Mathematics: Arithmetic, Algebra and Geometry Essentials
Core concepts
The mathematics paper covers fractions and decimals, percentage, ratio and proportion, profit and loss, simple and compound interest, basic algebra (simplification, linear equations, formulae), and geometry of triangles, circles and rectangles including area and perimeter. Measurement units and the Pythagoras relation are frequent topics.
Common traps
- Percentage change: a 20% increase followed by a 20% decrease does not return to the original value; the net change is a 4% decrease. Always apply each percentage to the new base.
- Profit and loss base: percentage profit is calculated on cost price, not selling price, unless the question states otherwise.
- Unit mismatch: convert centimetres to metres before calculating area or volume; many options differ only by a power of ten.
- Ratio sharing: total parts, not the number of people, determine each share.
Rule of thumb
For successive percentage changes, multiply the factors: a 20% rise is ×1.20, a 20% fall is ×0.80. The product 0.96 means a 4% net decrease.
Worked example
A shirt costs 800 taka and is sold at a 15% profit. Selling price = 800 × 1.15 = 920 taka. If instead the selling price were 920 with a 15% profit on cost, cost = 920 ÷ 1.15 = 800 taka. Notice that dividing by the factor reverses the operation - a useful check in exam questions.