Karnataka SSLC Mathematics (KSEAB) study plan

Prove irrationality of √2, √3 and √5 by contradiction and state the theorem used at each step.

Compute HCF and LCM by prime factorisation and verify the relation HCF × LCM = product of the two numbers on ten pairs.

Classify every number in a mixed list of twenty as rational, irrational, terminating or non-terminating recurring without a calculator.

Solve quadratic equations by factorisation and by completing the square, showing the method chosen and why.

Derive and apply the discriminant to decide the nature of roots for twelve equations, including cases with equal and no real roots.

Derive the six trigonometric ratios from a right triangle and reproduce the table of values at 0°, 30°, 45°, 60° and 90° from memory.

Prove the standard identities involving sin²θ + cos²θ and its rearrangements, then use them to simplify ten expressions.

Convert between angle of elevation and angle of depression in word problems by drawing a labelled diagram before calculating.

Solve heights-and-distances problems involving one and two right triangles, keeping answers in surd form where exact.

Identify and correct the common error of applying the wrong ratio when the given side is the hypotenuse.

State and prove the Basic Proportionality Theorem and its converse, writing each step of the construction in the proof.

Apply the AA, SSS and SAS similarity criteria to decide whether given pairs of triangles are similar, justifying the criterion used.

Use the ratio of areas of similar triangles theorem to find unknown areas and side lengths in six problems.

Apply the Pythagoras theorem and its converse, including the result for the altitude to the hypotenuse.

Construct a triangle similar to a given triangle with a stated scale factor greater and less than one.

Compute the area of a sector, the length of an arc and the area of a segment for given radii and central angles, converting degrees to radians where useful.

Find the area of the shaded region in composite figures by subtracting or adding standard shapes, drawing the decomposition first.

Calculate surface area and volume of combinations of cylinder, cone, sphere and hemisphere, keeping π in the answer until the final step.

State and apply the tangent–radius perpendicularity theorem and the equal-tangents theorem in numerical and proof problems.

Construct tangents to a circle from an external point and from a point on the circle, writing the construction steps in order.

Find the nth term and the sum of the first n terms of an arithmetic progression, and derive both formulas rather than only quoting them.

Solve real-life AP word problems involving savings, seats in rows and multi-year totals, defining the first term and common difference explicitly.

Solve pairs of linear equations by substitution, elimination and cross-multiplication, choosing the fastest method per problem.

Determine whether a pair of linear equations is consistent, inconsistent or dependent from the ratio of coefficients, and interpret the graph.

Set up two-variable equations from word problems about ages, fractions, work and geometry, and check the solution against the original conditions.

Find the zeroes of a quadratic polynomial and verify the relationship between zeroes and coefficients.

Divide one polynomial by another and apply the remainder and factor theorems to test for factors.

Apply the distance formula and section formula, including the midpoint case, to find lengths and points of division.

Compute the area of a triangle from coordinates and use collinearity to test three given points.

Derive and use the relationship between slopes or coordinates to identify simple geometric figures such as parallelograms and right triangles.

Compute mean by the direct, assumed-mean and step-deviation methods for grouped data and confirm all three give the same value.

Find median and mode for grouped frequency distributions and interpret what each measure says about the data.

Draw a cumulative frequency curve and read the median from it.

Compute the probability of simple events using the classical definition and verify that probabilities sum to one over the sample space.

Solve probability problems involving dice, cards, coins and bag-and-ball experiments, listing the sample space before counting favourable outcomes.

Attempt two full-length timed papers under exam conditions and record the time spent per section.

Re-solve every question marked wrong in weeks one to seven without looking at the earlier solution.

Recite from memory the formula sheet for all twelve domains and fill any gap found within the same session.

Practise the construction questions under a strict time limit since they reward accuracy and clear steps.

Review the previous three years' paper patterns to confirm the mark distribution and question style across domains.