BSEB Inter Mathematics study plan

Compute determinants of 2x2 and 3x3 matrices by cofactor expansion and verify results using row operations

Classify matrices as symmetric, skew-symmetric, or neither and prove basic transpose identities

Find inverses of 3x3 matrices using the adjoint method and state the condition for invertibility

Determine whether a relation is reflexive, symmetric, and transitive on small finite sets

Compose two functions and find the inverse of a bijection given by an explicit formula

Solve systems of three linear equations using Cramer's rule and the matrix inverse method, and identify inconsistent systems from vanishing determinants

Apply properties of determinants (row swap, scalar multiple, row addition) to evaluate determinants without full expansion

Solve quadratic equations and inequalities that arise inside matrix and function problems

Use the binomial theorem to expand expressions up to the fourth power and pick out a specified term

Prove elementary identities involving matrices such as (AB)^T = B^T A^T on 2x2 examples

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

Write the vector and Cartesian equations of a line through a given point in a given direction and of a plane through a point with a given normal

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

Evaluate principal values of inverse trigonometric functions including composite expressions such as sin(arctan x)

Simplify expressions using the standard inverse-trig identities for sums and double angles within principal ranges

Test continuity of piecewise functions at a point using left-hand and right-hand limits, and find unknown constants that make a function continuous

Differentiate composite, implicit, and inverse-trigonometric functions using chain rule and logarithmic differentiation

Verify Rolle's theorem and the mean value theorem for given functions on given intervals by finding the required point

Find intervals of increase and decrease and locate local maxima and minima using the first derivative test

Solve applied optimisation problems such as maximising volume or minimising cost with a single constraint

Integrate standard forms using substitution, including trigonometric and algebraic substitutions

Evaluate integrals by parts and by partial fractions, choosing the method deliberately

Compute definite integrals using the fundamental theorem and apply the properties of definite integrals to simplify symmetric limits

Find the area bounded by a curve, the x-axis, and given ordinates, and the area between two curves

Set up and evaluate the area of a region bounded by a circle or parabola and a line

Classify differential equations by order and degree and solve variable-separable equations

Solve first-order linear equations using the integrating factor and homogeneous equations by substitution

Apply conditional probability and the multiplication theorem to two-stage experiments

Use Bayes' theorem to reverse conditional probabilities in a stated scenario

Compute mean and variance of a binomial distribution and apply it to word problems

Formulate a linear programming problem from a word problem by writing the objective function and all constraints

Solve two-variable linear programming problems graphically and identify the feasible region and corner points

Determine whether a linear programming problem is bounded or unbounded and interpret the optimum

Compute probabilities using the addition theorem for mutually exclusive and overlapping events

Solve problems on independent events and verify independence from given probabilities

Revise the weakest three domains identified from earlier error logs by redoing missed problems without notes

Complete two full-length timed mock papers under exam conditions and record section-wise scores

Memorise and self-test the standard formula list for all twelve domains in a single sitting

Practise selecting the fastest method for mixed-topic questions by reviewing each mock error and naming the correct approach