Mathematical Methods — Class 11 Maharashtra HSC Physics revision notes
A 4-page visual revision sheet for Mathematical Methods, written for Class 11 Maharashtra HSC Physics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Mathematical Methods in one look
vectors, and just enough calculus to read the rest of physics
Scalars and vectors
- magnitude and a unit only, no direction
- mass, time, speed, work, energy, temperature, density, electric charge
- adds and subtracts by ordinary algebra
- magnitude and direction, both needed to describe it
- displacement, velocity, acceleration, force, angular velocity
- drawn as an arrow: length to scale is the magnitude, tail to head is the direction
Types of vector
- zero (null) vector: magnitude zero, direction arbitrary
- e.g. the velocity of a body at rest, the acceleration of one moving uniformly
- negative vector: same magnitude, opposite direction
- equal vectors: same magnitude and same direction, and they must describe the same physical quantity
- position vector: from the chosen origin to the particle
- unit vector: magnitude 1, direction only, M = fracM|M|. So M = |M|M
- resultant: the single vector that does what all of them together do
Multiplying a vector by a scalar
- Q = sP keeps the direction of P and multiplies the magnitude by s
- a negative s reverses the direction as well
- i, j, k are the unit vectors along x, y and z of a rectangular coordinate system
- only vectors of the same type may be added: force to force, never force to velocity
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Mathematical Methods sheet covers
- scalar
- vector analysis
- Scalars and vectors
- Vector
- Types of vector
- Multiplying a vector by a scalar
- vector addition
- Triangle law and parallelogram law
- Magnitude and direction of the resultant
- resultant magnitude
- angle α the resultant makes with P
- Special cases of the resultant
- Resolution of a vector into components
- dot product
- Scalar product, the dot product
- definition
- in components
- parallel, θ = 0°
- perpendicular, θ = 90°
- a vector with itself
- the unit vectors
- cross product
- Vector product, the cross product
- order matters
- parallel or antiparallel
- perpendicular
- area of the parallelogram on them
- Cross product in components
- Write the array
- Expand
- Mind the middle sign
- Physics that is a cross product
- linear velocity in a rotation
- torque about a point
- angular momentum
- force on a moving charge
- calculus
- differential calculus
- Differentiation, the calculus toolkit
- Derivatives worth memorising
- a constant
- a power
- a scalar multiple
- a product
- a quotient, u over v
- sine
- cosine
- exponential
- logarithm
- integral calculus
- Integration, the area under the curve
- Standard integrals
- a power, n ≠ -1
- the exception
- trigonometric
- sum rule
- Symbols
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Physics chapter by chapter against your real exam dates and free hours, and when the plan reaches Mathematical Methods the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.