CBSE Grade 10 Mathematics Exam Survival Guide

Window: Board Pattern | Units: Number Systems, Algebra, Coordinate Geo, Geometry, Trigonometry, Mensuration, Statistics & Probability

Must-do topics

• Real numbers: Euclid’s division lemma, HCF–LCM applications
• Polynomials: zeros↔coeff relations; quadratic factorization
• Pair of linear equations: elimination/substitution; consistency
• Quadratic equations: factor/complete square/formula; nature of roots
• Arithmetic/Geometric progressions: nth term, sum
• Coordinate geometry: distance, section, area of triangle
• Triangles: similarity (AAA/SAS/SSS), Pythagoras and converse
• Trigonometry: T-ratios, identities, heights & distances
• Circles & constructions: tangents (pt of contact, length)
• Mensuration: frustum, TSA/CSA/volume (cyl/cone/sphere)
• Statistics & Probability: mean/median/mode (grouped), cumulative freq, simple probability

Top traps (avoid)

• Mixing AP sum vs nth term; wrong n
• Forgetting discriminant check before roots
• Trig angle in wrong quadrant; unit/degree slips

Time split

• Algebra 30% | Geometry+Trig 40% | Mens+Stats 30%
• 5–6 markers: ~10–12 min with crisp steps

Last-48h checklist

• Re-do 2 quadratic sets + 2 similarity proofs
• Trig identity sheet (sin²θ+cos²θ=1, 1+tan²θ=sec²θ, etc.)
• Mensuration mixed set (3D combos + frustum)

Quick facts/formulas

• Quadratic roots: x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=2a−b±b2−4ac​​
• AP: an=a+(n−1)da_n=a+(n-1)dan​=a+(n−1)d, Sn=n2[2a+(n−1)d]S_n=\frac{n}{2}[2a+(n-1)d]Sn​=2n​[2a+(n−1)d]
• Distance: (x2−x1)2+(y2−y1)2\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}(x2​−x1​)2+(y2​−y1​)2​
• Pythagoras: a2+b2=c2a^2+b^2=c^2a2+b2=c2

Speed tactics

• Box your final value with units; sanity-check order of magnitude
• For constructions, light pencil + labeled steps

Exam-day mini-plan

• Start with Algebra short-marks → Triangles/Trig → Mensuration → Stats