Odisha BSE HSC Mathematics study plan

Classify given numbers as rational or irrational, and prove the irrationality of √2, √3 and √5 by contradiction.

Convert recurring decimals into p/q form and place irrational numbers on the number line by geometric construction.

Simplify and compare surds, including rationalising denominators with one and two terms and using conjugates.

Apply the HCF–LCM relationship and Euclid's division algorithm to solve word problems on divisibility and remainders.

Factorise quadratic polynomials by splitting the middle term and by completing the square.

Solve pairs of linear equations in two variables by substitution, elimination and cross-multiplication, and identify when a system is inconsistent or dependent.

Derive the quadratic formula from ax² + bx + c = 0 and use the discriminant to classify roots as real, equal, distinct or imaginary.

Formulate and solve word problems on ages, speed–distance–time and work that reduce to linear or quadratic equations.

Find the sum and product of roots from a quadratic equation and construct an equation from given roots.

Compute the nth term and the sum of the first n terms of an arithmetic progression, including problems where a and d must first be found from two given terms.

Solve AP problems using symmetric three-term and four-term selections, and find the number of terms or a specific term from a sum condition.

State and apply the Basic Proportionality Theorem and its converse to divide a line segment in a given ratio.

Prove two triangles similar using AA, SSS and SAS criteria, and apply the theorem that the ratio of areas of similar triangles equals the square of the ratio of corresponding sides.

Apply the Pythagoras theorem and its converse, including the altitude-to-hypotenuse relation and the 30°–60°–90° triangle ratio.

Solve circle problems using tangent–radius perpendicularity, equal tangents from an external point, and the alternate segment theorem.

Prove standard circle theorems: angle in a semicircle is a right angle, and opposite angles of a cyclic quadrilateral are supplementary.

Construct a triangle similar to a given triangle with a given scale factor, and construct tangents to a circle from an external point, writing the construction steps in order.

Reproduce the trigonometric ratio table for 0°, 30°, 45°, 60° and 90° from memory without reference.

Prove trigonometric identities by converting every term to sine and cosine and by using the Pythagorean identities.

Evaluate expressions using complementary-angle relations and standard identities, without a calculator.

Find all six ratios when one ratio and the sign (quadrant) of the angle are given.

Draw and label angle-of-elevation and angle-of-depression diagrams before solving any heights-and-distances problem.

Solve heights-and-distances problems involving one observer, two observers, towers and objects moving along a line.

Compute the surface area and volume of combination solids such as cylinder + cone, hemisphere + cylinder and cone + hemisphere.

Apply volume conservation to melting, recasting and flow-rate problems, converting units consistently between cm, m and litres.

Compute the area of sectors and segments, and of shaded regions formed by circles combined with triangles or squares.

Compute the mean of grouped data by the direct, assumed-mean and step-deviation methods, and the median and mode from a grouped frequency table.

Draw a cumulative frequency curve and read the median from the graph, verifying it against the computed value.

Compute the curved surface area, total surface area and volume of a frustum of a cone.

Compute classical probability for single and double coin, dice and playing-card experiments, including complementary events.

List sample spaces systematically to solve two-dice and two-coin probability problems without missing outcomes.

Re-solve every question missed in the weeks 1–7 error log and re-derive the correct method from first principles.

Complete full-length papers under timed exam conditions, allocating time per section before starting.