Haryana BSEH Secondary Mathematics - Standard study guide
Haryana BSEH Secondary Mathematics - Standard · Work through your exam, one topic at a time.
The Haryana Board of School Education (BSEH, often called HBSE) Secondary Mathematics examination is the Class 10 maths paper taken by students in Haryana board schools. It is a school-leaving and board-certification assessment: a pass is normally needed to move into senior secondary study, and the grade is used for admission to Class 11 streams and for some vocational and polytechnic pathways. The Haryana BSEH Secondary Mathematics - Standard study guide has 12 sections and about 3,514 words.
01Number Systems
This domain tests real numbers through Euclid's division lemma, the Fundamental Theorem of Arithmetic, HCF and LCM, and proofs that numbers such as √2, √3 and √5 are irrational. Euclid's division lemma: for positive integers a and b, a = bq + r with 0 ≤ r < b.
299 words, about 1 min02Polynomials
The exam tests zeros of linear, quadratic and cubic polynomials, the division algorithm, and the relationships between coefficients and zeros, especially for quadratics. If α is a zero of p(x), then p(α) = 0 and (x − α) is a factor of p(x).
322 words, about 2 min03Pair of Linear Equations in Two Variables
This domain tests graphical interpretation, consistency conditions, and the substitution, elimination and cross-multiplication methods for two equations in x and y. For a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0: Unique solution when a₁/a₂ ≠ b₁/b₂; the lines intersect at one point.
271 words, about 1 min04Quadratic Equations
The exam tests solving quadratic equations by factorisation and the quadratic formula, interpreting the discriminant, and translating word problems into quadratics. Standard form: ax² + bx + c = 0, a ≠ 0.
301 words, about 2 min05Arithmetic Progressions
This domain tests recognition of an AP, the nth term, the sum of n terms, and applications such as counting terms and finding unknown terms. An AP has a constant common difference d = aₙ − aₙ₋₁.
332 words, about 2 min06Triangles and Similarity
The exam tests the criteria for similar triangles, the Basic Proportionality Theorem (Thales' theorem), and the relationship between the areas of similar triangles. AA similarity: two equal corresponding angles are enough.
273 words, about 1 min07Coordinate Geometry
This domain tests the distance formula, the section and midpoint formulas, and the area of a triangle from coordinates, including collinearity. Distance between (x₁, y₁) and (x₂, y₂): √[(x₂ − x₁)² + (y₂ − y₁)²].
297 words, about 1 min08Introduction to Trigonometry and Its Applications
This domain tests the six trigonometric ratios, standard angles, identities, and heights-and-distances problems using angles of elevation and depression. In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent; cosec, sec and cot are reciprocals.
304 words, about 2 min09Circles and Constructions
The exam tests tangent and chord properties, the equality of tangents from an external point, and standard ruler-and-compass constructions involving circles and similar triangles. A tangent is perpendicular to the radius at the point of contact.
286 words, about 1 min10Areas Related to Circles and Surface Areas and Volumes
This domain tests sector and segment areas, arc length, and the surface areas and volumes of cylinders, cones, spheres, hemispheres and frustums, including combinations of solids. Arc length = (θ/360) × 2πr; sector area = (θ/360) × πr².
281 words, about 1 min11Statistics
This domain tests the mean, median and mode of grouped data, cumulative frequency, and reading ogives. Direct mean: x̄ = Σfᵢxᵢ / Σfᵢ, where xᵢ is the class mark.
278 words, about 1 min12Probability
This domain tests classical probability for simple events, complementary events, and standard experiments with coins, dice and cards. P(E) = number of favourable outcomes / total number of equally likely outcomes.
270 words, about 1 min