# Profit, Loss & Discount

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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:

$$Profit = \frac{Profit Percent}{100} \times Cost Price$$

$$CostPrice = \frac{Profit}{ProfitPercent} \times 100$$

$$CostPrice = \frac{100}{ProfitPercent + 100} \times SalePrice$$

# Trigonometry Functions, Formulas and Identities

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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

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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

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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.