Real Numbers (6 marks focus)
- Use Euclid’s division lemma to show the square of any positive integer is 3m or 3m+1.
- Express 7429 as product of primes; find HCF/LCM of 12, 15, 21.
- Prove √2 is irrational; sum of rational + irrational is irrational.
- LCM of x,y where y multiple of x.
- Fundamental Theorem of Arithmetic application to decimals.
Polynomials (Algebra cluster)
- Find zeroes of (x-3)²-4; quadratic if zeroes 0, √5.
- Zeroes of x³-3x²+x+1 as a-b, a, a+b; find a,b.
- Cubic polynomial with sum zeroes=3, sum products=3, product=-1.
- Verify if x=2,y=1 satisfies linear pair.
- Divide x³-3x²+x+2 by x²-2x+1.
Pair of Linear Equations (Algebra)
- Fraction becomes 9/11 adding 2 to num/den; 5/6 adding 3.
- Form equations: ages double in 8 years sum 78 now.
- Solve 2x+3y=14, 4x-2y=10 by elimination.
- Word problem: boats upstream/downstream.
- Graphical solution: consistent/inconsistent pairs.
Quadratic Equations (Algebra)
- Solve 2x²-7x+3=0 by formula.
- √2 x² +7x +5√2=0 by factorisation.
- 100x²-20x+1=0 roots.
- Nature of roots: discriminant analysis.
- Word: ladder against wall slips.
Arithmetic Progressions (Algebra)
- nth term if a=5,d=3,n=10.
- Sum of first 20 terms AP: 2,7,12,….
- AP word: saves Rs 5 more daily.
- Common difference if sum=210,n=20.
- Last term if sum=465,n=15.
Triangles & Circles (Geometry, 15 marks)
- Prove BPT converse; similar triangles areas ratio.
- In ΔPQR right at Q, PR+QR=25,PQ=5; sinP,cosP,tanP.
- Tangent from point to circle equal.
- Circle theorem: angle in semicircle.
- Similar triangles heights ratio.
Trigonometry & Coordinate Geometry (6+ marks)
- Evaluate 2 tan²45° + cos²30° – sin²60°.
- tan(A+B)=√3, tan(A-B)=1/√3; find A,B.
- Distance formula: points (1,2),(4,6).
- Section formula divides 3:2 internally.
- Area of triangle with vertices (0,0),(6,0),(0,4).
Mensuration, Statistics, Probability (Remaining)
- Surface area cylinder open top.
- Volume cone + hemisphere.
- Mean/median of 10,20,…,100.
- Probability even number dice.
- Mode of grouped data.
Competency-Based (Case Studies/MCQs, 20% paper)
- Case: Two trains speeds; relative. (MCQ: time meet?)
- Assertion: Euclid lemma for primes. Reason true?
- Fill: HCF(26,91)=__.
- Case: Polynomial graph touches x-axis. (Double root?)
- Heights shadows similar triangles.
46-50 (Top PYQs): Quadratic max/min value; AP infinite sum; trig identities sin²+cos²=1 app; circle chord bisect; stats cumulative freq.
These are the most important question for class 10th mathematics for boards exam 2025-2026 for cbse and state boards as well .