Mathematics
Mathematics in the SAMPAD Grade 7 entrance test checks whether you can apply school arithmetic and early algebra to short, unfamiliar problems. Expect number operations, fractions, decimals and percentages, ratio and proportion, simple equations, basic geometry and mensuration, and data interpretation.
Core rules
- Follow BODMAS: brackets, orders/powers, division and multiplication left to right, then addition and subtraction left to right.
- Convert fractions, decimals and percentages to one form before comparing; 0.375 = 37.5% = 3/8.
- In ratio problems, find the value of one part first: total ÷ sum of ratio parts.
- Solve linear equations by doing the same operation to both sides; check by substitution.
- For mensuration, keep units consistent: area in square units, volume in cubic units; 1 cm³ = 1 mL.
Worked example
A shop marks an item at x taka, gives a 20% discount, then adds 10% VAT. The final price is 880 taka. Find the marked price.
Let x taka be the marked price. After the 20% discount, the price is 0.80x. VAT is 10% of that discounted price, so final price = 1.10 × 0.80x = 0.88x. Set 0.88x = 880; x = 880 ÷ 0.88 = 1000. Check: 1000 → 800 after discount → 880 after VAT. The 20% discount and 10% VAT do not simply cancel.
Traps that cost marks
- Adding percentage changes directly: a 20% discount followed by 10% VAT is not a 10% discount overall.
- Mixing perimeter and area, or writing cm instead of cm².
- Cancelling across addition, for example (x+2)/2 is not x.
- Rounding before the final step.
- Forgetting that a ratio total must be divided by the sum of all ratio parts, not by one part.