Assam ASSEB Higher Secondary Mathematics study plan

Evaluate one-sided and two-sided limits of polynomial, rational, trigonometric, exponential and logarithmic functions, including 0/0 and ∞/∞ forms, using the standard limit results and the squeeze idea where needed.

Test continuity of piecewise-defined functions at the join point by comparing the left-hand limit, right-hand limit and the value of the function, and state the type of discontinuity when continuity fails.

Decide differentiability at a point from first principles for functions containing modulus or piecewise definitions, and explain why continuity does not imply differentiability with a concrete counterexample.

Differentiate composite, implicit, parametric and inverse-trigonometric functions using the chain, product and quotient rules without consulting notes.

Verify the hypotheses of Rolle's Theorem and Lagrange's Mean Value Theorem on a stated interval and find the value of c guaranteed by each.

Solve rate-of-change problems by setting up the correct relation between the variables and differentiating with respect to time.

Determine intervals of strict increase and decrease of a function using the sign of its first derivative, and verify the intervals on a rough sketch.

Locate local maxima and minima using both the first-derivative test and the second-derivative test, and distinguish local from absolute extrema on a closed interval.

Write equations of tangents and normals to a curve at a given point, including curves given in parametric form.

Solve applied optimisation word problems (maximising area or volume, minimising cost or surface) by translating the statement into a single-variable function with a stated domain.

Integrate standard algebraic, trigonometric, exponential and rational forms using the direct standard integrals and linear substitution.

Evaluate integrals by parts, choosing the first function by the ILATE order, including repeated integration by parts and integrals of the form ∫e^x(f(x)+f′(x))dx.

Decompose proper rational functions into partial fractions and integrate each resulting term.

Apply the properties of definite integrals, including ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a−x)dx, to evaluate definite integrals that resist direct antidifferentiation.

Compute the area of a region bounded by a curve, the x-axis and two ordinates, and the area between two intersecting curves, setting up the correct integral with correct limits.

Classify a differential equation by order and degree and identify linear versus non-linear equations.

Solve variable-separable and homogeneous first-order differential equations by the appropriate substitution, including y = vx for homogeneous equations.

Solve linear first-order equations of the form dy/dx + Py = Q using the integrating factor e^∫Pdx.

Find particular solutions from a given initial condition and model simple growth, decay and rate problems as differential equations.

Consolidate the whole Calculus domain by re-solving the questions missed in weeks 1 to 3 under time pressure.

Compute dot and cross products of vectors and use them to find the angle between two vectors, the projection of one vector on another, and the area of a triangle or parallelogram.

Apply the scalar triple product to test coplanarity of three vectors and to find the volume of a parallelepiped.

Convert between vector and Cartesian forms of the equation of a line, and find the angle between two lines and the shortest distance between two skew lines.

Derive the vector and Cartesian equations of a plane in normal form and in three-point form, and find the angle between a line and a plane and the distance of a point from a plane.

Find the foot of the perpendicular and the image of a point in a given plane or line using vector methods.

Carry out matrix addition, multiplication and scalar multiplication, and verify properties such as non-commutativity of multiplication with a specific counterexample.

Classify matrices as symmetric or skew-symmetric and prove statements about their sums using transposes.

Find the inverse of a 2×2 and 3×3 matrix by the adjoint method and by elementary row operations, checking the answer by multiplication.

Use determinant properties to evaluate determinants without full expansion, and apply determinants to find the area of a triangle and to test collinearity.

Solve a system of two or three linear equations by the matrix method and by Cramer's rule, and state when the system has no solution or infinitely many.

Evaluate principal values of inverse trigonometric functions and simplify expressions using the standard inverse-trigonometric identities.

Compute conditional probability using P(A|B) = P(A∩B)/P(B) and verify independence of two events both by definition and by the multiplication rule.

Apply the theorem of total probability and Bayes' theorem to problems stated in words, writing out the partition of the sample space before calculating.

Define a random variable, construct its probability distribution, and compute its mean and variance.

Solve repeated-independent-trial problems using the binomial distribution, identifying n, p and the required number of successes before computing.

Classify relations as reflexive, symmetric, transitive or equivalence on a given finite set, and test functions for one-one and onto using algebraic and graphical arguments.

Find the composition of two functions and the inverse of a bijection, verifying that f∘f⁻¹ is the identity on the stated sets.

Formulate a linear programming problem from a word problem by defining the decision variables, writing the objective function and listing every constraint including the non-negativity conditions.

Draw the feasible region for a two-variable LPP on graph paper, shade it correctly, and list its corner points.

Solve LPPs by the corner-point method and by the objective-function line method, and identify problems with unbounded or infeasible regions.

Re-solve the highest-yield Calculus question types from the error logs of weeks 1 to 4 without referring to the earlier solutions.

Complete two full-syllabus mock papers under strict exam timing and convert each into a ranked list of the five topics needing the most revision in the final days.