Important Formulas and Equations in Class 10 Science and Mathematics:

Science:

1. Newton's Laws of Motion:
- First Law: F = m * a (Force equals mass times acceleration)
- Second Law: F = m * a (Force equals mass times acceleration)
- Third Law: F1 = -F2 (For every action, there is an equal and opposite reaction)

2. Ohm's Law:
- V = I * R (Voltage equals current times resistance)

3. Speed, Distance, and Time:
- Speed = Distance / Time
- Distance = Speed * Time
- Time = Distance / Speed

4. Work, Power, and Energy:
- Work = Force * Distance
- Power = Work / Time
- Energy = Power * Time

5. Reflection and Refraction:
- Snell's Law: n1 * sinθ1 = n2 * sinθ2 (The ratio of the sines of the angles of incidence and refraction is equal to the ratio of the speeds of light in the two media)

6. Simple Pendulum:
- Period (T) = 2π * √(L/g) (The time taken for one complete oscillation of a simple pendulum depends on its length (L) and acceleration due to gravity (g))

Mathematics:

1. Quadratic Equations:
- Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a (To find the roots of a quadratic equation)

2. Surface Area and Volume:
- Cube: Surface Area = 6a^2, Volume = a^3
- Cylinder: Surface Area = 2πr(r + h), Volume = πr^2h
- Sphere: Surface Area = 4πr^2, Volume = (4/3)πr^3

3. Trigonometry:
- Pythagoras Theorem: a^2 + b^2 = c^2 (In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides)
- Sine Rule: a/sinA = b/sinB = c/sinC (In a triangle, the ratio of a side to the sine of its opposite angle is constant)
- Cosine Rule: a^2 = b^2 + c^2 - 2bc*cosA (In a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice their product and the cosine of the included angle)

4. Probability:
- Probability of an Event = Number of Favorable Outcomes / Total Number of Possible Outcomes

These are some of the important formulas and equations highlighted in the chapter notes for Class 10 Science and Mathematics. Understanding and applying these formulas can help students solve various problems and equations related to these subjects.