MESL (YELLOW BOOK 1.2) Flashcards
In the proportion of four quantities, the first and the fourth terms are referred to as the
Extremes
The first term of a ratio is called ____.
Antecedent
The second term of a ratio is called ____.
Consequent
The ____ is the square root of the product of the extremes.
Mean proportional
If the means of a proportion are equal, their common value is called
Mean proportional
The theorem that in every arithmetic progression a, a+d, a=2d, …., where a and d are relatively prime
Dirichlet theorem
A statement that one mathematical expression is greater than or less than another is called ___.
Inequality
If an equality is true for all values of the variable, it is a/an
Absolute inequality
If the same number is added to both sides of an inequality, the inequality
Is preserved
An inequality is preserved if both sides are multiplied by
A positive number
An inequality is reversed if both sides are multiplied by
-1
Division of a population or same into two groups based either on measurable variables (e.g., age under 18, age over 180) or on attributes (e.g., male, female)
Dichotomy
If there are as many equations as unknowns, the matrix of the coefficient is a
Square matrix
A 3 x 2 matric can be multiplied to a
2 x 5 matrix
A method of solving linear equation with several unknowns simultaneously using determinants
Cramer’s rule
Using Cramer’s rule, the determinant of the coefficient is always the
Denominator of a quotient
In any square matrix, when the elements of any two rows are exactly the same (i.e., row 1 = row 2 or row 1 = row 3, or row 2 = row 3…) the determinant is
Zero
When the corresponding elements of two rows of a determinant are proportional. Then the value of the determinant is
Zero
An array of m x n which represent a single number and is composed of elements in rows and columns is known as
Matrix
When two rows are interchanged in position, the value of the determinant will
Be multiplied by -1
If every elements of a row (or column) are multiplied by a constant k, then the value of the determinant is
Multiplied by k
If two rows of a determinant are interchanged, the determinant
Changes sign
Which of the following cannot be an operation of matrices?
Division
An irrational number which is a root of a positive integer of fraction is called
Surd
The symbol n√b means the principal nth root “n” is called the
Index
In the preceding item, “b” is called the
Radicand
The symbol √ is called
a. Radical
b. Radical symbol
c. Index
d. A or B
d. A or B
The rules combining radicals follow the rules for
Fractional exponents
When a number has both a positive and negative nth root, the principal nth root is
The positive root
Every positive number has ___ nth root.
Two
The principal nth root of a negative number is the negative root if n is
Odd
To eliminate a surd, multiply is by its
Conjugate
A radical which is equivalent to a non-terminating and non-repeating decimal.
Surd
A radical expressing an irrational number is called a
Surd
A surd which contains at least one rational term
Mixed surd
A surd that contains no rational number, that is, all its factors or terms are surds, example √3 or √3 + √2
Pure surd
The process of removing the surd from a denominator is to
Rationalize the denominator
A quadratic equation of the form ax2 + c = 0, without the coefficient of the first-degree term is a/an
Pure quadratic equation
In the quadratic equation Ax2 + Bx + C = 0, when two roots are multiplied, the result is
C/A
In the quadratic equation Ax2 + Bx + C = 0, when two roots are added, the result is
-B/A
If the discriminant of a quadratic equation is less than zero, the equation has
No real root
When can we say that the two roots of a quadratic equation are equal?
When the discriminant is zero
What is the discriminant of the quadratic equation Ax2 + Bx + C = 0?
B^2-4AC
What determines the nature of the roots of a quadratic equation?
Discriminant
The real roots of a cubic equation are the
Points of intersection of the graph of the equation with the x-axis.
For a cubic equation, if the discriminant is equal to zero, we produce
Three real root, of which two are unequal
For a cubic equation, we produce three distinct roots only if the discriminant is
Less than zero
For a cubic equation, the discriminant is found to be greater than zero. The roots are
One real and two conjugate complex roots
A succession of numbers in which one number is designated at first, another as third and so on is called
Sequence
And indicated sum of a1 + a2 +a3 …. Is called
Series
The repeating decimal 0.3333 is a geometric series of a1= 0.3 and r=
1/10
A progression whose reciprocal forms and arithmetic progression
Harmonic progression
the number between two geometric terms
Geometric mean
The sum of the first terms of a series is called the nth ____.
