Mathematics Revision Checklist
Everything to revise for BSE Telangana Class 10 Mathematics — all chapters with key topics and formulas, sorted by how many marks they carry in the public exam.
Ch. 1 Real Numbers (incl. Logarithms) & Ch. 2 Sets — High Weight
High- Ch. 1 Real Numbers: Euclid's Division Lemma a=bq+r; HCF × LCM = product of two numbers
- Ch. 1: Prime factorisation; prove √2, √3, √5 irrational by contradiction method
- Ch. 1: Terminating decimal ↔ denominator has only 2 and 5 as prime factors
- Ch. 1 Logarithms: definition aˣ=N ⟺ logₐN=x; product law logₐ(xy)=logₐx+logₐy
- Ch. 1 Logarithms: quotient law logₐ(x/y)=logₐx−logₐy; power law logₐ(xⁿ)=n·logₐx
- Ch. 1 Logarithms: logₐa=1; logₐ1=0; simplify and evaluate logarithmic expressions
- Ch. 2 Sets: roster and set-builder forms; types of sets; union, intersection, difference, complement
- Ch. 2: n(A∪B) = n(A)+n(B)−n(A∩B); three-set formula; Venn diagram word problems
Ch. 3, 4, 5, 6 Algebra — High Weight
High- Ch. 3 Polynomials: zeros from graph, sum of zeros = −b/a, product = c/a, division algorithm
- Ch. 4 Pair of Linear Equations: graphical (intersecting/parallel/coincident), substitution, elimination, cross-multiplication
- Ch. 5 Quadratic Equations: factorisation, completing the square, quadratic formula, discriminant D = b²−4ac
- Ch. 5: Nature of roots — D > 0 (two distinct real), D = 0 (equal), D < 0 (no real roots)
- Ch. 6 Progressions (AP): nth term aₙ = a + (n−1)d, sum Sₙ = n/2[2a+(n−1)d]; word problems
- Ch. 6 Progressions (GP): nth term aₙ = arⁿ⁻¹, sum Sₙ = a(rⁿ−1)/(r−1); identify GP from common ratio
Ch. 7, 8, 9 Geometry — High Weight
High- Ch. 7 Coordinate Geometry: distance formula, section formula (internal/external), midpoint, area of triangle
- Ch. 7: Slope of line — two-point form, equation of a line passing through given points
- Ch. 8 Similar Triangles: Basic Proportionality Theorem (Thales) and its converse — proof required
- Ch. 8: AA, SAS, SSS similarity criteria — application problems with ratios
- Ch. 8: Area ratio of similar triangles = (ratio of corresponding sides)²; Pythagoras theorem
- Ch. 9 Tangents and Secants to a Circle: tangent-radius ⊥, equal tangents from external point (PA=PB), length = √(d²−r²)
Ch. 11, 12 Trigonometry — High Weight
High- Ch. 11: Values of sin, cos, tan at 0°, 30°, 45°, 60°, 90° — memorise all 15 values
- Ch. 11: Identities — sin²θ+cos²θ=1, 1+tan²θ=sec²θ, 1+cot²θ=cosec²θ — derive and apply
- Ch. 11: Complementary angles — sin θ = cos(90°−θ), tan θ = cot(90°−θ)
- Ch. 12 Applications: angle of elevation (looking up) and depression (looking down) — draw triangle first
- Ch. 12: Two-observation problems — height using angles from two points on same side
Ch. 10 Mensuration — Medium Weight
Medium- Cylinder: V = πr²h, CSA = 2πrh, TSA = 2πr(r+h)
- Cone: V = ⅓πr²h, CSA = πrl, TSA = πr(r+l), slant l = √(r²+h²)
- Sphere: V = 4/3πr³, SA = 4πr² · Hemisphere: V = ⅔πr³, CSA = 2πr², TSA = 3πr²
- Frustum of cone: V = πh/3(r₁²+r₂²+r₁r₂), CSA = π(r₁+r₂)l
- Combination of solids: cylinder+cone, hemisphere on cylinder — add volumes
Ch. 13, 14 Statistics & Probability — Medium Weight
Medium- Ch. 14 Mean: direct method Σfx/Σf, assumed mean A + Σfd/Σf, step-deviation A + (Σfu/Σf)×h
- Ch. 14 Median: find n/2, locate cumulative frequency class, l + [(n/2−cf)/f]×h
- Ch. 14 Mode: modal class has highest frequency, l + [(f₁−f₀)/(2f₁−f₀−f₂)]×h
- Ch. 13 Probability: P(E) = favourable outcomes / total outcomes; 0 ≤ P(E) ≤ 1; P(E)+P(Ē)=1
- Ch. 13: Cards (52), dice (6), coins (2) — know sample spaces by heart