Mathematics Revision Checklist
Everything to revise for BSE AP Class 10 Mathematics — all 14 NCERT chapters with key topics and formulas, sorted by how many marks they carry.
Ch. 1 — Real Numbers
High- Euclid's division lemma and algorithm; the Fundamental Theorem of Arithmetic (prime factorisation)
- HCF × LCM = product of the two numbers; finding HCF and LCM by prime factorisation
- Prove √2, √3, √5 are irrational; terminating vs non-terminating decimals (denominator = 2ᵃ × 5ᵇ)
Ch. 2 — Polynomials
High- Zeros of a polynomial; relationship between zeros and coefficients (sum = −b/a, product = c/a)
- Form a quadratic polynomial from its zeros; geometrical meaning of zeros (graph)
- Division algorithm for polynomials; remainder and factor theorems
Ch. 3 — Pair of Linear Equations in Two Variables
High- Graphical solution — intersecting (unique), parallel (none), coincident (infinite)
- Algebraic methods: substitution, elimination, cross-multiplication
- Consistency conditions: a₁/a₂ vs b₁/b₂ vs c₁/c₂; word problems (age, fractions, speed)
Ch. 4 — Quadratic Equations
High- Standard form ax²+bx+c=0; solving by factorisation and completing the square
- Quadratic formula x = [−b ± √(b²−4ac)]/2a; discriminant and nature of roots
- Word problems leading to quadratic equations (numbers, area, speed/time)
Ch. 5 — Arithmetic Progressions
High- nth term aₙ = a + (n−1)d; finding which term equals a given value
- Sum of n terms Sₙ = n/2[2a + (n−1)d] = n/2(a + l)
- Word problems on APs; aₙ = Sₙ − Sₙ₋₁
Ch. 6 — Triangles
High- Basic Proportionality Theorem (Thales) and its converse — statement and proof
- Similarity criteria (AAA, SSS, SAS); area ratio = (ratio of corresponding sides)²
- Pythagoras theorem and its converse; applications to similar triangles
Ch. 7 — Coordinate Geometry
High- Distance formula; section formula (internal division); midpoint formula
- Area of a triangle from coordinates; condition for collinearity (area = 0)
- Finding ratio in which a point divides a line segment
Ch. 8 — Introduction to Trigonometry
High- Trigonometric ratios sin/cos/tan/cosec/sec/cot; values at 0°, 30°, 45°, 60°, 90°
- Identities: sin²θ+cos²θ=1, 1+tan²θ=sec²θ, 1+cot²θ=cosec²θ — prove and apply
- Trigonometric ratios of complementary angles — sin θ = cos(90°−θ)
Ch. 9 — Some Applications of Trigonometry
High- Angle of elevation and angle of depression — always draw the right triangle first
- Height-and-distance problems with a single observer
- Two-observation problems (two points/observers viewing the same object)
Ch. 10 — Tangents and Secants to a Circle
High- Tangent is perpendicular to the radius at the point of contact — proof
- Lengths of tangents from an external point are equal (PA = PB) — proof
- Number of tangents from a point; tangent length = √(d²−r²)
Ch. 11 — Areas Related to Circles
Medium- Area of a circle and circumference; area of a sector = (θ/360)×πr²
- Length of an arc = (θ/360)×2πr; area of a segment = sector − triangle
- Areas of combinations of plane figures (shaded regions)
Ch. 12 — Surface Areas and Volumes
Medium- Cylinder, cone, sphere, hemisphere — CSA, TSA and volume formulas
- Combination of solids (cone on cylinder, hemisphere on cylinder) — add surface areas/volumes
- Frustum of a cone: volume and curved surface area; conversion of solids (melting and recasting)
Ch. 13 — Statistics
Medium- Mean of grouped data — direct, assumed-mean, and step-deviation methods
- Median: l + [(n/2 − cf)/f] × h — locate the median class from cumulative frequency
- Mode: l + [(f₁−f₀)/(2f₁−f₀−f₂)] × h — identify the modal class
Ch. 14 — Probability
Medium- Theoretical (classical) probability P(E) = favourable outcomes / total outcomes
- P(E) + P(Ē) = 1; 0 ≤ P(E) ≤ 1; impossible and certain events
- Sample spaces for coins, dice, and a deck of 52 cards — know them by heart