MESL (YELLOW BOOK) Flashcards
For a given function, it is found that f(t) = f(-t). what type of symmetry does f(t) have?
Even symmetry
Which number has four significant figures?
0.0014
0.01414
0.141
1.4140
0.01414
Napierian logarithm have a base closest to which number?
2.72 ≈ e
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 _____.
A Sinusoid
To find the angle of a triangle, given only the lengths of the sides, one would use
The law of cosines
Which is true regarding the signs of the natural functions for angles 90 and 180?
The cosine is negative
What is the inverse natural function of the cosecant?
Sine
The graphical presentation of a cumulative frequency distribution in a set of statistical data is called ________.
Ogive
A statement of truth which allows with little or no proof from a theorem.
Corollary
It is a sequence of numbers such that the successive terms differ by a constant.
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.
Histogram
If the roots of an equation are zero, then they are classified as _______.
Trivial Solution
Convergent series is a sequence of decreasing number or when the succeeding term is ____ the preceding term.
Lesser than
If a = b then b = a. This illustrates what axiom in algebra?
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?
Pab/Pa
Two or more equations are equal if and only if they have the same:
Solution set
In any square matrix, when the elements of any two rows are exactly the same, the determinant is:
Zero
The ration or product of two expressions in direct or inverse relation with each other is called:
Constant of variation
Is a sequence of terms whose reciprocals form an arithmetic progression.
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:
Matrix
Binary number system is a system of notation for real number that uses the place value method with 2 as the base. What is the other name of the binary number system?
Dyadic number system
The number 0.123123123…. is a/am
Rational number
MCMXCIV is the roman numeral equivalent to
1994
A sequence of numbers where the succeeding term is greater than the preceding term is called
Divergent series
Terms that differ only in numeric coefficients are known as
Like terms
In complex algebra, we use diagram to represent complex plane commonly called
Argand Diagram
7 +0i is _________.
Real number
The number of successful outcomes divided by the number of possible outcomes is
Probability
If a two-digit number has x for its unit digit and y for its tens digit, the number is represented as
10y + x
A statement of truth which is admitted without proof
Axiom
The part of theorem which is assumed to be true
Hypothesis
A statement if truth which follows with little or no proof from the theorem
Corollary
Refers to the construction of drawing of lines and figures the possibility of which is admitted without proof
Postulate
The mathematical statement which has neither been proved nor denied by counterexamples.
Conjecture
A proved proposition which is useful mainly as a preliminary to the proof of a theorem
Lemma
Axioms are propositions of a general logical nature (about equal or unequal) while ____ propositions concerning objects and constructions.
Postulate
A ____ is an ancillary theorem whose result is not target for the proof.
Lemma
Statements that are accepted without discussion or proof are called axioms. The word “axiom” comes from the Greek “axioma” which means:
Worth
In mathematical and other fields of logical reasoning, axioms are used as basis for the formulation of statements called:
Hypothesis
“The product of two or more number is the same in whatever order they are multiplied.” This refers to
Commutative law of multiplication
If a = b, then b can replace a in any equation. This illustrates what law of identity?
Substitution law
If a = a, then it illustrates what law or identity?
Reflexive law
If a = b, and b = c, then a = c. This illustrates
Transitive law
The axiom which relates addition and multiplication is the _______ law.
Distributive law
Any combination of symbols and numbers related by the fundamental operation of algebra is called a/a:
Algebraic expression
The algebraic expression consisting a sum of any number of terms is called a
Multinomial
An equation which is satisfied by all values of the variable for which the members of the equation defined is known as
Rational equation
An equation in which some or all of the known quantities are represented by letters is called
Literal equation
An equation in which the variable appears under the radical symbol
Irrational equation
An equation which, because of some mathematical process, has required an extra root is sometimes called as
Redundant equation
Any equation which, because of some mathematical process, has fewer roots than its original is sometimes called as
Defective equation
An algebraic expression which can be represented as a quotient of two polynomials
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.
Open sentence
Any algebraic term is a/an ______ term in certain representing numbers if it consists of the product of possible integral powers of these numbers and a factor not containing them
Integral rational
An equation in x and y which is not easily solved for y in terms of x is called
Implicit function
The numbers which are represented with letters
Literal numbers
Equations whose members are equal only for certain or possibly no value of the unknown.
Conditional equations
An algebraic expression consisting of one term
Monomial
In algebra, this consists of products and quotients of ordinary numbers and letters which represent numbers.
Term
An expression of two terms is called _____.
Binomial
The degree of a polynomial or equation is the ____.
Maximum sum of exponents
What is the degree of the polynomial 3x4y + 2x3z3-4yz2?
6th
Any fraction which contains one or more fractions in either numerator or denominator, or both is called:
Complex fraction
A common fraction with unity for numerator and a positive integer as denominator (i.e., 1/n)
Unit fraction
If the absolute value of the numerator of a fraction is smaller than the denominator, it is called
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.
Decimal fraction
Considered as the “counting numbers.”
Natural numbers
A number represented by a non-terminating, non-repeating decimal
Irrational number
The completeness axiom proved that the real number system has numbers other than
Rational numbers
The concept of spread of a random variable or a set of observations
Dispersion
A number containing a non-terminating but repeating decimal is a/an ________.
Rational number
A positive integer which has no perfect-square factor greater than 1
Square-free integer
Numbers are used to describe a:
Magnitude and position
Are symbols or combinations of symbols which describe a number
Numerals
Which of the following is not classified as an integer?
Negative numbers
Positive numbers
Zero
Imaginary numbers
Imaginary numbers
When an imaginary number is raised to an even exponent, it:
Becomes a real number
The complex number is in the for a + bi. If a = 0, what do you call the resulting number?
Pure imaginary 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
All of the above
The _____ product of two complex numbers is found by multiplying each term of the one by every term of the other.
Product
A number which can be expressed as a quotient of two integers (division of zero excluded) is called
Rational number
A prime number has exactly how many divisors?
2
A prime number is an integer greater than 1 which has
1 and itself as its only positive divisors
An integer which is the product of two integers, both different from 1 and -1 is called
Composite number
A composite number has at least ____ divisors,
3
Two natural numbers a and b are. If their greatest common divisor is 1
Relatively prime
Numbers used to count the objects or ideas in a given collection
Cardinal numbers
Numbers which are used to stated position of individual objects in a sequence
Ordinal numbers
An integer that is equal to the sum of all its possible divisors except the number itself is called
Perfect number
An integer that is equal to the sum of all its possible divisors except the number itself is greater than the integer is called
Abundant number
An integer that is equal to the sum of all its possible divisors except the number itself is less than the integer is called
Defective number
What is the smallest perfect number possible?
6
All perfect numbers are ____.
Even numbers
Two integer numbers are said to be ___ if each is the sum of all possible divisors of the other
Amicable numbers
What is the other name for amicable numbers?
Friendly numbers
What is the smallest pair of friendly number?
220 and 284
Prime numbers that appear in pair and differ by 2 (e.g., 3 and 5, 11 and 13 etc.) are called:
Twin primes
“Every even integer greater than 2 can be written as the sum of two primes.” This is known as
Goldbach conjecture
“every positive integer greater that 1 is a prime number or can be expressed as a unique product of primes and powers.” This is known as ____.
Fundamental theorem of arithmetic
“Every sufficiently large off number can be expressed as a sum of three prime numbers.” This is known as
Vinogradov’s theorem
The term “ratio” comes from the Latin verb “ratus” meaning ____.
To estimate
