RBSE SS Mathematics study plan

Derive and state the conditions for continuity and differentiability at a point, then classify five given piecewise functions as continuous, differentiable, both, or neither with written justification

Compute derivatives of composite, implicit, inverse-trigonometric, and parametric forms, completing 25 mixed practice items without notes by the end of the week

Apply Rolle's Theorem and the Mean Value Theorem to verify hypotheses and locate the guaranteed point for six stated functions on given intervals

Perform matrix addition, scalar multiplication, multiplication, and transposition, and verify non-commutativity of matrix multiplication with a worked counterexample

Reduce a 3x3 matrix to row-echelon form by elementary row operations and state its rank

Solve maxima and minima word problems (volume, area, cost, distance) by setting up the objective function and constraint, then confirming the extremum with the first or second derivative test

Determine intervals of increase and decrease and locate points of inflection and concavity changes for four polynomial and rational functions

Compute indefinite integrals using substitution, integration by parts, partial fractions, and trigonometric identities, completing 30 items

Evaluate definite integrals using the fundamental theorem and properties such as symmetry and interval splitting

Sketch the region bounded by two curves and set up the definite integral giving its area before evaluating it

Find the area between curves and the volume of solids of revolution about the x-axis and y-axis using disk, washer, and shell setups

Classify differential equations by order and degree and identify linear versus nonlinear forms

Solve variable-separable first-order differential equations, including initial value problems with a stated particular solution

Solve homogeneous differential equations by substituting y = vx and solve first-order linear equations using an integrating factor

Model one growth-and-decay and one cooling scenario as differential equations and interpret the constant of integration in context

Compute dot and cross products, and use them to find angles, projections, areas of triangles and parallelograms, and the volume of a parallelepiped via the scalar triple product

Determine collinearity and coplanarity of points and vectors and justify each conclusion algebraically

Find equations of lines in vector and Cartesian form and of planes in normal and Cartesian form, including the angle between a line and a plane

Compute shortest distances between skew lines and from a point to a plane

Evaluate 2x2 and 3x3 determinants, apply properties to simplify without full expansion, and use Cramer's rule and the adjoint method to solve a 3x3 linear system

Verify consistency of a system of three linear equations using determinants and state the geometric interpretation of the result

Determine domain, range, and whether a function is one-one and onto, and compute inverse functions for bijections

Compose functions and verify inverse relationships algebraically and by restricting domains

Evaluate inverse trigonometric expressions and simplify composite forms using principal value ranges

Solve equations involving inverse trigonometric functions and prove two standard identities from scratch

Classify relations as reflexive, symmetric, and transitive and identify equivalence classes with a worked example

Apply conditional probability, the multiplication rule, and Bayes' theorem to at least eight multi-stage word problems

Compute probabilities using the binomial distribution and distinguish it from cases requiring the general multiplication rule

Identify independent events and verify independence numerically rather than by assumption

Formulate a linear programming problem from a word description by defining decision variables, the objective function, and all constraints including non-negativity

Solve a two-variable linear programming problem graphically, identify the feasible region and corner points, and state the optimal value with justification

Draft the internal assessment project report structure: aim, rationale, mathematical formulation, analysis, and conclusion, and confirm the topic with the supervisor

Collect and tabulate the data or examples needed for the project and complete the mathematical working section

Assemble the practical file with all required activities, each with aim, apparatus or materials, procedure, observations, and conclusion

Compile the portfolio with a topic-wise index, corrected error log, and self-assessment against the syllabus

Complete one full-length timed mock covering all domains and record section-wise scores

Revise the project and portfolio based on supervisor feedback and finalize presentation and viva talking points

Re-solve every item from the week 1-6 error logs and confirm each is now correct without notes

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

Target the three weakest domains identified by mock scores with focused drills of 15 items each

Recite from memory all key formulas across continuity, integrals, differential equations, vectors, and probability in a final rapid-recall pass