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WorksheetsYellow Book - Algebra B
Total questions: 100
Worksheet time: 50mins
In the proportion of four quantities, the first and fourth terms are referred to as the
means
extremes
denominators
numerators
The first term of a ratio is called
antecedent
consequent
mean
extreme
The second term of a ratio is called
antecedent
mean
consequent
extreme
The _____ is the square root of the product of the extremes.
antecedent
consequent
mean proportional
mean
If the means of a proportion are equal, their common value is called
mean
extreme
mean proportional
extreme proportional
The theorem that in every arithmetic progression a, a + d, a = 2d,…, where a and d are relatively prime.
Fibonacci theorem
Gauss theorem
Lejeune theorem
Dirichlet Theorem
A statement that one mathematical expression is greater than or less than another is called
absolute condition
non-absolute condition
inequality
conditional expression
If an equality is true for all values of the variable, it is a/an
conditional inequality
equivalent inequality
absolute inequality
non-conditional inequality
If the same number is added to both sides of an inequality, the inequality
becomes negative
becomes positive
is reversed
is preserved
An inequality is preserved if both sides are multiplied by
zero
– 1
a positive number
a negative number
An inequality is reversed if both sides are multiplied by
zero
– 1
a positive number
a negative number
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).
decomposition
denomination
deviance
dichotomy
A 3 x 2 matrix can be multiplied to a
3 x 2 matrix
3 x 3 matrix
2 x 5 matrix
row matrix
If there are as many equations as unknowns, the matrix of the coefficient is a
row matrix
column matrix
square matrix
rectangular matrix
A method of solving linear equation with several unknowns simultaneously using determinants.
Simpson’s rule
Cramer’s rule
Trapezoidal rule
Chain rule
Using Cramer’s rule, the determinant of the coefficient is always the
numerator of a quotient
denominator of the quotient
the quotient itself
none of the above
In any square matrix, when the elements of any two rows are exactly the same (i.e. row 1 = row 2 = row 3, or row 2 = row 3…), the determinant is
zero
positive integer
negative integer
unity
When the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is
one
indeterminate
infinite
zero
An array of m x n quantities which represent a single number and is composed of elements in rows and columns is known as
transpose of a matrix
determinant
co-factor of a matrix
matrix
When two rows are interchanged in position, the value of the determinant will
remain unchanged
be multiplied by – 1
become zero
become infinite value
If every elements of a row (or column) are multiplied by a constant, k, then the value of the determinant is
multiplied by – k
zero
one
multiplied by k
If two rows of a determinant are interchange, the determinant
changes sign
changes sign and value
remains unchanged
becomes the inverse of the former
Which of the following cannot be an operation of matrices?
addition
subtraction
multiplication
division
An irrational number which is a root of a positive integer of fraction is called
radical
radix
surd
radicant
The symbol √(n&b) means the principal nth root “n” is called the
radicand
radical
radix
index
In the preceding item, “b” is called the
radicand
radical
radix
index
The symbol √( ) is called
radical
radical symbol
index
A or B
The rules of combining radicals follow the rules for
signed numbers
logarithms
fractional exponents
factoring
When a number has both a positive and negative nth root, the principal nth root is
the positive root
the negative root
both the positive and negative root
none of the above
Every positive number has _____ nth root
zero
two
one
three
The principal nth root of a negative number is the negative root if n is
even
odd
positive
negative
To eliminate a surd, multiply it by its
square
cube
reciprocal
conjugate
A radical which is equivalent to a non-terminating and non-repeating decimal
irrational number
natural number
surd
transcendental number
A radical expressing an irrational number is called a
surd
radix
index
complex number
A surd which contains at least one rational term.
pure surd
mixed surd
binomial surd
conjugate surd
A surd that contains no rational number, that is, all its factors or terms are surds, example √3 or √3+√2
mixed surd
pure surd
binomial surd
conjugate surd
The process of removing surd from a denominator is to
rationalize the denominator
invert the divisor and proceed to multiplication
get its multiplicative inverse
multiply it why its additive inverse
A quadratic equation of the form ax^2 + c = 0, without the coefficient of the first degree term is a/an
general quadratic equation
pure quadratic equation
quadratic polynomial
incomplete quadratic equation
In the quadratic equation Ax^2 + Bx + C = 0, when the roots are multiplied, the result is
C/A
– B/A
– C/A
A/C
In the quadratic equation Ax^2 + Bx + C = 0, when the roots are added, the result is
C/A
– B/A
– C/A
A/C
If the discriminant of a quadratic equation is less than zero, the equation has
no real roots
one root only
two real roots
none of the above
When can we say that the two roots of a quadratic equation are equal?
when discriminant is greater than 1
when discriminant is zero
when the coefficient of the second degree term is equal to the coefficient of the first degree term
none of the above
What is the discriminant of the quadratic equation Ax2+Bx+C=0
B2−4AC
B2−4AC
B2+4AC
B2+4AC
What determines the nature of the roots of the quadratic equation?
coefficient
discriminant
factors
all of the above
The real roots of a cubic equation are the
points of inflection of the graph of the equation
points of intersection of the graph of the equation with the x-axis
points of intersection of the graph of the equation with the y-axis
obtained by using the quadratic formula
For a cubic equation, we produce three distinct real roots only if the discriminant is
equal to zero
less than zero
greater than zero
either less than or greater 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
three distinct roots
three real roots , which two are equal
none of these
A succession of numbers in which one number is designated as first , another as second, another as third and so on is called
series
arrangement
arrangement
sequence
An indicated sum a1+a2+a3...is called
Series
Sequence
Arrangement
Partial sum
The repeating decimal 0.333 . . is a geometric series of a1= 0.3 and r =
3/10
1/10
10
5
The number between two geometric terms.
means
arithmetic means
geometric means
median
The sum of the first terms of a series is called the nth ______.
sum
sequence
arrangement
partial sum
The sum of the terms of an arithmetic progression
arithmetic means
arithmetic sequence
arithmetic series
all of the above
The harmonic mean between a and b.
