Integrated Course 1 - Algebra mk2

2 x 5 matrix

A 3 x 2 matrix can be multiplied to a

q/p

A and B are two independent events. The probability that A can occur is p and that for A and B to occur is q. The probability that event B can occur is

square number

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

Cramer's Rule

A method of solving linear equation with several unknowns simultaneously using determinants.

Additive Identity

A number 0 such that 0+a=a for all a is called the

triangular number

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

Median

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

harmonic means

A progression whose reciprocal forms an arithmetic progression

pure quadratic equation

A quadratic equation of the form ax² + c = 0, without the coefficient of the first degree term is a/an

surd

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

tetrahedral numbers

A sequence 1, 4, 10, 20, 35, 56...is known as

pentagonal number

A sequence 1, 5, 12, 22, 35... Is known as

pyramid numbers

A sequence of numbers where every term is obtained by adding all the prededing terms a square number series such as 1, 5, 14, 30, 55, 91...

Fibonacci 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...

Cubic numbers (correct)

A sequence1, 8, 27, 64, 125, 216... is known as

Inequality

A statement that one mathematical expression is greater than or less than another is called

sequence

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

pure surd

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

mixed surd

A surd which contain at least one rational term

index

A symbol n√b means the principal nth. "n" is called the

pascal's triangle

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

Reciprocals

All real numbers except zero have multiplicative inverse, commonly called

opposites

All real numbers have additive inverse, commonly called

Matrix

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

series

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

a positive number

An inequality is preserved if the both sides are multiplied by

a positive number

An inequality is reversed if both sides are multiplied by

surd

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

dichotomy

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).

two

Every positive number has ______ nth root.

three real roots, of which two are equal

For a cubic equation, if the discriminant is equal to zero, we produce

one real root and two conjugate complex roots

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

less than zero

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

By getting the sum of the two numbers directly above it

How is a number in Pascal's triangle obatained?

Absolute inequality

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

multiplied by -k

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

Reliable digit

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

no real root

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

Mean Proportional

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

1-Pa

If the probability of occurence of a is Pa, what is the probability that will not occur?

is preserved

If the same number is added to both sides of an inequality, the inequality

alternating starting positive

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

square matrix

If there as many equations as unknowns, the matrix of the coefficient is a

Pa + Pb

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 happen is Pb, then the probability tahat A nd B happen is

changes sign

If two rows a determinant are interchange, the determinant

zero

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

Venn diagram

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

the exponent of y+1

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 preceding term and exponent of x of preceding term by _______ of the preceding term.

radicand

In the preceding item, "b" is called the

-B/A

In the quadratic equation Ax² + Bx + C = 0 , when the two roots are added, the result is

C/A

In the quadratic equation Ax² + Bx + C = 0 , when the two roots are multiplied, the result is

permutation

Is the arrangement of the objects in specific order.

combination

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

Relative error

Is the qoutient of the absolute error divided by the true value.

Approximate value

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

Mean Proportional

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

Accuracy

The ________ is stated in the magnitude of the absolute or relative error of the approximated value.

(a+b)/2

The arithmetic mean of a and b is

n

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

Absolute error

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

Range

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

m x n

The fundamental principle of counting states that in 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.

√ab

The geometric mean of a and b is

Ogive

The graph of cumulative frequency distribution plotted at class marks and connected by straight lines.

2ab/(a+b)

The harmonic mean between a and b.

2

The most significant digit of the number 0.2015 is

geometric means

The number between two geometric terms.

Degree

The number of elements in the collection being permuted is the _______ of the permutation.

Mode

The number that occurs most frequent in a group of numbers

odd

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

rationalize the denominator

The process of removing surd from a denominator is to

surd

The radical expressing an irrational number is called

probability

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

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

The real roots of a cubic equation are the

1/10

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

fractional exponents

The rules of combining radicals follows the rule for

Variance

The second power of the standard deviation is called

Consequent

The second term of a ratio is called

cyclic permutation

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 cahanging the order of the elements in the sequence is called

arithmetic series

The sum of the terms of an arithmetic progression

radical or radical symbol

The symbol √ is called

Dirichlet Theorem

The theorem that in every arithmetic progression a, a+b, a=2d,...., where a and d are relatively prime.

1

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

conjugate

To eliminate a surd, multiply it by its

denominator of the quotient

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

-a-bi

What additive inverse of a complex number a+bi is

discriminant

What determine the nature of the roots of a quadratic equation?

0

What is the additive identity element?

-a-bi

What is the additive inverse of a+bi?

B²-4AC

What is the discriminant of the quadratic equation Ax²+Bx+C=0 ?

1

What is the multiplicative identity element?

(a/(a2+b2)-bi(a2+b2)

What is the multiplicative inverse of a+bi?

1/5

What is the multiplicative inverse of the integer 5?

the positive root

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

when the discriminant is zero

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

zero

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

be multiplied by -1

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

division

Which of the following cannot be an operation of matrices?

number of terms = n-1

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

Multiplicative Inverse

the number zero has no