Tamil Nadu HSE Second Year Business Mathematics and Statistics study plan

Compute determinants of 2×2 and 3×3 matrices by cofactor expansion and by the Sarrus rule, and verify one against the other on five matrices.

Classify square matrices as singular or non-singular from their determinant value and state what that implies for invertibility.

Find the inverse of a non-singular 3×3 matrix using the adjoint method, showing the cofactor matrix explicitly at each step.

Solve a system of three linear equations in three unknowns by Cramer's rule and check the solution by back-substitution.

Apply matrix properties (row/column operations, determinant of a product, determinant of a transpose) to shorten computations rather than expanding blindly.

Solve two word problems that require setting up a linear system from given conditions and then solving it by matrix inversion.

Derive and use the standard forms of the straight line (slope-intercept, two-point, intercept, normal) and convert between them.

Compute the angle between two lines, the distance from a point to a line, and the perpendicular distance between parallel lines.

Find the equation of a circle given centre and radius, given endpoints of a diameter, and given three points on it.

Determine the centre and radius of a circle from its general second-degree equation by completing the square.

Find the tangent and normal to a circle at a given point, and use the condition for a line to be a tangent (perpendicular distance from centre equals radius).

Identify the conic type from its equation and state the focus, directrix, vertex or eccentricity as appropriate for parabola, ellipse and hyperbola.

Differentiate products, quotients, composites and implicit functions accurately, and use logarithmic differentiation where it shortens work.

Find second derivatives and use them to classify stationary points as maxima, minima or points of inflection.

Solve applied optimisation problems: cost, revenue and profit maximisation, and minimum average cost.

Compute elasticity of demand and interpret its sign and magnitude in a short sentence.

Integrate standard forms, by substitution, by parts and by partial fractions, choosing the method deliberately before starting.

Evaluate definite integrals and use them to find area under a curve and between two curves.

Solve first-order differential equations by separation of variables and by the integrating-factor method for linear equations.

Set up a differential equation from a simple growth, decay or cost scenario and interpret the constant of integration in context.

State the conditions for a binomial distribution and compute probabilities, mean and variance for given n and p without a table.

Apply the Poisson distribution as a limit of the binomial and compute probabilities for rare-event scenarios.

Use the normal distribution with standardisation and read areas from the standard normal table in both tails and between two values.

Distinguish when to use binomial, Poisson or normal for a described real situation and justify the choice in one sentence.

Distinguish population and sample, and explain simple random, stratified and systematic sampling with an appropriate use case for each.

Compute standard error of the mean and construct confidence intervals for a mean with known variance at 95% and 99% levels.

State null and alternative hypotheses for a described claim and identify whether a one-tailed or two-tailed test applies.

Carry out a large-sample z-test for a mean and for a proportion, and state the conclusion in the language of the original problem.

Construct Laspeyres, Paasche and Fisher index numbers from a given price-and-quantity table and interpret the difference between them.

Compute a 3-year and 4-year moving average and a simple trend line by least squares from a short time-series.

Re-solve one hard problem from each of matrices, differentiation and integration under timed conditions to confirm retention.

Complete two full-length timed mock papers and log every question type you lost marks on.