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Worksheets

Yellow Book - Algebra B

Total questions: 100

Worksheet time: 50mins

Name
Class
Date
1.

In the proportion of four quantities, the first and fourth terms are referred to as the

a)

means

b)

extremes

c)

denominators

d)

numerators

2.

The first term of a ratio is called

a)

antecedent

b)

consequent

c)

mean

d)

extreme

3.

The second term of a ratio is called

a)

antecedent

b)

mean

c)

consequent

d)

extreme

4.

The _____ is the square root of the product of the extremes.

a)

antecedent

b)

consequent

c)

mean proportional

d)

mean

5.

If the means of a proportion are equal, their common value is called

a)

mean

b)

extreme

c)

mean proportional

d)

extreme proportional

6.

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

7.

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

8.

If an equality is true for all values of the variable, it is a/an

a)

conditional inequality

b)

equivalent inequality

c)

absolute inequality

d)

non-conditional inequality

9.

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

10.

An inequality is preserved if both sides are multiplied by

a)

zero

b)

– 1

c)

a positive number

d)

a negative number

11.

An inequality is reversed if both sides are multiplied by

a)

zero

b)

– 1

c)

a positive number

d)

a negative number

12.

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).

a)

decomposition

b)

denomination

c)

deviance

d)

dichotomy

13.

A 3 x 2 matrix can be multiplied to a

a)

3 x 2 matrix

b)

3 x 3 matrix

c)

2 x 5 matrix

d)

row matrix

14.

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

15.

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

16.

Using Cramer’s rule, the determinant of the coefficient is always the

a)

numerator of a quotient

b)

denominator of the quotient

c)

the quotient itself

d)

none of the above

17.

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

a)

zero

b)

positive integer

c)

negative integer

d)

unity

18.

When the corresponding elements of two rows of a determinant are proportional, then the value of the determinant is

a)

one

b)

indeterminate

c)

infinite

d)

zero

19.

An array of m x n quantities which represent a single number and is composed of elements in rows and columns is known as

a)

transpose of a matrix

b)

determinant

c)

co-factor of a matrix

d)

matrix

20.

When two rows are interchanged in position, the value of the determinant will

a)

remain unchanged

b)

be multiplied by – 1

c)

become zero

d)

become infinite value

21.

If every elements of a row (or column) are multiplied by a constant, k, then the value of the determinant is

a)

multiplied by – k

b)

zero

c)

one

d)

multiplied by k

22.

If two rows of a determinant are interchange, the determinant

a)

changes sign

b)

changes sign and value

c)

remains unchanged

d)

becomes the inverse of the former

23.

Which of the following cannot be an operation of matrices?

a)

addition

b)

subtraction

c)

multiplication

d)

division

24.

An irrational number which is a root of a positive integer of fraction is called

a)

radical

b)

radix

c)

surd

d)

radicant

25.

The symbol √(n&b) means the principal nth root “n” is called the

a)

radicand

b)

radical

c)

radix

d)

index

26.

In the preceding item, “b” is called the

a)

radicand

b)

radical

c)

radix

d)

index

27.

The symbol √( ) is called

a)

radical

b)

radical symbol

c)

index

d)

A or B

28.

The rules of combining radicals follow the rules for

a)

signed numbers

b)

logarithms

c)

fractional exponents

d)

factoring

29.

When a number has both a positive and negative nth root, the principal nth root is

a)

the positive root

b)

the negative root

c)

both the positive and negative root

d)

none of the above

30.

Every positive number has _____ nth root

a)

zero

b)

two

c)

one

d)

three

31.

The principal nth root of a negative number is the negative root if n is

a)

even

b)

odd

c)

positive

d)

negative

32.

To eliminate a surd, multiply it by its

a)

square

b)

cube

c)

reciprocal

d)

conjugate

33.

A radical which is equivalent to a non-terminating and non-repeating decimal

a)

irrational number

b)

natural number

c)

surd

d)

transcendental number

34.

A radical expressing an irrational number is called a

a)

surd

b)

radix

c)

index

d)

complex number

35.

A surd which contains at least one rational term.

a)

pure surd

b)

mixed surd

c)

binomial surd

d)

conjugate surd

36.

A surd that contains no rational number, that is, all its factors or terms are surds, example √3 or √3+√2

a)

mixed surd

b)

pure surd

c)

binomial surd

d)

conjugate surd

37.

The process of removing surd from a denominator is to

a)

rationalize the denominator

b)

invert the divisor and proceed to multiplication

c)

get its multiplicative inverse

d)

multiply it why its additive inverse

38.

A quadratic equation of the form ax^2 + c = 0, without the coefficient of the first degree term is a/an

a)

general quadratic equation

b)

pure quadratic equation

c)

quadratic polynomial

d)

incomplete quadratic equation

39.

