square integer
d. square-free integer
square-free integer
number are used to describe a
a. magnitude
b. position
c. magnitude and position
d. none of the above
magnitude and position
are symbols or combinations of symbols which describe a number.
a. numerals
b. digits
c. terms
d. notations
numerals
which of the following is not classified as an integer?
a. negative numbers
b. positive numbers
c. zero
d. imaginary numbers
imaginary numbers
when an imaginary number is raised to an even exponent, it
a. becomes infinite
b. becomes negative imaginary numbers
c. becomes relatively small number
d. becomes real number
becomes real number
the complex number is in the form of a + bi. if a=0, what do you call the resulting number?
a. absolute value of the complex number
b. pure imaginary number
c. argument
d. irrational number
pure imaginary number
for a complex number a+bi, the real number √ a^2+b^2 is _____ of the complex number.
a. absolute value
b. magnitude
c. modulus
d. all of the above
all of the above
the _____ of two complex number is found by multiplying each term of the one by every term of the other.
a. sum
b. difference
c. product
d. quotient
product
a number which can be expressed as a quotient of two integers (division of zero excluded) is called
a. irrational number
b. rational number
c. imaginary number
d. real number
rational number
a prime number has exactly how many divisors?
a. 1
b. 2
c. 3
d. 4
2
a prime number is an integer greater than 1 which has
a. 1 as its only positive divisor
b. itself as its only positive divisor
c. 1 and itself as its only positive divisors
d. 1 and its additive inverse as its only positive divisor
1 and itself as its only positive divisors
an integer which is the product of two integers, both different from 1 and -1 called
a. prime number
b. composite number
c. rational number
d. compound number
composite number
a composite number has a least _____ divisors.
a. 1
b. 2
c. 3
d. 4
3
two natural numbers a and b are ____ if their greatest common divisor is 1.
a. relatively prime
b. relatively composite
c. equal
d. reciprocal
relatively prime
numbers used to count the objects or ideas in a given collection.
a. cardinal numbers
b. irrational numbers
c. ordinal numbers
d. numerals
cardinal numbers
numbers which is used to state the position of individual objects in a sequence.
a. cardinal numbers
b. irrational numbers
c. ordinal numbers
d. numerals
ordinal numbers
an integer number that is equal to the sum of all its possible divisors except the number itself is called.
a. amicable number
b. perfect number
c. defective number
d. redundant number
perfect number
an integer the sum of all its possible divisors except the number itself is greater than the integer is called
a. abundant number
b. perfect number
c. defective number
d. amicable number
abundant number
an integer the sum of all its possible divisors except the number itself is less than the integer is called
a. abundant number
b. amicable number
c. friendly number
d. defective number
defective number
what is the smallest perfect number possible?
a. 1
b. 6
c. 12
d. 8
6
all perfect numbers are
a. even numbers
b. odd numbers
c. prime numbers
d. composite numbers
even numbers
two integer numbers are said to be _____ if each is the sum of all possible divisors of the other.
a. perfect numbers
b. defective numbers
c. amicable numbers
d. fermat’s numbers
amicable numbers
what is another name for amicable numbers?
a. compatible numbers
b. friendly numbers
c. fermats numbers
d. inconsistent numbers
friendly numbers
what is the smallest pair of friendly number?
a. 180 and 190
b. 200 and 120
c. 220 and 284
d. 220 and 264
220 and 284
prime number that appear in pair and differ by (eg. 3 and 5,11 and 13 etc.) are called
a. mersenne primes
b. prime number theorem
c. twin primes
d. pseudo primes
twin primes
every even integer greater than 2 can be written as the sum of two primes. this is known as
a. fermats last theorem
b. goldbach conjecture
c. prime number theorem
d. mersenne primes
goldbach conjecture
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
a. fundamental theorem of arithmetic
b. pseudo prime theorem
c. prime number theorem
d. mersenne’s theorem
fundamental theorem of arithmetic
every sufficiently large off number can be expresses as a sum of three prime numbers. this known as
a. goldbach conjecture
b. vinogradovs theorem
c. pascals law
d. mersennes theorem
vinogradovs theorem
the term “ratio” comes from Latin verb “ratus” meaning
a. to divide
b. to estimate
c. to get the mean
d. to make a proportion
to estimate
in the proportion of four quantities, the first and fourth terms are referred to as the
a. means
b. extremes
c. denominators
d. numerators
extremes
the first term of a ratio is called
a. antecedent
b. consequent
c. mean
d. extreme
antecedent
the second term of a ratio is called
a. antecedent
b. mean
c. consequent
d. extreme
consequent
the ____ is the square root of the product of the extremes.
a. antecedent
b. consequent
c. mean proportional
d. mean
mean proportional
if the means of a proportion are equal, their common value is called
a. mean
b. extreme
c. mean proportional
d. extreme proportional
mean proportional
the theorem that in every arithmetic progression a, a+d, a=2d,…, where a and d are relatively prime.
a. Fibonacci theorem
b. gauss theorem
c. lejeune theorem
d. dirichlet theorem
dirichlet theorem
a statement that one mathematical expression is greater than or less than another is called
a. absolute condition
b. non-absolute condition
c. inequality
d. conditional expression
inequality
if an equality is true for all values of the variable, it is a/an
a. conditional equality
b. equivalent equality
c. absolute inequality
d. non-conditional inequality
absolute inequality
if the same number is added to both sides of an inequality, the inequality
a. becomes negative
b. becomes positive
c. is reversed
d. is preserved
is preserved
an inequality is preserved if both sides are multiplied by
a. zero
b. -1
c. a positive number
d. a negative number
a positive number
an inequality is reversed if both sides are multiplied by
a. zero
b. -1
c. a positive number
d. a negative number
a positive number
division of a population or same into two groups based either on measurable variables (eg. age under 18, age over 180) or on attributes (e.g. male, female).
a. decomposition
b. denomination
c. deviance
d. dichotomy
dichotomy
a 3x2 matrix can be multiplied to a
a. 3x2 matrix
b. 3x3 matrix
c. 2x5 matrix
d. row matrix
2x5 matrix
if there are as many equations as unknowns, the matrix of the coefficient is a
a. row matrix
b. column matrix
c. square matrix
d. rectangular matrix
square matrix
a method of solving linear equation with several unknowns simultaneously using determinants
a. simpson’s rule
b. cramer’s rule
c. trapezoidal rule
d. chain rule
cramer’s rule
using cramer’s rule, the determinant of the coefficient is always is always the
a. numerator of a quotient
b. denominator of a quotient
c. the quotient itself
d. none of the above
denominator of a quotient
in any square matrix, when the elements of any tow rows are exactly the same (i.e. row 1 = row 2 or row 1 = row 3, or row 2 = row 3…), the determinant is
a. zero
b.
