Why quick algebra tricks matter for SSC exams
Time is the toughest opponent in SSC tests – you need to solve problems faster than the clock ticks.
💡 In Simple Words: Algebra tricks are like shortcuts on a road map. They let you reach the answer with fewer turns, so you can answer more questions in the same amount of time.
Common algebra shortcuts you should know
1. Fast multiplication using the difference of squares
The difference of squares is a pattern: a² – b² = (a + b)(a – b). Think of it as splitting a big chocolate bar into two easier pieces.
Example: Find 49 × 51 without a calculator.
- Notice 49 = 50 – 1 and 51 = 50 + 1.
- Apply the pattern: (50 – 1)(50 + 1) = 50² – 1² = 2500 – 1 = 2499.
2. Quick square of numbers ending in 5
Any two‑digit number ending in 5 follows: n5² = n × (n+1) followed by 25. It’s like a magic trick where the last two digits are always 25.
Example: 75² = ?
- Take the tens digit 7, multiply by the next number 8 → 7 × 8 = 56.
- Append 25 → 5625.
3. Simplifying linear equations with the ‘cross‑multiply’ trick
A linear equation is an equation where the highest power of the variable is 1, like 3x + 5 = 2x + 9. Instead of moving terms one by one, cross‑multiply the coefficients when the equation is in the form ax + b = cx + d.
Steps:
- Bring the x‑terms together: a – c.
- Bring the constants together: d – b.
- Divide (d – b) by (a – c) to get x.
Example: 4x – 7 = 2x + 5
- a – c = 4 – 2 = 2
- d – b = 5 – (–7) = 12
- x = 12 ÷ 2 = 6
4. Factoring quadratics using the ‘ac’ method
A quadratic is an equation where the variable is squared, like ax² + bx + c = 0. The ‘ac’ method works when a ≠ 1.
Procedure:
- Multiply a × c.
- Find two numbers that multiply to ac and add to b.
- Split the middle term using those numbers and factor by grouping.
Example: 2x² + 7x + 3 = 0
- ac = 2 × 3 = 6.
- Numbers that give 6 and add to 7 are 6 and 1.
- Rewrite: 2x² + 6x + x + 3.
- Group: (2x² + 6x) + (x + 3) → 2x(x + 3) + 1(x + 3).
- Factor out (x + 3): (2x + 1)(x + 3) = 0.
When to use each trick – quick reference table
| Trick | Typical Question Type | Key Cue |
|---|---|---|
| Difference of squares | Multiplying numbers close to a round number | Numbers like (n‑1)(n+1) |
| Square of numbers ending in 5 | Find square of any two‑digit number ending in 5 | Ends with 5 |
| Cross‑multiply linear | Simple linear equations with x on both sides | ax + b = cx + d |
| ‘ac’ method for quadratics | Factorising ax² + bx + c when a ≠ 1 | Need factors of a × c |
How to practice these tricks efficiently
Think of each trick as a tool in a toolbox. The more you use it, the quicker you’ll reach for it.
📝 Likely Exam Questions
- Q1: Compute 98 × 102 using a shortcut.
Ans: Treat as (100‑2)(100+2)=100²‑2²=10000‑4=9996. - Q2: Find the square of 85 without a calculator.
Ans: 85² = 8 × 9 = 72 → 7225. - Q3: Solve 5x + 3 = 2x + 12 quickly.
Ans: (5‑2)x = 12‑3 → 3x = 9 → x = 3. - Q4: Factorise 3x² + 14x + 8.
Ans: ac = 24; numbers 12 and 2 give 14. 3x² + 12x + 2x + 8 → 3x(x + 4) + 2(x + 4) → (3x + 2)(x + 4). - Q5: Using the difference of squares, evaluate 199 × 201.
Ans: (200‑1)(200+1)=200²‑1²=40000‑1=39999.