Free Practice Questions for Odisha BSE HSC Mathematics

Real Numbers

Euclid's division lemma and algorithm, fundamental theorem of arithmetic, HCF and LCM using prime factorization, irrationality ideas, and terminating versus non-terminating recurring decimals.

Polynomials

Zeros of linear and quadratic polynomials, relationship between zeros and coefficients, and the division algorithm for polynomials with remainder and quotient interpretation.

Linear Equations in Two Variables

Graphical representation of a pair of linear equations, algebraic solution by substitution, elimination, and cross-multiplication, and conditions for unique, infinite, or no solution.

Quadratic Equations

Standard form ax² + bx + c = 0, solution by factorization, completing the square, and the quadratic formula; nature of roots from the discriminant Δ = b² − 4ac.

Arithmetic Progressions

General term aₙ = a + (n − 1)d, sum Sₙ = n/2 [2a + (n − 1)d], and application problems involving series of payments, seating, or equally spaced quantities.

Triangles

Basic proportionality (Thales) theorem, criteria for similarity (AAA, SAS, SSS), areas of similar triangles, and the Pythagorean theorem with applications.

Coordinate Geometry

Distance formula, section (internal/external) formula, midpoint, area of a triangle from coordinates, and collinearity of three points.

Trigonometry

Trigonometric ratios of acute angles, standard values (0°, 30°, 45°, 60°, 90°), complementary-angle relations, and fundamental identities such as sin²θ + cos²θ = 1.

Applications of Trigonometry

Heights and distances: angle of elevation and depression, two-position problems, and multi-step calculations using right triangles.

Circles

Tangent perpendicular to radius at the point of contact, equal tangents from an external point, and related angle/length properties.

Constructions

Conceptual questions on dividing a line segment in a given ratio, constructing tangents from an external point, and constructing a triangle similar to a given triangle.

Areas Related to Circles

Area and circumference formulas, area of a sector and segment, and areas of combinations of circles with triangles, squares, or other plane figures.

Surface Areas and Volumes

Surface area and volume of cubes, cuboids, cylinders, cones, spheres, and hemispheres, including combinations such as cone on a cylinder or hemisphere on a cuboid.

Statistics

Mean of grouped data (direct, assumed-mean, and step-deviation methods), median and mode of grouped frequency distributions, cumulative frequency, and ogives.

Probability

Classical definition P(E) = n(E)/n(S), complementary events, simple experiments with coins, dice, cards, and equally likely outcomes.