CLASS 9 · FREE LEARNING CORNER

Polynomials, lines & geometry

Practise algebraic structure, coordinate ideas and clear mathematical reasoning.

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अपना Maths Level जानें

Five questions. No timer, no registration. Keep a notebook nearby and show your working. This is a small practice snapshot, not a full assessment or rank prediction.

CLASS 9 · SAMPLE MODULE

Understand. Work it out. Check.

IMORS EDUCARE · themathclasses.com · Class 9 · Name: __________________ · Date: __________

One idea to remember

The identity (a + b)² = a² + 2ab + b² includes a middle term. Expanding as (a + b)(a + b) gives a² + ab + ab + b².

Worked example: Expand (x + 3)².

  1. Write (x + 3)(x + 3).
  2. Multiply each term: x² + 3x + 3x + 9.
  3. Combine like terms: x² + 6x + 9.

Your turn

Write your method before opening the answer. These original questions are for practice, not official past-exam papers.

1. Factorise x² − 9.

Show answer & explanation

(x − 3)(x + 3)

Use the difference-of-squares identity a² − b² = (a − b)(a + b), with a = x and b = 3.

2. Find the area of a triangle with base 12 cm and height 5 cm.

Show answer & explanation

30 cm²

Area = (1/2) × base × perpendicular height = (1/2) × 12 × 5 = 30 cm².

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