CUSAT CAT B.Tech study plan

Map the full Mathematics syllabus onto a one-page checklist and tag every topic as strong, shaky, or unseen

Solve 25 timed problems each on sets, relations and functions, and on complex numbers, holding to 90 seconds per problem

Re-derive the sum-and-product-of-roots relations for quadratics and solve 15 discriminant-based problems without notes

Compile a handwritten formula sheet covering AP, GP, HP and AM-GM inequalities in your own notation

Classify each logged mistake as concept gap, calculation slip, or misread question

Memorise and then reproduce from memory all standard trigonometric identities, including compound, multiple and sum-to-product forms

Solve 20 problems each on matrices, determinants and their properties, including row-reduction and consistency of linear systems

Work 25 permutation and combination problems, explicitly choosing between arrangement and selection before computing

Apply the binomial theorem to find general terms, middle terms and specific coefficients in 20 expansions

Time-box a 40-question algebra set to 60 minutes and mark it the same day

Derive standard equations, eccentricity, foci and directrices for the circle, parabola, ellipse and hyperbola, then tabulate them

Solve 20 straight-line problems involving slope forms, distance formulae and family-of-lines conditions

State and apply the three equations of motion to 20 kinematics numericals, sketching v-t and a-t graphs first

Apply Newton's laws, including friction and pulley systems, to 15 free-body-diagram problems

Reserve two short sessions to review week 1-2 error-log entries and re-solve every logged mistake

Evaluate limits using standard forms, L'Hopital's rule and expansions across 25 problems

Test continuity and differentiability at a point for piecewise functions in 15 cases

Differentiate implicitly, parametrically and logarithmically across 20 practice problems

Apply derivatives to maxima-minima, tangents and normals in 15 word problems

Sit one full-length timed mock across all three domains and classify every error by cause

Integrate using substitution, by parts and partial fractions across 25 indefinite integrals

Evaluate definite integrals and compute areas under curves for 12 standard regions

Solve 12 first-order differential equations, separating variables and identifying the integrating factor

Resolve vectors into components and apply dot and cross products to 15 geometry and work problems

Apply work-energy theorem and conservation of energy to 15 mechanics numericals, plus solve 10 rotational-motion problems using torque and moment of inertia

Apply Coulomb's law, superposition and Gauss's law to 20 electrostatics problems

Solve 15 current-electricity circuits using Kirchhoff's rules, including Wheatstone bridge balance conditions

Compute magnetic force on charges and wires and apply Ampere's law in 15 problems

Apply Faraday's and Lenz's laws to induced-EMF problems, then handle AC circuits with reactance and impedance in 10 cases

Re-derive the formula for energy stored in a capacitor and in an inductor, and use each in one numerical

Solve 12 ray-optics problems using the mirror and lens formulae with sign conventions, plus 8 wave-optics problems on interference and diffraction

Apply photoelectric-effect and de Broglie relations to 10 numericals and state the Bohr model postulates from memory

Draw and explain the electronic configuration, periodic trends and hybridisation of 15 specified elements and molecules

Apply the first law of thermodynamics and Hess's law to 12 enthalpy problems, and use Le Chatelier's principle to predict equilibrium shifts in 10 cases

Compute rate constants and reaction order from given data in 10 kinetics problems

Name and classify 25 organic compounds, identifying functional groups and predicting major reaction products

Write mechanisms for nucleophilic substitution, elimination, and aldehyde-ketone addition reactions from memory

Explain bonding, geometry and isomerism in coordination compounds and apply crystal-field splitting to 10 complexes

Re-solve every entry in the error log from weeks 1-7 and mark any still unsolved as a final-revision priority

Sit two full-length timed mocks on consecutive days and compare section-wise scores to confirm upward movement in Mathematics