Haryana BSEH Secondary Mathematics - Standard study plan

Derive and memorise the six trigonometric ratios from a right triangle, and write the exact-value table for 0°, 30°, 45°, 60° and 90° from memory without referring to notes

Prove the three Pythagorean identities sin²θ + cos²θ = 1, 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ, then use them to simplify at least 10 mixed expressions

Solve at least 8 height-and-distance word problems by drawing the correct diagram, marking the angle of elevation or depression, and choosing the right ratio

Compute the surface area and volume of a sphere, hemisphere, cone, cylinder and frustum, and write the full formula sheet in one page from memory

Solve at least 6 problems on combinations of solids, such as a cone on a hemisphere or a cylinder with two hemispherical ends, keeping units consistent

Solve 12 trigonometric-identity proof problems, showing each step from LHS to RHS and stating the identity used at every line

Evaluate expressions involving complementary angles, such as sin(90° − θ) = cos θ, and simplify at least 8 such expressions

Handle two-angle height-and-distance problems where the observer moves between two points, and solve at least 6 of them

Compute the volume of material removed or remaining in problems involving a solid melted and recast into another shape, and solve at least 5 such problems

Work through 5 problems on the curved surface area of a frustum and the volume of a frustum, and verify each answer with a rough estimate

State and prove the Basic Proportionality Theorem (Thales theorem) and its converse in full, writing the construction and the proof independently

Apply the similarity criteria AA, SSS and SAS to prove at least 10 pairs of triangles similar, naming the criterion used in each case

Prove and use the theorem that the ratio of areas of two similar triangles equals the square of the ratio of corresponding sides, and solve at least 6 area-ratio problems

Solve pairs of linear equations by substitution, elimination and cross-multiplication, and check each answer by back-substitution

Classify a pair of linear equations as consistent, inconsistent or dependent by comparing a1/a2, b1/b2 and c1/c2, and sketch the graph for at least 4 pairs

Solve at least 8 word problems that reduce to a pair of linear equations, including age, speed-and-time, fraction and work problems, and define the variables explicitly in each solution

Solve 4 graphical problems by plotting both lines on graph paper and reading off the intersection point, and state the region bounded by the lines and the axes

Solve 6 problems that combine similarity with the midpoint theorem or with the diagonals of a trapezium, such as proving that the diagonals divide each other proportionally

Attempt a mixed set of 10 questions drawn from domains 1 to 6 to keep earlier topics active

Find the roots of quadratic equations by factorisation, by completing the square and by the quadratic formula, and solve at least 12 equations using all three methods

Use the discriminant to decide the nature of the roots, and find the value of k for which an equation has equal roots, in at least 8 problems

Solve at least 6 quadratic word problems on speed, area, age and consecutive numbers, and reject the root that does not fit the context with a written reason

Divide polynomials by linear and quadratic divisors using the division algorithm, and verify that dividend = divisor × quotient + remainder

Find the zeros of a quadratic polynomial and verify the relations between the zeros and the coefficients, namely the sum = −b/a and the product = c/a

Apply Euclid's division lemma and Euclid's division algorithm to find the HCF of at least 8 pairs of numbers, including three-digit pairs

Find the HCF and LCM of pairs of numbers by prime factorisation, and verify the relation HCF × LCM = product of the two numbers

Prove that √2, √3 and √5 are irrational by contradiction, writing the proof in full without notes

Find the nth term and the sum of the first n terms of an AP, and solve at least 10 problems involving a, d, n, aₙ and Sₙ

Solve at least 5 AP application problems, such as instalments, savings growth or the number of terms in a finite sequence

Apply the distance formula and the section formula, including the midpoint formula, to at least 12 coordinate-geometry problems

Find the area of a triangle from its vertices using the coordinate formula, and use it to check whether three given points are collinear in at least 5 problems

State and use the two tangent theorems: the tangent is perpendicular to the radius at the point of contact, and the lengths of tangents from an external point are equal

Solve at least 6 circle problems involving chords, equal chords being equidistant from the centre, and the angle between two tangents

Perform the three board constructions with ruler and compass only: divide a line segment in a given ratio, construct a triangle similar to a given triangle, and draw tangents to a circle from an external point

Compute the mean of grouped data by the direct, assumed-mean and step-deviation methods, and cross-check the same data set using all three

Compute the median and mode of grouped data, and identify the modal class and the median class before substituting into the formula

Draw a less-than ogive and a more-than ogive on the same axes, and read the median from the point of intersection

Compute classical probability for simple events involving dice, cards, coins and balls, and verify that the probabilities of all outcomes sum to 1

Complete two full-length timed practice papers covering all 12 domains and record the score and time taken for each