1. Simple interest = ( Principal * Annual Interest Rate * Time in years) / 100


2. Amount = Principal + S.I.


3. For Compound interest: Amount = P(1 + R/100) ⁿ


4. Compound interest = Amount - Principal


5. If interest rate is compounded half yearly then Amount = P(1 + (R/2)/100) ²ⁿ


6. The above formula shows that rate of interest is halved and time period is doubled.

Q. Find CI paid when a sum of Rs 10,000 is invested for 1 year and 3 months at 8 and 1/2% per annum compounded annually.

Ans.Find the amount for the whole part, i.e., 1 year in this case. Then use this as principal to get simple interest for for 1/4 year more

A = 10000(1+17/200)¹

A = 10850

For next three months calculate Simple interest: SI = 10850*(17/2)*(1/4) / 100

SI = 230.56

Q.The population of a city was 20,000 in the year 1997. It increased at the rate of 5% p.a. Find the population at the end of the year 2000.

Ans.Use compound interest formula with P = 20000, R = 5 and n=3. The amount = 23153.

Q.A TV was bought at a price of Rs 21,000. After one year the value of the TV was depreciated by 5% (Depreciation means reduction of value due to use and age of the item). Find the value of the TV after one year.

Ans.Use compound interest formula with P = 21000, R = -5 and n=3. The amount = 19950. Negative sign in interest is for decrease.

1. (a+b)² = a²+2ab+b²


2. (a-b)² = a² - 2ab + b²


3. (a+b)(a-b) = a² - b²


4. (x+a)(x+b) = x² + (a+b)x + ab

Q.501 × 502

Ans.Solve as (500+1)(500+2) i.e. (x+a)(x+b) = x² + (a+b)x + ab

Q.95 × 103

Ans.Solve as (100-5)(100+3) i.e. (x+a)(x+b) = x² + (a+b)x + ab

1. Eulers Formula = ‘V’ stands for number of vertices, ‘F’ stands for number of faces and ‘E’ stands for number of edges


2. F + V – E = 2


3. Area of trapezium = (height) * (sum of parallel sides) / 2


4. Area of a rhombus is half the product of its diagonals


5. Surface Area of a cuboid = 2(lb + bh + hl )


6. The side walls (the faces excluding the top and bottom) make the lateral surface area of the cuboid = 2h (l + b)


7. Total surface area of cuboid = lateral surface area + 2 × area of base


8. Total surface area of a cube of side l is 6l²


9. Lateral (or curved) surface area of a cylinder is 2πrh. lateral surface area of a cylinder is the circumference of base × height of cylinder.


10. Total surface area of a cylinder = 2πr (r + h)


11. Volume of cuboid = l × b × h . Volume of cuboid = area of the base × height


12. Volume of cube = l × l × l = l ³


13. Volume of cylinder = area of base × height = πr²h


14. 1 mL = 1 cm³ ,1 L = 1000 cm ³ . Thus, 1 m ³ = 1000000 cm = 1000 L

1. x and y are in direct proportion, if x/y = k or x = k*y


2. When x and y are in direct proportion (x₁/y₁) = (x₂/y₂) . y₁, y₂ are values of y corresponding to x₁ , x₂


3. Two quantities x and y are said to vary in inverse proportion, if there exists a relation of the type xy = k between them, k being a constant. If y₁ , y₂ corresponding to the values x₁ , x₂ then x₁ * y₁ = x₂* y₂(= k)

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