In the quadratic equation Ax^2 + Bx + C = 0, when the roots are multiplied, the result is

a)

C/A

b)

– B/A

c)

– C/A

d)

A/C

40.

In the quadratic equation Ax^2 + Bx + C = 0, when the roots are added, the result is

a)

C/A

b)

– B/A

c)

– C/A

d)

A/C

41.

If the discriminant of a quadratic equation is less than zero, the equation has

a)

no real roots

b)

one root only

c)

two real roots

d)

none of the above

42.

When can we say that the two roots of a quadratic equation are equal?

a)

when discriminant is greater than 1

b)

when discriminant is zero

c)

when the coefficient of the second degree term is equal to the coefficient of the first degree term

d)

none of the above

43.

What is the discriminant of the quadratic equation  Ax2+Bx+C=0Ax^2+Bx+C=0  

a)

 B24AC\sqrt{B^2-4AC}  

b)

 B24ACB^2-4AC  

c)

 B2+4ACB^2+4AC  

d)

 B2+4AC\sqrt{B^2+4AC}  

44.

What determines the nature of the roots of the quadratic equation?

a)

coefficient

b)

discriminant

c)

factors

d)

all of the above

45.

The real roots of a cubic equation are the

a)

points of inflection of the graph of the equation

b)

points of intersection of the graph of the equation with the x-axis

c)

points of intersection of the graph of the equation with the y-axis

d)

obtained by using the quadratic formula

46.

For a cubic equation, we produce three distinct real roots only if the discriminant is

a)

equal to zero

b)

less than zero

c)

greater than zero

d)

either less than or greater than zero

47.

For a cubic equation, the discriminant is found to be greater than zero. The roots are

a)

one real and two conjugate complex roots

b)

three distinct roots

c)

three real roots , which two are equal

d)

none of these

48.

A succession of numbers in which one number is designated as first , another as second, another as third and so on is called

a)

series

b)

arrangement

c)

arrangement

d)

sequence

49.

An indicated sum a1+a2+a3...is called

a)

Series

b)

Sequence

c)

Arrangement

d)

Partial sum

50.

The repeating decimal 0.333 . . is a geometric series of a1= 0.3 and r =

a)

3/10

b)

1/10

c)

10

d)

5

51.

The number between two geometric terms.

a)

means

b)

arithmetic means

c)

geometric means

d)

median

52.

The sum of the first terms of a series is called the nth ______.

a)

sum

b)

sequence

c)

arrangement

d)

partial sum

53.

The sum of the terms of an arithmetic progression

a)

arithmetic means

b)

arithmetic sequence

c)

arithmetic series

d)

all of the above

54.

The harmonic mean between a and b.

a)

(a + b)/2

b)

2ab/(a + b)

c)

(a + b)/ab

d)

ab/(a + b)

55.

The arithmetic mean of a and b is

a)

(a + b)/2

b)

2ab/(a + b)

c)

(a + b)/ab

d)

ab/(a + b)

56.

The geometric mean of a and b is

a)

(a + b)/2

b)

2(a + b)

c)

ab/(a + b)

d)

ab\sqrt{ab}

57.

Are numbers which can be drawn as dots and arranged in triangular shape ( i.e. 1, 3, 6, 10, 15, 21…)

a)

triangular number

b)

square numbers

c)

pentagonal numbers

d)

tetrahedral numbers

58.

A figure numbers which can be drawn as dots and arranged in square shape ( i.e. 1, 4, 9, 16, 25…)

a)

cubic numbers

b)

square numbers

c)

pyramid numbers

d)

pentagon numbers

59.

A sequence 1, 5, 12, 22, 35… is known as

a)

oblong numbers

b)

pentagonal numbers

c)

cubic numbers

d)

pyramid numbers

60.

A sequence 1, 8, 27, 64, 125, 216… is known as

a)

Pyramid numbers

b)

Cubic numbers

c)

tetrahedral numbers

d)

square numbers

61.

A sequence 1, 4, 10, 20, 35, 56… is known

a)

Pyramid numbers

b)

Cubic numbers

c)

tetrahedral numbers

d)

square numbers

62.

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…

a)

Pyramid numbers

b)

Tetrahedral numbers

c)

Euler’s numbers

d)

Triangular numbers

63.

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

a)

Fermat’s numbers

b)

Fibonacci numbers

c)

Gaussian numbers

d)

Archimedean numbers

64.

What is the multiplicative inverse of the integer 5?

a)

1

b)

5

c)

– 5

d)

1/5

65.

What is the additive identity element?

a)

0

b)

1

c)

– 1

d)

infinity

66.

What is the multiplicative identity element?

a)

0

b)

1

c)

– 1

d)

infinity

67.

