Profit, Loss & Discount

Posted in Terms Defined

Cost Price = CP

Sale Price = SP

If SP > CP it is profitable situation. Therefore, Profit (P) = SP - CP

If SP < CP it is a loss making situation. Therefore, Loss (L) = CP - SP

\( Profit Percent = \frac{Profit}{Cost Price} \times 100 \)

\( Profit Percent = \frac{Sale Price - Cost Price}{Cost Price} \times 100 \)

On rearranging the above formulas we get the following:

\( Profit = \frac{Profit Percent}{100} \times Cost Price \)

Trigonometry Functions, Formulas and Identities

Posted in Terms Defined

Please refer to the following figure of right-angled triangle:

Trigonometry Functions:

\( Sine \theta = \frac{opposite}{hypotenuse} = \frac{AC}{AB} \)

\( Secant \theta = \frac{hypotenuse}{adjacent} = \frac{AB}{BC} \)

\( Cosine \theta = \frac{adjacent}{hypotenuse} = \frac{BC}{AB} \)

\( Tangent \theta = \frac{opposite}{adjacent} = \frac{AC}{BC} \)

\( Co-Secant \theta = \frac{hypotenuse}{opposite} = \frac{AB}{AC} \)

\( Co-Tangent \theta = \frac{adjacent}{opposite} = \frac{BC}{AC} \)

Direct Proportion and Indirect Proportion

Posted in Terms Defined

Two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant. That is if \( \frac{x}{y} = k \) [ k is a positive number], then x and y are said to vary directly. In such a case if \( y_1, y_2 \) are the values of y corresponding to the values \( x_1, x_2 \) of a respectively then \( \frac{x_1}{y_1} = \frac{x_2}{y_2} \).

 

Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y (and vice-versa) in such a manner that the product of their corresponding values remains constant. That is, if \( xy = k \), then x and y are said to vary inversely. In this case if \( y_1, y_2 \) are the values of y corresponding to the values of x respectively then \( x_1y_1 = x_2y_2 \) or \( \frac{x_1}{x_2} = \frac{y_2}{y_1} \).

Polynomials

Posted in Terms Defined

Polynomial:- An algebraic expression consisting of one or more terms comprising of constants and / or variables and non-negative exponents of the variables.

e.g.            x + 1,         x2 + 2,    y2 - 2y + 1

Zero polynomial:- The constant polynomial 0 is called the zero polynomial.

Constant polynomials:- Polynomials which do not have terms with variables are termed as constant polynomials e.g. 2, -3, 14.

Polynomials in one variable:- e.g. x2 - 2,  y3 + 3y - 4

Each term of a polynomial has a coefficient. So in x2 - 2 the coefficient of x2 is 1, and that of x0 is -2.

Monomials:- Polynomials having only one term.

Binomials:- Polynomials having only two terms are called binomials.

Trinomials:- Polynomials having only three terms are called trinomials.

Degree of a polynomial:- The degree of a non-zero constant polynomial is zero.

Linear polynomial:- A polynomial of degree one is called a linear polynomial.

Quadratic polynomial:- A polynomial of degree two is called a quadratic polynomial.

Cubic polynomial:- A polynomial of degree three is called a cubic polynomial.

Degree of zero polynomial:- The degree of zero polynomial is not defined.

Quadrilateral

Posted in Terms Defined

Quadrilateral is a type of polygon with four sides.

Sum of all interior angles: Sum of all interior angles of a quadrilateral is 360°.

Types of quadrilaterals and their properties:

Quadrilateral Properties

Parallelogram

A quadrilateral with each pair of opposite sides equal.

(1) Opposite sides are equal.

(2) Opposite angels are equal.

(3) Diagonals bisect one another.

Rhombus

A parallelogram with sides of equal length.

(1) All the properties of a parallelogram.

(2) Diagonals are perpendicular to each other.

Rectangle

A parallelogram with a right angle.

(1) All the properties of a parallelogram.

(2) Each of the angles is a right angle.

(3) Diagonals are equal.

Square

A rectangle with sides of equal length.

All the properties of a parallelogram, rhombus and a rectangle.

Kite

A quadrilateral with exactly two pairs of equal consecutive sides.

(1) The diagonals are perpendicular to one another.

(2) One of the diagonals bisects the other.

(3) In the figure m∠B = m∠D but m∠A≠m∠C.