SEE Optional Mathematics Nepal study plan

Classify algebraic functions as one-to-one, onto or neither; evaluate composite functions f(g(x)) and inverse functions f⁻¹(x), stating domain restrictions.

Apply the remainder and factor theorems to find remainders and factorise cubic polynomials completely.

Compute the nth term and partial sum of arithmetic and geometric sequences, including infinite geometric sums where |r| < 1.

Derive the Pythagorean, quotient and reciprocal identities and prove at least six simple trigonometric identities from first principles.

Solve quadratic equations by factorisation, completing the square and the quadratic formula, and classify the roots using the discriminant.

Formulate a two-variable linear programming problem from a word problem, graph the feasible region, and test corner points for the optimum.

Solve trigonometric equations for 0° ≤ θ ≤ 360°, listing every solution in the required range and discarding extraneous values.

Convert between degrees and radians and evaluate trigonometric ratios of standard and allied angles without a calculator.

Draw accurate diagrams for angles of elevation and depression and solve two-triangle height-and-distance problems, including cases with a shared side.

Prove the sine rule, cosine rule and area formula, then apply all three to non-right triangles.

Prove the congruence and similarity criteria for triangles and use them to establish unknown side and angle relations.

Use bearings and compass directions to set up and solve a practical distance problem.

Apply the midpoint theorem and the properties of parallelograms, rectangles, rhombi and trapeziums to calculate unknown lengths and angles.

State and apply circle theorems - central and inscribed angle, cyclic quadrilateral, tangent–radius, alternate segment - in multi-step proofs.

Construct triangles, quadrilaterals and circles from given conditions using compass and straightedge, leaving all construction arcs visible.

Perform and describe translations, rotations, reflections and enlargements, giving the coordinates of each image.

Compute distance, midpoint, internal section ratio and the area of a triangle directly from coordinates.

Derive equations of straight lines in slope-intercept, point-slope and two-point forms, and test lines for parallelism and perpendicularity.

Find the acute angle between two lines and the perpendicular distance from a point to a line.

Write the equation of a circle in standard and general form and read off its centre and radius.

Represent vectors in component and column form and compute magnitude, unit vector, addition, subtraction and scalar multiples.

Apply the scalar product to find the angle between two vectors and to test perpendicularity.

Use position vectors to prove collinearity and a simple geometric result such as diagonals bisecting one another.

Build frequency tables, histograms and cumulative frequency curves from raw data and read the median and quartiles from the curve.

Compute mean, median, mode, quartile deviation and standard deviation for grouped and ungrouped data, showing the working table.

Calculate probabilities using the classical definition, the addition and multiplication rules and complementary events.

Enumerate a two-dice or card sample space and compute the probability of compound events from it.

Interpret a dispersion measure and a probability value in context, stating the assumptions behind each.

Re-solve every item in the personal error log and confirm each one is now correct without help.

Sit two complete mock papers under 3-hour exam conditions, using only a self-compiled formula sheet.

Rank the five domains by mock score and reallocate remaining study time to the two weakest.