Algebra
About 6 min · Mathematics · English
Time worked out from the lesson's 368 words at 150 words a minute, plus a minute for each question.
Algebra forms the bridge between arithmetic and higher mathematics. In AP TET Paper I (Classes 1-5) and Paper II (Classes 6-8), algebra tests your ability to work with unknown quantities, manipulate expressions, and solve equations—skills essential for teaching mathematical reasoning to young learners.
Key ideas
- Variable: A symbol (usually x, y, z) that represents an unknown or changeable quantity. Unlike constants (fixed numbers like 5 or -3), variables can take different values.
- Algebraic Expression: A combination of variables, constants, and operations (+, −, ×, ÷). Examples: 3x + 5, 2a² − 4b + 7. Expressions do NOT have an equals sign.
- Terms, Coefficients, and Constants: In 4x² + 3x − 7, there are three terms. The coefficient of x² is 4, coefficient of x is 3, and −7 is the constant term.
- Like and Unlike Terms: Like terms have identical variable parts (3x and 5x are like; 3x and 3x² are unlike). Only like terms can be combined.
- Equation vs Expression: An equation has an equals sign and states that two expressions are equal. 2x + 3 = 11 is an equation; 2x + 3 is an expression.
Watch out for
- Confusing expressions with equations → Remember: expressions have no equals sign. You simplify expressions but solve equations.
- Wrong sign during transposition → When moving +5 to the other side, it becomes −5, not +5. Always reverse the sign.
- Adding unlike terms → Students write 3x + 2y = 5xy. This is wrong. Unlike terms cannot be combined; 3x + 2y stays as is.
Quick reference
- Variable = letter representing unknown; Constant = fixed number
- Like terms: same variable with same power → can be combined
- (a + b)² = a² + 2ab + b² — never forget the middle term
- (a + b)(a − b) = a² − b² — no middle term here
- To solve linear equations: isolate the variable using transposition or balance method
Check yourself: 3 questions
1. If 3x + 7 = 22, then what is the value of x?
2. Simplify the expression: 5(2x - 3) - 3(x + 4)
3. The sum of three consecutive integers is 78. What is the smallest of these integers?
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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