Maharashtra HSC Mathematics & Statistics - Arts & Science (MSBSHSE) study plan

Derive and apply the product, quotient and chain rules to differentiate composite, implicit and parametric functions

Differentiate logarithmic, exponential, inverse-trigonometric and second-order derivatives without formula sheets

Use logarithmic differentiation on functions of the form u^v and v^u

Solve increasing/decreasing and maxima-minima problems by sign analysis of the first derivative

Compute second-derivative tests and interpret concavity for polynomial and trigonometric curves

Apply Rolle's theorem and the mean value theorem to verify conditions and find the guaranteed point c

Model and solve optimisation word problems (area, volume, cost, revenue) end to end

Use derivative tests to find points of inflection and sketch curves with asymptotes where relevant

Solve velocity-acceleration kinematics problems using successive differentiation

Time yourself solving past-paper application questions under exam conditions

Integrate standard algebraic, trigonometric, exponential and reciprocal forms from memory

Apply substitution, integration by parts, and partial fractions to choose the correct technique per integrand

Evaluate definite integrals and apply the fundamental theorem with correct limits handling

Compute areas bounded by curves, lines and axes, including regions split across the x-axis

Set up and evaluate integrals for volumes of revolution about the x-axis

Classify differential equations by order, degree and linearity and form equations from general solutions

Solve variable-separable first-order equations and apply them to growth and decay models

Solve first-order linear equations using the integrating factor method

Solve homogeneous equations via the substitution y = vx

Recheck integration accuracy by differentiating answers back

Compute dot and cross products and use them to find angles, projections and areas

Determine collinearity, coplanarity and perpendicularity conditions for vectors

Find direction ratios and direction cosines of lines and write symmetric and vector forms of line equations

Find the shortest distance between skew lines and the distance from a point to a plane

Solve plane equations in normal and Cartesian forms and find angles between lines and planes

Translate statements into symbolic logic and test truth values using truth tables and negation rules

State and apply De Morgan's laws, the algebra of statements, and identify tautologies and contradictions

Identify statement patterns including converse, inverse and contrapositive

Perform matrix operations, find inverses by adjoint method and solve linear systems by matrix inversion

Formulate and solve linear programming problems graphically, including identifying feasible regions and unbounded cases

Construct probability distributions for discrete random variables and verify total probability equals 1

Compute expectation, variance and standard deviation of a discrete random variable

Apply the binomial distribution formula and recognise when its assumptions hold

Compute range, quartile deviation, mean deviation, variance and standard deviation for grouped and ungrouped data

Compute Karl Pearson's and Bowley's coefficients of skewness and interpret bivariate correlation and regression lines

Sit two full-length timed mock papers under exam conditions and record per-domain scores

Re-teach the two weakest domains using condensed notes and re-solve every missed question unaided

Drill speed on standard results by repeating formula recall in under 10 minutes per domain

Finalise a one-page per-domain revision sheet covering formulas, conditions and common traps