AP TET · Bite-size lessons

Algebra

About 6 min · Mathematics and Science (Paper II) · English

Time worked out from the lesson's 343 words at 150 words a minute, plus a minute for each question.

Algebra forms the backbone of upper primary mathematics in the AP TET Paper II syllabus. It introduces students to abstract thinking—moving from concrete numbers to variables and generalised relationships. For the TET exam, you must demonstrate both content mastery (solving problems correctly) and pedagogical understanding (how to teach these concepts effectively to classes 6–8).

Key ideas

• Variable: A symbol (usually x, y, z) representing an unknown or changing quantity. Constants have fixed values; variables can take multiple values.
• Algebraic Expression: A combination of variables, constants and operations (e.g., 3x + 5, 2ab − 7). No equality sign present.
• Polynomial: An expression with non-negative integer exponents only. Examples: x² + 3x + 2 (polynomial), x⁻¹ + 2 (not a polynomial).
• Degree of Polynomial: The highest power of the variable. In 4x³ + 2x − 1, degree is 3. Constant polynomials have degree 0.
• Types by Terms: Monomial (one term: 5x²), Binomial (two terms: x + 3), Trinomial (three terms: x² + x + 1).

Watch out for

• Wrong: Adding exponents when bases are different → 2³ × 3² = 6⁵ Correct: Product rule applies only when bases are same. Calculate separately: 8 × 9 = 72
• Wrong: (a + b)² = a² + b² (forgetting middle term) Correct: (a + b)² = a² + 2ab + b². The middle term 2ab is crucial.
• Wrong: Treating −x² as (−x)² Correct: −x² means −(x²), while (−x)² = x². For x = 3: −x² = −9, but (−x)² = 9

Quick reference

• Polynomial degree = highest exponent of variable in the expression
• Identity vs Equation: Identity is true for all values; equation is true for specific values only
• (a + b)² − (a − b)² = 4ab — useful shortcut for products
• Linear equation in one variable: Only one solution exists
• To factorise: First check for common factors, then try standard identities

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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