ICSE Class 10 Mathematics Formula Sheet

Vocabulary and formula-based flashcards for ICSE Class 10 Mathematics, focusing on GST, Banking, Shares, Linear Inequations, and Quadratic Equations.

Intra-State Supply

Supply of goods and services where the location of the supplier and the place of supply are within the same State or Union Territory (UT).

Inter-State Supply

Supply of goods and services from one State/UT to another.

Interest Formula (Recurring Deposit)

$$I = P \times \frac{n(n + 1)}{2 \times 12} \times \frac{r}{100}$$

P (Banking)

The monthly installment amount in a Recurring Deposit account.

n (Banking)

The total number of months for which the Recurring Deposit is held.

Maturity Value Formula (MV)

$$MV = (P \times n) + I$$

Investment Formula (Shares)

$$\text{Investment} = \text{Number of Shares} \times \text{Market Value (MV)}$$

At Premium (Shares)

$$MV = \text{Nominal Value (NV)} + \text{Premium}$$

At Discount (Shares)

$$MV = \text{Nominal Value (NV)} - \text{Discount}$$

At Par (Shares)

$$MV = \text{Nominal Value (NV)}$$

Annual Income / Total Dividend Formula

$$\text{Annual Income} = \text{Number of Shares} \times \text{Dividend \%} \times \text{Nominal Value (NV)}$$

The Balancing Master Equation

$$\text{Nominal Value (NV)} \times \text{Dividend \%} = \text{Market Value (MV)} \times \text{Yield \%}$$

Yield (%)

$$\text{Yield (\%)} = \frac{\text{Annual Income}}{\text{Total Investment}} \times 100$$

N (Natural Numbers)

$$N = \{1, 2, 3, \dots\}$$

W (Whole Numbers)

$$W = \{0, 1, 2, \dots\}$$

Z or I (Integers)

$$Z \text{ or } I = \{\dots, -2, -1, 0, 1, 2, \dots\}$$

R (Real Numbers)

Set containing all points on the number line.

Linear Inequation Sign-Flip Rule (Negative)

If $a > b$, then $-a < -b$; the sign flips when multiplying or dividing by a negative number.

Linear Inequation Sign-Flip Rule (Reciprocal)

If $a > b$, then $\frac{1}{a} < \frac{1}{b}$; the sign flips when taking the reciprocal.

Standard Form (Quadratic Equation)

$ax^2 + bx + c = 0$ where $a \neq 0$

Sridharacharya's Method (Quadratic Formula)

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

The Discriminant (D)

$$D = b^2 - 4ac$$

Nature of Roots: $D > 0$ and a perfect square

Real, Distinct (Unequal), and Rational.

Nature of Roots: $D > 0$ and NOT a perfect square

Real, Distinct (Unequal), and Irrational.

Nature of Roots: $D = 0$

Real and Equal; each root = $\frac{-b}{2a}$

Nature of Roots: $D < 0$

Imaginary / No Real Roots.