Maharashtra HSC Mathematics & Statistics - Commerce (MSBSHSE) study plan
Maharashtra HSC Mathematics & Statistics - Commerce (MSBSHSE) · Give each week a clear focus.
8 weeks · About 7 hours per week
Differentiation & Applications of Derivatives (Commerce Contexts)
Derive derivatives of standard functions (polynomial, exponential, logarithmic) from first principles and by rules
Apply product, quotient and chain rules to composite commerce-style functions such as cost and demand expressions
Compute marginal cost, marginal revenue and elasticity from given total functions
Solve first-order conditions to locate maxima and minima of profit and revenue functions
Classify stationary points using the second derivative test
Your checkpoint
A handwritten worked set of 20 differentiation and optimisation problems with full steps, scored against the answer key, targeting at least 16/20
Integration and Definite Integrals & Applications of Definite Integrals (Area, Cost, Revenue)
Integrate standard forms using substitution and by parts on 15 mixed exercises
Evaluate definite integrals using the fundamental theorem and correct limits
Compute area between a curve and the x-axis and between two curves
Derive total cost and total revenue from given marginal functions by definite integration
Interpret the constant of integration in an economic context
Your checkpoint
A one-page formula sheet of integration techniques plus 12 solved application problems (area, cost from marginal cost, revenue from marginal revenue) with numeric answers verified
Mathematical Logic and Set Theory & Matrices and Determinants
Construct truth tables for compound statements and identify tautologies and contradictions
State and apply De Morgan's laws and the laws of logic to simplify statements
Perform set operations (union, intersection, complement, difference) and verify identities
Compute determinants of 2x2 and 3x3 matrices by expansion
Apply Cramer's rule to solve a 2-variable or 3-variable system
Find the inverse of a 2x2 matrix and use it to solve a matrix equation
Your checkpoint
A timed 45-minute mock test covering logic, sets, determinants and Cramer's rule, self-marked with every error reworked
Probability Distributions (Binomial and Poisson) & Random Variables, Mean and Variance
Distinguish between discrete and continuous random variables and construct a probability distribution table
Compute expected value and variance of a discrete random variable from its distribution
Identify when a binomial distribution applies and compute probabilities using the formula
Identify when a Poisson distribution applies and compute probabilities, including cumulative cases
Compare mean and variance of binomial and Poisson models to check fit
Your checkpoint
A comparison table of binomial versus Poisson (conditions, mean, variance, formula) plus 15 solved probability problems with at least 80% accuracy
Differential Equations
Classify differential equations by order and degree
Solve variable-separable first-order equations by integration
Solve linear first-order equations using the integrating factor
Model simple growth and decay situations as differential equations and solve them
Apply a given initial condition to determine the particular solution
Your checkpoint
A worked portfolio of 10 differential equation problems, each showing classification, method chosen, general solution and particular solution
Index Numbers & Time Series Analysis
Compute Laspeyres, Paasche and Fisher price index numbers from given price and quantity data
Interpret the time reversal and factor reversal tests for index numbers
Compute a simple moving average of order 3 and 4 from a given series
Estimate trend values by the method of least squares for a linear trend
Distinguish seasonal, cyclical and irregular variation in a time series
Your checkpoint
A completed index number and time series worksheet: three index types computed for one dataset plus a moving-average and least-squares trend fitted to one series
Differentiation & Integration and Definite Integrals & Probability Distributions (Binomial and Poisson)
Re-solve previously missed differentiation and integration problems without notes
Recompute binomial and Poisson probabilities under timed conditions
Build a personal error log categorising mistakes as conceptual, computational or misreading
Practise exam-style questions mixing calculus with probability in a single paper
Your checkpoint
A personal error log with at least 25 entries, each with the corrected method, and a re-test on those items scoring at least 85%
Mathematical Logic and Set Theory & Matrices and Determinants & Applications of Derivatives (Commerce Contexts) & Applications of Definite Integrals (Area, Cost, Revenue) & Differential Equations & Random Variables, Mean and Variance & Index Numbers & Time Series Analysis
Complete two full-length timed mock papers under exam conditions
Review each mock within 24 hours, reworking every wrong answer
Recite key formulas from memory for determinants, integration, distributions and index numbers
Identify the three weakest sub-topics and do 10 targeted questions on each
Your checkpoint
Two completed mock papers with scores recorded, plus a one-page final revision sheet of formulas and recurring pitfalls
Milestones
Week 2: Score at least 70% on a self-made calculus test covering differentiation, optimisation, integration and area/cost-revenue applications; all errors logged
Week 4: Score at least 75% on a combined test of logic, sets, matrices, determinants, random variables and binomial/Poisson distributions
Week 6: Complete the index number and time series worksheet with all numeric answers verified, and solve 8 of 10 differential equation problems correctly
Week 8: Achieve at least 80% on both full-length mock papers, with every incorrect item reworked and the error log closed out