Nepal SEE Mathematics study plan

Simplify expressions using the laws of indices with integer, fractional and negative exponents, including problems such as (a^(2/3) · a^(1/2)) / a^(1/6).

Rationalise denominators of surds (e.g. 1/(√5 + √2), 3/(√7 − 2)) and simplify products and quotients of surds.

Factorise polynomials using common factors, difference of two squares, and splitting the middle term of trinomials.

Find HCF and LCM of algebraic expressions and use them to simplify rational expressions.

Solve linear equations in one variable and simultaneous equations in two variables by both elimination and substitution.

Solve quadratic equations by factorisation, completing the square, and the quadratic formula, and check roots by substitution.

Solve linear inequalities in one variable and represent the solution set on a number line and in set notation.

Use set notation and two- and three-set Venn diagrams to compute n(A ∪ B), n(A ∩ B), n(A − B) and complements from word problems.

Prove the angle-sum and exterior-angle theorems of a triangle and apply the SSS, SAS, ASA and RHS congruence criteria to identify congruent triangles.

Apply the properties of parallelograms, rhombus, rectangle, square and trapezium to calculate unknown angles, sides and diagonals.

Write two-column (statement–reason) proofs of the midpoint theorem and standard parallelogram results.

Construct triangles, parallelograms and angle bisectors from given data using ruler and compass only, leaving construction arcs visible.

State and prove the circle theorems on central angle vs inscribed angle, angle in a semicircle, angles in the same segment, and the cyclic quadrilateral.

Apply tangent–radius perpendicularity and the alternate segment theorem to find unknown angles in circle diagrams.

Construct tangents to a circle from an external point and construct the incircle/circumcircle of a triangle.

Re-solve 20 past-paper geometry questions under timed conditions without consulting solutions.

Compute the perimeter and area of triangles, quadrilaterals, circles, sectors and circular segments, choosing the correct formula for each given figure.

Calculate the lateral surface area and total surface area of prisms, pyramids, cylinders, cones and spheres.

Calculate the volume of the same solids and solve problems involving composite solids such as a cylinder capped by a hemisphere.

Solve cost-estimation problems in Nepali rupees - painting a room, plastering a wall, fencing a field, or capacity of a water tank in litres.

Solve marked-price, discount and profit–loss problems, including successive discounts and cases where cost price must be recovered from selling price.

Compute simple interest and compound interest for annual, half-yearly and quarterly compounding, and solve depreciation problems using the same formula.

Calculate 13% VAT and income tax using current Nepal slab rates and rebates, distinguishing assessable income from taxable income.

Convert amounts using buying and selling exchange rates and solve two-step money-changing problems such as NRs → USD → EUR.

Evaluate trigonometric expressions and prove simple identities using the exact ratios at 0°, 30°, 45°, 60° and 90°.

Solve heights-and-distances problems involving angles of elevation and depression, including two-observer and two-building cases, drawing a correct diagram before calculating.

Compute mean, median, mode and quartiles from both ungrouped and grouped frequency data, showing the working formula for each.

Calculate probabilities of simple events with dice, coins, cards and spinners, giving answers as fractions in lowest terms.

Perform and describe reflections, rotations, translations and dilations of points and figures on the coordinate plane, stating the image coordinates.

Add and subtract vectors, multiply by scalars, and compute magnitude and direction from components.

Complete two full-length mock SEE papers under 2-hour timed conditions and self-mark against the marking scheme.

Consolidate every recurring mistake from the mocks into a single final revision sheet and re-solve those items until correct.