Mathematical tools
Topics to be covered:
1. Quadratic equation
2. Binomial theorem
3. Basic trigonometric formulas and small angle approximations
4. ASTC rule
5. Basic Graph theory
6. Differentiation
maxima minima
7. integration
,Quadratic equation
Single variable, highest degree : 2
𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0
Its solution is:
−𝑏 ± 𝑏 − 4𝑎𝑐
𝑥=
2𝑎
If 𝑏 − 4𝑎𝑐 > 0 then two real roots
If 𝑏 − 4𝑎𝑐 < 0 then no real root
If 𝑏 − 4𝑎𝑐 = 0 then one root
, Binomial theorem
(1 + 𝑥) = 1 + 𝑛𝑥 (if x<<1)
Find the value of
1. (1.01) =
2. (1.02) =
3. (1.5) =
4. (2.04) =
5. (0.96) =
6. (1.98) =
7. (99) =
8. 101 =
9. Two bodies having same mass kept at a separation of 1m experience
gravitational force of 10N. If the separation is increased by 1cm, find the
new force acting between the masses
Topics to be covered:
1. Quadratic equation
2. Binomial theorem
3. Basic trigonometric formulas and small angle approximations
4. ASTC rule
5. Basic Graph theory
6. Differentiation
maxima minima
7. integration
,Quadratic equation
Single variable, highest degree : 2
𝑎𝑥 + 𝑏𝑥 + 𝑐 = 0
Its solution is:
−𝑏 ± 𝑏 − 4𝑎𝑐
𝑥=
2𝑎
If 𝑏 − 4𝑎𝑐 > 0 then two real roots
If 𝑏 − 4𝑎𝑐 < 0 then no real root
If 𝑏 − 4𝑎𝑐 = 0 then one root
, Binomial theorem
(1 + 𝑥) = 1 + 𝑛𝑥 (if x<<1)
Find the value of
1. (1.01) =
2. (1.02) =
3. (1.5) =
4. (2.04) =
5. (0.96) =
6. (1.98) =
7. (99) =
8. 101 =
9. Two bodies having same mass kept at a separation of 1m experience
gravitational force of 10N. If the separation is increased by 1cm, find the
new force acting between the masses
