NEB Class 12 Mathematics study plan

Compute powers and roots of complex numbers with De Moivre's theorem and solve equations whose roots are complex.

Solve quadratic equations over the complex numbers, classify roots using the discriminant, and form an equation from given roots.

Derive and apply the nth-term, sum, and mean formulas for arithmetic and geometric sequences, including the convergence condition for infinite geometric series.

Translate word problems on growth, depreciation, and instalment saving into AP or GP models and carry them to a numerical answer.

Expand binomials using the general term and extract a named term, coefficient, or middle term without full expansion.

Solve counting problems with permutations and combinations, including repetition, restriction, and 'at least one' cases.

Carry out matrix addition, multiplication, and inversion via the adjoint, then solve 2x2 and 3x3 systems with Cramer's rule.

Formulate a two-variable linear programming problem, shade the feasible region, and locate the optimal vertex algebraically.

Prove trigonometric identities by chaining Pythagorean, sum-and-difference, double-angle, and sum-to-product formulas.

Solve trigonometric equations and state general solutions correctly in both degrees and radians.

Apply the sine rule, cosine rule, and area formula to oblique triangles and to height-and-distance situations.

Evaluate principal values of inverse trigonometric functions and simplify composite inverse expressions.

Sketch the graphs of the six trigonometric functions and read off period, amplitude, and asymptotes.

Compute distance, section-ratio, slope, angle between lines, and perpendicular distance from a point to a line, then use them to find line equations in all standard forms.

Solve locus problems by translating a geometric condition into an algebraic equation.

Derive the standard equations of the circle, parabola, ellipse, and hyperbola and list centre, vertex, focus, directrix, axis, and eccentricity for each.

Test tangency and intersection of a line with a conic by substituting and applying the discriminant condition.

Classify a general second-degree equation by completing the square into standard conic form.

Compute dot and cross products and interpret each result as an angle, projection, or area.

Test collinearity, coplanarity, and perpendicularity of points and vectors using product conditions.

Derive vector and Cartesian equations of lines and planes and calculate the angle and shortest distance between them.

Apply the scalar triple product to find volumes and to test coplanarity of four points.

Solve 3D geometry problems by choosing a coordinate origin and resolving everything into vector form.

Evaluate limits by factoring, rationalising, using standard limits, and applying L'Hopital's rule only where the form permits.

Differentiate with the product, quotient, chain, implicit, parametric, and logarithmic rules without hesitating over which rule applies.

Apply derivatives to tangents and normals, monotonicity, maxima and minima, related rates, and curve sketching.

Integrate standard forms by substitution, by parts, and by partial fractions, and evaluate definite integrals to find areas under curves.

Compute mean, median, mode, quartiles, range, variance, and standard deviation for grouped and ungrouped data.

Solve combined-mean and combined-standard-deviation problems and interpret dispersion in context.

Apply the addition and multiplication rules, conditional probability, and Bayes' theorem to multi-stage problems.

Calculate binomial and Poisson probabilities, means, and variances, and recognise which model a situation requires.

Standardise normal variables into z-scores and use the table to find probabilities and cut-off values.

Consolidate the weekly error logs into a single ranked list of weak question types and re-solve every missed item unaided.

Sit two full-length timed papers under exam conditions with no notes and record per-section timing.

Allocate exam time across the six domains in proportion to their weight and practise a 30-second decision on whether to attempt or skip a question.

Recite the six-domain formula card from memory and drill the twenty formulas most often misremembered.