Kochi Entrance Mathematics study plan

Compute limits of rational and irrational functions by factoring, rationalising numerators, and dividing by the highest power of the variable.

Differentiate products, quotients, and composite functions, plus trigonometric, exponential, and logarithmic functions, without consulting a formula sheet.

Derive the tangent line at a given point and determine intervals of increase and decrease from the sign of the first derivative.

Convert between limit definitions and derivative computations so that a derivative can be built from first principles when asked.

Apply differentiation to optimisation problems such as maximising volume or minimising surface area under a constraint.

Use the second derivative to locate inflection points, determine concavity, and sketch the graph of a rational or trigonometric function.

Carry out indefinite and definite integration by substitution, by parts, and by splitting into partial fractions.

Set up and evaluate the area between two curves, including cases where the integrand must be split at an intersection point.

Compute volumes of revolution about the x-axis and y-axis using disc and washer setups, choosing the correct variable of integration.

Integrate rational and trigonometric integrands that require rewriting an identity or dividing out before the standard form applies.

Solve area problems where the intersection points must be found first and the upper and lower functions swap roles.

Reproduce from memory the standard integral formulas and the substitution patterns they pair with.

Compute vector sums, scalar multiples, magnitudes, and dot products, and use them to find angles and test perpendicularity.

Write position-vector equations for lines and segments, including points that divide a segment in a given ratio.

Convert complex numbers between rectangular and polar form, apply De Moivre's theorem, and extract n-th roots.

Translate complex-number locus conditions into geometric figures and back again.

Complete the square to find the vertex and the maximum or minimum of a quadratic over a restricted domain.

Solve quadratic inequalities and use the discriminant to decide the number of real roots and the sign of the expression.

Use vectors to compute triangle area and use complex multiplication to describe rotations and scalings in the plane.

Solve mixed problems that require both a quadratic argument and a vector or complex-plane interpretation.

Count arrangements and selections, including circular permutations, repeated elements, and cases split by a 'at least' condition.

Compute probabilities of dependent and conditional events and calculate expected value for a discrete distribution.

Compute mean, variance, and standard deviation from raw data and interpret correlation and the shape of a scatter plot.

Apply the Euclidean algorithm, congruence arithmetic, and base conversion to short integer problems.

Apply the sine and cosine rules to solve triangles and use radian measure and the unit circle to evaluate trigonometric values.

Solve trigonometric equations and inequalities on a stated interval and sketch graphs with amplitude, period, and phase changes.

Solve exponential and logarithmic equations and inequalities while checking domain restrictions, and use logarithms to handle maxima and minima.

Handle arithmetic and geometric sequences, recurrence relations, summation notation, and telescoping sums.

Consolidate every error from weeks 1 to 7 into one sheet and re-solve each missed item closed-book until it is clean.

Sit two full-length mocks under exam conditions, allocating time in proportion to domain weight and reserving ten minutes for checks.

Rehearse a fixed opening routine: scan all questions, rank them by expected yield, and start with the highest-confidence large-mark item.

Drill the highest-weight techniques (tangents, optimisation, area, volume, vector geometry) until each can be started within one minute.