Maths Algebra Quick Revision
Algebra Quick Revision for RRB (Group-D, NTPC, ALP)
Last-day cheat sheet – scan, recall, solve!
1. Key Concepts – 30-sec bullets
- Variable: letter that hides a number; Constant: open number.
- Equation: balance-scale; do same thing to both sides.
- Degree: highest power decides name → 1 = linear, 2 = quadratic.
- Linear equation in 2 variables: ax + by + c = 0; needs two conditions (equations) to fix x, y.
- Quadratic: ax² + bx + c = 0; always 2 roots (real or fake).
- Inequality: <, > flip when ×/÷ by –ve.
- Algebraic identity: ready-made expansion; saves 30 sec in simplification.
- HCF of polynomials: lowest power of common factors; LCM = highest power of all factors.
2. Must-Know Formulas – Mug in 5 min
| Formula | Quick Look | Trick to Recall |
|---|---|---|
| (a + b)² | a² + 2ab + b² | “Square, Twice, Square” |
| (a – b)² | a² – 2ab + b² | “Same, minus 2ab” |
| a² – b² | (a – b)(a + b) | “Difference = product of sum & diff” |
| (a + b)³ | a³ + b³ + 3ab(a + b) | “Cube + 3ab-friend” |
| (a – b)³ | a³ – b³ – 3ab(a – b) | “Minus twin” |
| a³ + b³ | (a + b)(a² – ab + b²) | “Same sign, opposite middle” |
| a³ – b³ | (a – b)(a² + ab + b²) | “Opposite sign, same middle” |
| (a + b + c)² | a² + b² + c² + 2(ab + bc + ca) | “All squares + twice pairs” |
| Quadratic roots | x = [-b ± √(b²-4ac)] / 2a | “Minus b, root below, over 2a” |
| Discriminant (D) | b² – 4ac | D > 0 → real, D = 0 → equal, D < 0 → imaginary |
3. Exam Shortcuts & Tricks
- 99² → (100 – 1)² = 10000 – 200 + 1 = 9801 (10 sec)
- 47 × 53 → (50 – 3)(50 + 3) = 50² – 3² = 2500 – 9 = 2491
- Sum of 1st n odd numbers = n² → 1+3+5+…19 = 10² = 100
- If ax²+bx+c=0 has reciprocal roots, then a = c (swap co-effs)
- Zeroes of x² – 5x + 6 → factor fast: (x-2)(x-3); roots 2,3
- Put x = 1 or 0 to check identity in option-elimination MCQs
4. Mnemonics (1-liner)
- SCAM for signs while expanding: Same, Change, Alternate, Maintain (watch +/– inside brackets).
- “Friend-3ab” → whenever you see (a+b)³, auto-write 3ab(a+b).
- “Flip the Fish” → multiply/divide inequality by –ve → flip sign like a fish jumps.
5. Common Exam Question Types
Q1. If 3x + 5 = 17, then 5x + 3 = ?
3x = 12 → x = 4 → 5×4 + 3 = 23Q2. Factor: x² – 7x + 12
(x – 3)(x – 4)Q3. Sum of roots of 2x² – 8x + 1 = 0?
–b/a = 8/2 = 4Q4. If a + b = 7 and ab = 10, find a² + b²
Use (a+b)² = a²+b²+2ab → 49 = a²+b²+20 → a²+b² = 29Q5. Simplify: (0.3)³ – (0.2)³ / (0.3 – 0.2)
a³–b³/(a–b) = a²+ab+b² = 0.09+0.06+0.04 = 0.196. Quick Facts Table – Revise in 1 min
| Word | Means | Exam Hint |
|---|---|---|
| Linear | Power 1 | 1 variable → 1 equation; 2 variables → need 2 equations |
| Quadratic | Power 2 | Always factor/Sridhar; check D for nature |
| Root | Value that kills equation | Sum = –b/a, Product = c/a |
| Identity | True for all x | Expansion/simplification MCQs |
| Inequality | Range answer | Graph on number line; remember flip |
| HCF | Smallest common factor | Polynomial division rarely asked; stick to factors |
| LCM | Largest common multiple | Use in word problems (LCM of times) |
7. 60-Second Strategy in Exam Hall
- Spot type → linear / quadratic / identity.
- Pick formula → write discriminant or factor form instantly.
- Use options → plug x = 0,1, –1 to eliminate 2 options in 10 sec.
- Watch sign –ve ×/÷ → flip inequality; square-root gives ± both.
- Double-check unit/decimal – RRB loves 0.1, 0.01 traps.
You’re set! Glance sheet twice, walk into hall → score +10. ALL THE BEST!
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