BSEH Class 12 Maths study plan

Build a one-page table of standard integrals (power, exponential, trigonometric, 1/(a²+x²), 1/√(a²−x²), partial fractions) and reproduce it from memory twice by week's end

Classify and solve 30 indefinite integrals by substitution, choosing u yourself and writing one line justifying each choice

Evaluate 15 definite integrals using the fundamental theorem and by splitting the interval at points where the integrand changes sign or definition

Prove that a function is one-one and onto for 6 given functions, and compute inverses where they exist

Write the domain and range of inverse trigonometric functions from memory and verify each with a sketch

Apply integration by parts to 20 problems, including repeated application and the ∫eˣ(f(x)+f′(x))dx pattern

Solve 10 definite integrals using the properties ∫₀ᵃf(x)dx = ∫₀ᵃf(a−x)dx and the odd/even symmetry rules

Compute the total probability theorem and Bayes' theorem for 12 two-stage experiments, drawing a tree diagram for each

State and apply the binomial distribution formula to 10 problems, computing mean and variance

Distinguish clearly between independent events and mutually exclusive events using 5 counterexample pairs

Solve 15 conditional probability problems, including those requiring P(A|B) from a table or a stated sample space

Compute areas bounded by curves using vertical strips for 10 regions, then repeat 4 of them with horizontal strips and confirm the answers match

Find the area between a parabola and a line, and between a circle and a line, by locating intersection points first

Apply Bayes' theorem to 6 diagnostic-test style problems and interpret the result in words

Set up, but do not yet fully solve, 5 linear programming problems by identifying decision variables, objective function and constraints

Solve 8 linear programming problems graphically, shading the feasible region and testing every corner point

Identify infeasible and unbounded feasible regions in 4 constructed examples and state why no optimum exists

Perform matrix addition, scalar multiplication and multiplication on 20 problems, checking conformability before each product

Find the inverse of a 2×2 and a 3×3 matrix by the adjoint method and verify AA⁻¹ = I

Solve a 2-variable and a 3-variable system of linear equations using matrix inversion

Evaluate 3×3 determinants by cofactor expansion and by the property-based shortcut, cross-checking both answers

Apply determinant properties (row/column operations, identical rows, scalar multiples) to evaluate 15 determinants without full expansion

Find the area of a triangle using determinants for 8 coordinate sets, including collinearity checks

Use Cramer's rule and the consistency condition (Δ, Δ₁, Δ₂) to classify 8 systems as unique, infinite or no solution

Prove 6 determinant identities using row and column operations written out step by step

Test continuity and differentiability at a point for 15 piecewise functions, computing both one-sided limits explicitly

Differentiate 25 functions using chain, product, quotient and implicit differentiation, and 8 using logarithmic differentiation

State and apply Rolle's theorem and the mean value theorem to 8 functions, verifying the hypotheses before finding c

Find intervals of increase and decrease and classify local maxima and minima for 10 functions using the first derivative test

Solve 8 maxima/minima word problems (area, volume, cost) by forming the function and stating the domain restriction

Compute dot and cross products for 20 vector pairs and use them to find angles and areas of triangles and parallelograms

Determine collinearity of three points and coplanarity of four points using scalar triple products in 8 problems

Write equations of lines in both vector and Cartesian form for 10 lines, and convert between the two forms

Find the shortest distance between two skew lines and the distance from a point to a plane in 8 problems

Find the angle between two lines and between a line and a plane for 8 configurations

Solve 6 first-order differential equations by separation of variables and 4 linear equations using the integrating factor

Reproduce from memory the derivatives of all six inverse trigonometric functions and the standard inverse-trig integral results

Complete two full-length timed mock papers under exam conditions and mark them against the scheme

Re-solve every question missed across weeks 1–7 and confirm each is now correct without notes

Rank all twelve domains by mock-paper accuracy and allocate the final two days to the two lowest