Algebra forms the bridge between arithmetic and higher mathematics. For TN TET Paper I, you need a solid grasp of foundational algebraic concepts that primary teachers must understand and eventually introduce to young learners. The exam tests your ability to work with variables, solve equations, simplify expressions, and apply standard identities.
This topic typically contributes 3–5 questions in the Mathematics section. Questions range from direct computation (solve for x, simplify an expression) to conceptual understanding (which identity applies here?). Mastery of algebra also supports your performance in mensuration and data-handling problems where algebraic manipulation is often required.
Focus on speed and accuracy. Most TET algebra questions are straightforward if you know your identities and can set up equations correctly. Careless sign errors are the main point-losers.
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Key Concepts
**Variable and Constant**: A variable (x, y, n) represents an unknown or changing quantity; a constant (3, -7, π) has a fixed value.
**Algebraic Expression**: A combination of variables, constants, and operations. Example: 3x² + 5x - 2. Terms are separated by + or - signs.
**Polynomial**: An expression with one or more terms where variables have whole-number exponents only. Classified by degree (highest power) and number of terms (monomial, binomial, trinomial).
**Coefficient and Like Terms**: Coefficient is the numerical part of a term (in 7x², coefficient is 7). Like terms have identical variable parts (3x and -5x are like terms; 3x and 3x² are not).
**Linear Equation**: An equation where the highest power of the variable is 1. Standard form: ax + b = 0. Solution gives exactly one value of x.
**Algebraic Identity**: An equation true for all values of the variables involved. Identities are used to expand or factorise expressions quickly.
**Factorisation**: Writing an expression as a product of its factors. Reverse of expansion. Essential for simplifying and solving equations.
**Degree of a Polynomial**: The highest exponent of the variable. Example: 4x³ + x - 9 has degree 3.
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Formulas / Key Facts
### Standard Algebraic Identities
1. **(a + b)² = a² + 2ab + b²** Used to expand square of a sum.
2. **(a - b)² = a² - 2ab + b²** Used to expand square of a difference.
3. **(a + b)(a - b) = a² - b²** Difference of two squares — very common in factorisation.
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1. **Sign errors when removing brackets** Wrong: -(3x - 5) = -3x - 5 Correct: -(3x - 5) = -3x + 5. The minus distributes to both terms.
2. **Confusing (a + b)² with a² + b²** Wrong: (x + 4)² = x² + 16 Correct: (x + 4)² = x² + 8x + 16. Never forget the middle term 2ab.
3. **Adding unlike terms** Wrong: 5x + 3x² = 8x³ Correct: These are unlike terms and cannot be combined. Expression stays 3x² + 5x.
4. **Wrong transposition sign** Wrong: 2x + 7 = 15 → 2x = 15 + 7 Correct: When +7 moves to RHS, it becomes -7. So 2x = 15 - 7 = 8.
5. **Applying wrong identity to factorise** Wrong: x² + 9 = (x + 3)(x - 3) Correct: x² + 9 is a sum of squares and does not factorise over real numbers using the difference-of-squares identity.
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Quick Reference
**(a + b)² = a² + 2ab + b²** — always include the 2ab term.
**(a - b)(a + b) = a² - b²** — the fastest way to factorise difference of squares.
**Linear equation ax + b = c → x = (c - b)/a** — isolate, then divide.
**Degree of polynomial = highest power** — determines its classification.
**Like terms only**: Combine terms with identical variable parts.
**Verify solutions** by substituting back into the original equation.