ABHYAS · CLASS 9 STUDENTS (CBSE AND STATE BOARDS)
Class 9 Maths कक्षा 9 गणित
Unlimited Class 9 maths practice: number systems, polynomials and identities, coordinate geometry, linear equations in two variables, lines and angles, circles, Heron’s formula, surface areas and volumes, statistics and probability, with hints and worked steps.
Number systems
- Convert recurring decimals to p/q formLet x be the decimal, multiply by 10, 100 … to line up the repeating part, subtract, and solve for x.
- Rationalise the denominatorMultiply top and bottom by a surd that removes the root below: √a × √a = a and (√a + √b)(√a − √b) = a − b.
- Fractional and negative exponentsa^(p/q) = (q-th root of a)^p and a^(−n) = 1/aⁿ. Take the root first to keep numbers small.
Polynomials
- Value of a polynomial at a pointTo find p(a), replace every x in p(x) by a and simplify.
- Remainder theoremWhen p(x) is divided by (x − a), the remainder is p(a). For (x + a), use p(−a).
- Factor theorem: find the missing coefficient(x − a) is a factor of p(x) exactly when p(a) = 0. Put x = a, set the result to 0 and solve.
- Algebraic identities (squares and cubes)x² + 1/x² = (x + 1/x)² − 2; a³ + b³ = (a + b)³ − 3ab(a + b); if a + b + c = 0 then a³ + b³ + c³ = 3abc.