Lesson 2.6: Algebra & Mensuration
Objective: Learn key concepts of algebra and mensuration and apply shortcut techniques for Banking Exams.
1. Algebra Basics
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Definition: Algebra involves letters (variables) representing numbers in expressions, equations, and formulas.
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Common Topics:
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Simplifying expressions: 2x+3x=5x2x + 3x = 5x
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Solving linear equations: 2x+5=152x + 5 = 15 → x=5x = 5
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Quadratic equations: ax2+bx+c=0ax^2 + bx + c = 0
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Word problems: Profit, Age, Mixture problems using algebraic expressions
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Tips:
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Always simplify expressions first.
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Substitute numbers carefully to solve equations quickly.
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Practice equation-based word problems regularly.
2. Mensuration Basics
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Definition: Mensuration deals with measurement of shapes—area, perimeter, and volume.
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Important Formulas:
2D Shapes:
| Shape | Area | Perimeter |
|---|---|---|
| Square | a2a^2 | 4a4a |
| Rectangle | l×bl × b | 2(l+b)2(l+b) |
| Triangle | 1/2×base×height1/2 × base × height | a+b+ca+b+c |
| Circle | πr2πr^2 | 2πr2πr |
3D Shapes:
| Shape | Volume | Surface Area |
|---|---|---|
| Cube | a3a^3 | 6a26a^2 |
| Cuboid | l×b×hl × b × h | 2(lb+bh+hl)2(lb + bh + hl) |
| Cylinder | πr2hπr^2h | 2πr(h+r)2πr(h+r) |
| Sphere | 4/3πr34/3 πr^3 | 4πr24πr^2 |
3. Shortcut Tricks
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Memorize formulas for common shapes.
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For triangles: Use Heron’s formula for area if sides known:
Area=s(s−a)(s−b)(s−c),s=a+b+c2Area = \sqrt{s(s-a)(s-b)(s-c)}, \quad s = \frac{a+b+c}{2}
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For quick volume calculations: Use factorization and approximate π = 3.14 if allowed.
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Use unit conversion carefully (cm → m, m³ → liters).
4. Tips for Banking Exams
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Practice algebraic simplification and solving equations daily.
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Memorize mensuration formulas; do not waste time deriving them during exams.
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Solve mixed problems combining algebra and mensuration for speed.
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Always check units in mensuration problems to avoid mistakes.
✅ Lesson Summary:
Algebra and Mensuration are important for quantitative sections. Mastering formulas, simplification techniques, and shortcut methods ensures accuracy and speed in Banking Exams.