The number 0 such that 0 + a = a for all a is called

a)

additive inverse

b)

additive identity

c)

commutative law of addition

d)

associative law of addition

68.

The additive inverse of a complex number a + bi is

a)

a – bi

b)

a + bi

c)

–a – bi

d)

–a + bi

69.

All real numbers have additive inverse, commonly called

a)

reciprocals

b)

opposites

c)

addends

d)

equivalent

70.

All real numbers except zero have multiplicative inverses, commonly called

a)

equivalent

b)

factors

c)

opposites

d)

reciprocals

71.

The number zero has no

a)

multiplicative inverse

b)

additive inverse

c)

multiplicative identity

d)

additive identity

72.

What is the additive inverse of a + bi?

a)

bi

b)

–a – bi

c)

1/(a + bi)

d)

a –bi

73.

What is the multiplicative inverse of a + bi?

a)

0

b)

1

c)

– a –bi

d)

(a/a2 – b2) – bi/(a2 + b2)

74.

Which of the following is NOT a property of a binomial expansion of (x + y)n?

a)

power is decreasing

b)

power of y is increasing

c)

sum of exponents in each term = n

d)

number of terms = n – 1

75.

A triangular array numbers forming the coefficient of the expansion of a binomial is called

a)

Egyptian triangle

b)

Golden triangle

c)

Pascal’s triangle

d)

Bermuda triangle

76.

The coefficient of the second term of the expansion of (x + y)n is always equal to

a)

n

b)

n – 1

c)

n + 1

d)

n/2

77.

How is a number in the Pascal’s triangle obtained?

a)

by getting the product of the two numbers directly above it

b)

by getting the sum of the two numbers directly above it

c)

by getting the difference of the two numbers directly above it

d)

by getting the mean of the two numbers directly above it

78.

If the sign between the terms of the binomial is negative, its expansion will have signs which are

a)

all positive

b)

all negative

c)

alternate starting with positive

d)

alternate starting with negative

79.

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.

a)

the exponent of y

b)

the exponent of y +1

c)

the exponent of y – 1

d)

the square root of y

80.

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.

a)

m + n

b)

m x n

c)

m! + n!

d)

mn

81.

Is the arrangement of the object s in specific order.

a)

permutation

b)

combination

c)

probability

d)

any two of the above

82.

Is the arrangement of the objects regardless of the order they are arranged.

a)

permutation

b)

combination

c)

probability

d)

any two of the above

83.

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

a)

inversion

b)

cyclic permutation

c)

transportation

d)

identical elements

84.

The number of elements in the collection being permuted is the _____ of the permutation

a)

degree

b)

sum

c)

index

d)

all of the above

85.

The ratio of the successful outcomes over the total possible outcomes is called

a)

combination

b)

permutation

c)

probability

d)

speculation

86.

The value of the probability of any outcome will never be equal to nor exceed

a)

0.1

b)

0.5

c)

0.75

d)

1

87.

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

a)

Pa + Pb

b)

Pa x Pb

c)

Pa/Pb

d)

Pb/Pa

88.

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

a)

p + q

b)

p – q

c)

p/q

d)

q/p

89.

If the probability of occurrence of a is Pa, what is the probability that will nor occur?

a)

1/Pa

b)

1 - Pa

c)

1 + Pa

d)

Pa\sqrt{Pa}

90.

In statistics, a pictorial description of the probability concepts of independent and dependent events is called

a)

Venn diagram

b)

histogram

c)

frequency polygon

d)

ogive

91.

The difference between the highest score and the lowest score in the distribution

a)

deviation

b)

range

c)

median

d)

mode

92.

The second power of the standard deviation is called

a)

mode

b)

central tendency

c)

variance

d)

dispersion

93.

A graph of cumulative frequency distribution plotted at class makes and connected by straight lines.

a)

histogram

b)

Venn diagram

c)

Ogive

d)

Scattergram

94.

A point in the distribution of scores at which 50 percent of the scores fall below and 50 percent of the scores fall above

a)

mode

b)

mean

c)

median

d)

range

95.

A number that occurs most frequent in a group of numbers.

a)

median

b)

mode

c)

means

d)

standard deviation

96.

The difference between an approximate value of a quantity and its exact value or true value

a)

relative error

b)

absolute error

c)

mistake

d)

relative error

97.

It is the quotient of the absolute error divided by the true value

a)

relative error

b)

relative change

c)

absolute error

d)

mistake

98.

Refers to a value which is not exact but might be accurate enough for some specific considerations.

a)

approximate value

b)

absolute value

c)

relative value

d)

accurate value

99.

If the absolute error does not exceed a half unit in the last digit, this digit is usually referred to as the

a)

significant digit

b)

leading digit

c)

reliable digit

d)

relative digit

100.

The most significant digit of the number 0.2015 is

a)

0

b)

1

c)

2

d)

5