Partial sum
The sum of the terms of an arithmetic progression.
Arithmetic series
The harmonic mean between a and b
2ab/ a + b
The arithmetic mean of a and b is ____.
(a + bi)
(a+b)/2
(a+b)/2
The geometric mean of a and b is
Square root of ab
Are numbers which can be drawin as dots and arranged un triangle shape (i.e., 1, 3, 6, 10, 15, 21…)
Triangular number
A figure numbers which can be drawn as dots and arranged in square shape (i.e., 1, 4, 9, 16, 25 …)
Square members of the pyramid
A sequence 1, 5, 12, 22, 35
Pentagonal numbers
A sequence 1, 8, 27, 64, 156, 216 … is
Cubic numbers
A sequence 1, 4, 10, 20, 35, 56 …
Tetrahedral numbers
A sequence of numbers where every term is obtained by adding all of the preceding terms a square series such as 1, 5, 14, 30, 55, 91
Pyramid numbers
A sequence of numbers where the number is equal to the sum of the two preceding numbers such as 1, 1, 2, 3, 5, 68, 13, 21 … is called ___.
Fibonacci numbers
What is the multiplicative inverse of the integer 5?
1/5
What is the additive identity element?
Zero
What is the multiplicative identity element?
1
The number 0 such that 0 = a = a for all a is called the
“Additive identity”
The additive inverse of a complex number is a +bi, is
-a-bi
All real numbers have been additive inverse, commonly called ___.
Opposites
All real numbers except zero have multiplicative inverses commonly called
Reciprocals
The number zero has no ___.
Multiplicative inverse
What is the additive inverse of a +bi
-a-bi
What is the multiplicative inverse of a+bi
((a/)a2 +b2)-bi/(a2 + b2)
Which of the following is not a property of a binomial expansion ( x +y ) n ?
Number of terms = n – 1
A triangular array numbers forming the coefficient of the expansion of a binomial is called
Pascal’s triangle
The coefficient of the second term of the expansion of (x + y) n is always equal to n
N
How is the number in Pascal’s triangle obtained?
By getting the sum of the two numbers directly abc it.
If the sign between the terms of the binomial is negative, its expansion will have the signs which are
Alternate starting with positive
In the absence of the Pascal’s triangle, the coefficient of any term of the binomial expansion can be obtained by dividing the product of coefficient of the preceding tern if the exponent of x of the preceding team by ___ of the preceding term
The exponent of y + 1
The fundamental principle of counting states that id one thing can be dust 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 x n
Is the arrangement of the object in specific order
Permutation
Is the arranged of objects regardless of the order they have arranged
Combination
The shifting of the entire order sequence of elements one or more steps forward to backward – the first element taking the position of the last, or vice versa without changing the order of the elements in the sequence is called
Cyclic permutation
The number of elements in the collection being permutated is the ___ of the permutation.
Degree
The ratio of the successful outcomes over the total possible outcomes is called
Probability
The value of probability of any outcome will never be equals to or no exceed
0.75
If two events A and B are mutually exclusive events and the probability that A will happened is Pa and the probability that B will happen is Pb, then the probability that A or B happen is
Pa + Pb
A and B are two independent events. The probability that A can occurs is p and that for both A and B to occurs is q. The probability that event 8 can occurs us
q/p
If the probability of occurrences pf a Pia, what is the probability that will not occur
Ans. 1-Pa
In statistics a pictorial description of the probability concepts of independent and dependent events is called
Venn diagram
The difference between the highest score and the lowest score in the distribution
Range
The second power of the standard deviation is called
Variance
A graph of cumulative frequency distribution plotted at class marks and connected by straight lines.
Ogive
A point in the distribution of scores at which 50 percent of the scores fall below and 50 percent of the scores fail above
Median
A number that occurs most frequent in a group of numbers
Mode
The difference between an approximate value of a quantity and its exact value or true value.
Absolute error
If the quotient of the absolute error divided by the true value
Relative error
Refers to a value which is not exact but might accurate enough for some specific considerations
Approximate value
