Mathematics
Core concepts
Expect arithmetic (percentage, profit and loss, ratio, average, simple and compound interest, time-work, speed-distance), algebra (simplification, linear equations, exponents), geometry (angles, triangles, circles, area and perimeter), and basic mensuration and data interpretation.
Learn the shortcut formulas: profit% = (profit/cost)×100; successive percentage change = a + b + ab/100; compound interest = P(1+r/100)^n − P; average = sum/count; work rate adds as 1/a + 1/b. In geometry, memorise the Pythagorean triples (3-4-5, 5-12-13, 8-15-17) and the rule that the exterior angle of a triangle equals the sum of the two opposite interior angles.
Traps
- Percentage change is always on the original base; a rise then equal fall does not return to the start.
- Profit/loss percentage is on cost price, not selling price, unless stated.
- Units must match before computing speed or area.
- In ratio problems, keep the total fixed when parts are transferred.
Worked example
A shirt costs 800 taka and is sold at 920 taka. Profit = 120; profit% = 120/800 × 100 = 15%. If instead a 15% discount were applied to a marked price of 920, the selling price would be 920 × 0.85 = 782 - a loss. Rule of thumb: identify the base (cost or marked price) before applying any percentage.