- Simple interest = ( Principal * Annual Interest Rate * Time in years) / 100
- Amount = Principal + S.I.
- For Compound interest: Amount = P(1 + R/100)
^{n} - Compound interest = Amount - Principal
- If interest rate is compounded half yearly then Amount = P(1 + (R/2)/100)
^{2n} - 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.

- (a+b)
^{2}= a^{2}+2ab+b^{2} - (a-b)
^{2}= a^{2}- 2ab + b^{2} - (a+b)(a-b) = a
^{2}- b^{2} - (x+a)(x+b) = x
^{2}+ (a+b)x + ab

**Q.**501 × 502

**Ans.**Solve as (500+1)(500+2) i.e. (x+a)(x+b) = x^{2} + (a+b)x + ab

**Q.**95 × 103

**Ans.**Solve as (100-5)(100+3) i.e. (x+a)(x+b) = x^{2} + (a+b)x + ab

- Eulers Formula = ‘V’ stands for number of vertices, ‘F’ stands for number of faces and ‘E’ stands for number of edges
- F + V – E = 2
- Area of trapezium = (height) * (sum of parallel sides) / 2
- Area of a rhombus is half the product of its diagonals
- Surface Area of a cuboid = 2(lb + bh + hl )
- The side walls (the faces excluding the top and bottom) make the lateral surface area of the cuboid = 2h (l + b)
- Total surface area of cuboid = lateral surface area + 2 × area of base
- Total surface area of a cube of side l is 6l
^{2} - Lateral (or curved) surface area of a cylinder is 2πrh. lateral surface area of a cylinder is the circumference of base × height of cylinder.
- Total surface area of a cylinder = 2πr (r + h)
- Volume of cuboid = l × b × h . Volume of cuboid = area of the base × height
- Volume of cube = l × l × l = l
^{3} - Volume of cylinder = area of base × height = πr
^{2}h - 1 mL = 1 cm
^{3},1 L = 1000 cm^{3}. Thus, 1 m^{3}= 1000000 cm = 1000 L

- x and y are in direct proportion, if x/y = k or x = k*y
- When x and y are in direct
proportion (x
_{1}/y_{1}) = (x_{2}/y_{2}) . y_{1}, y_{2}are values of y corresponding to x_{1}, x_{2} - 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 y
_{1}, y_{2}corresponding to the values x_{1}, x_{2}then x_{1}* y_{1}= x_{2}* y_{2}(= k)