Mental Math for Competitive Exams
Match exam prep to the skills that save time.
System shortcut
Read Cramer windows in place
For small systems, determinant windows reduce column-swapping in your head.
- 1Compute D first.
- 2Read the Dx and Dy windows.
- 3Divide only after signs are checked.
Use carefully
This is best for clean 2-variable systems and answer checks, not every algebra problem.
3-variable caution
Keep the sign pattern visible
For 3x3 systems, signs are the main danger; make them visible before expanding.
- 1Mark the cofactor signs.
- 2Expand through the cleanest row or column.
- 3Substitute only after D is stable.
Use carefully
If signs or numbers are crowded, switch to written work or elimination.
Timed exams reward choosing the right method before arithmetic consumes the clock.
Promise
Train reusable checks first: facts, signs, estimates, ratios, percentages, and small equations. These reduce friction across exams.
Worked Example
For 389 x 22, bracket before calculating: 400 x 20 = 8000. The exact answer, 8558, now has a quick sanity check.
Mistake to Avoid
Do not collect shortcuts randomly. A JEE, CAT, SAT, GRE, or GMAT plan should train the transformations that actually appear in that exam.
Practice Drill
Run a short timed set. Afterward, label each miss as fact recall, sign, decimal, method choice, reading, or time pressure. The next set targets one label.
Recap
The aim is not to avoid written work. It is to make basic computation quiet enough that attention stays on the problem.