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Algebra

About 6 min · Numerical & Mental Ability · English

Time worked out from the lesson's 317 words at 150 words a minute, plus a minute for each question.

Unlike the heavy computational arithmetic topics, algebra tests your ability to work with variables, solve equations, and apply mathematical identities. The exam focuses on practical problem-solving rather than abstract theory.

Key ideas

• Linear equations involve variables to the first power (x, not x²) and can have one or two variables; solving means finding the value that makes the equation true.
• Substitution method for two-variable linear equations: solve one equation for a variable, substitute into the other, then back-substitute to find both values.
• Elimination method adds or subtracts equations after multiplying by suitable constants to eliminate one variable, solving for the other.
• Quadratic equations have the form ax² + bx + c = 0 where a ≠ 0; they produce two solutions (roots) which may be real, equal, or involve negative discriminants.
• Factorization method works when the quadratic can be expressed as a product of two binomials: (x + p)(x + q) = 0, giving roots x = -p and x = -q.

Quick reference

• Linear equation solution in one step: isolate x by transposing all other terms and dividing by coefficient of x
• Two-variable linear equations need two equations; use elimination (faster) or substitution (safer) method
• Quadratic roots from factorization: split middle term so it becomes (x + p)(x + q) = 0
• Quadratic formula works always: x = [-b ± √(b² - 4ac)] / 2a — memorize this completely
• Identity shortcuts: (a + b)² ≠ a² + b²; always include 2ab term

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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