(a + b)/2
2ab/(a + b)
(a + b)/ab
ab/(a + b)
The arithmetic mean of a and b is
(a + b)/2
2ab/(a + b)
(a + b)/ab
ab/(a + b)
The geometric mean of a and b is
(a + b)/2
2(a + b)
ab/(a + b)
ab
Are numbers which can be drawn as dots and arranged in triangular shape ( i.e. 1, 3, 6, 10, 15, 21…)
triangular number
square numbers
pentagonal numbers
tetrahedral numbers
A figure numbers which can be drawn as dots and arranged in square shape ( i.e. 1, 4, 9, 16, 25…)
cubic numbers
square numbers
pyramid numbers
pentagon numbers
A sequence 1, 5, 12, 22, 35… is known as
oblong numbers
pentagonal numbers
cubic numbers
pyramid numbers
A sequence 1, 8, 27, 64, 125, 216… is known as
Pyramid numbers
Cubic numbers
tetrahedral numbers
square numbers
A sequence 1, 4, 10, 20, 35, 56… is known
Pyramid numbers
Cubic numbers
tetrahedral numbers
square numbers
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 numbers
Tetrahedral numbers
Euler’s numbers
Triangular 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, 8, 13, 21… is called
Fermat’s numbers
Fibonacci numbers
Gaussian numbers
Archimedean numbers
What is the multiplicative inverse of the integer 5?
1
5
– 5
1/5
What is the additive identity element?
0
1
– 1
infinity
What is the multiplicative identity element?
0
1
– 1
infinity
The number 0 such that 0 + a = a for all a is called
additive inverse
additive identity
commutative law of addition
associative law of addition
The additive inverse of a complex number a + bi is
a – bi
a + bi
–a – bi
–a + bi
All real numbers have additive inverse, commonly called
reciprocals
opposites
addends
equivalent
All real numbers except zero have multiplicative inverses, commonly called
equivalent
factors
opposites
reciprocals
The number zero has no
multiplicative inverse
additive inverse
multiplicative identity
additive identity
What is the additive inverse of a + bi?
bi
–a – bi
1/(a + bi)
a –bi
What is the multiplicative inverse of a + bi?
0
1
– a –bi
(a/a2 – b2) – bi/(a2 + b2)
Which of the following is NOT a property of a binomial expansion of (x + y)n?
power is decreasing
power of y is increasing
sum of exponents in each term = n
number of terms = n – 1
A triangular array numbers forming the coefficient of the expansion of a binomial is called
Egyptian triangle
Golden triangle
Pascal’s triangle
Bermuda triangle
The coefficient of the second term of the expansion of (x + y)n is always equal to
n
n – 1
n + 1
n/2
How is a number in the Pascal’s triangle obtained?
by getting the product of the two numbers directly above it
by getting the sum of the two numbers directly above it
by getting the difference of the two numbers directly above it
by getting the mean of the two numbers directly above it
If the sign between the terms of the binomial is negative, its expansion will have signs which are
all positive
all negative
alternate starting with positive
alternate starting with negative
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 term by ____ of the preceding term.
the exponent of y
the exponent of y +1
the exponent of y – 1
the square root of y
The fundamental principle of counting states that is 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
m x n
m! + n!
mn
Is the arrangement of the object s in specific order.
permutation
combination
probability
any two of the above
Is the arrangement of the objects regardless of the order they are arranged.
permutation
combination
probability
any two of the above
The shifting of the entire order sequence of elements one or more steps forwards 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
inversion
cyclic permutation
transportation
identical elements
The number of elements in the collection being permuted is the _____ of the permutation
degree
sum
index
all of the above
The ratio of the successful outcomes over the total possible outcomes is called
combination
permutation
probability
speculation
The value of the probability of any outcome will never be equal to nor exceed
0.1
0.5
0.75
1
If two events A and B are mutually exclusive events and the probability that A will happen is Pa and the probability that b will occur is Pb, then the probability that A or B happen is
Pa + Pb
Pa x Pb
Pa/Pb
Pb/Pa
A and B are two independent events. The probability that A can occur is p and that for both A and B to occur is q. the probability that event B can occur is
p + q
p – q
p/q
q/p
If the probability of occurrence of a is Pa, what is the probability that will nor occur?
1/Pa
1 - Pa
1 + Pa
Pa
In statistics, a pictorial description of the probability concepts of independent and dependent events is called
Venn diagram
histogram
frequency polygon
ogive
The difference between the highest score and the lowest score in the distribution
deviation
range
median
mode
The second power of the standard deviation is called
mode
central tendency
variance
dispersion
A graph of cumulative frequency distribution plotted at class makes and connected by straight lines.
histogram
Venn diagram
Ogive
Scattergram
A point in the distribution of scores at which 50 percent of the scores fall below and 50 percent of the scores fall above
mode
mean
median
range
A number that occurs most frequent in a group of numbers.
median
mode
means
standard deviation
The difference between an approximate value of a quantity and its exact value or true value
relative error
absolute error
mistake
relative error
It is the quotient of the absolute error divided by the true value
relative error
relative change
absolute error
mistake
Refers to a value which is not exact but might be accurate enough for some specific considerations.
approximate value
absolute value
relative value
accurate value
If the absolute error does not exceed a half unit in the last digit, this digit is usually referred to as the
significant digit
leading digit
reliable digit
relative digit
The most significant digit of the number 0.2015 is
0
1
2
5
