Mathematics (Arithmetic and Mensuration)
Mathematics tests arithmetic and mensuration at speed. One accurate line often decides rank, so learn formula families and unit conversions.
Arithmetic
- Percentage change = (change/original) x 100.
- Profit% and loss% are always on cost price unless stated otherwise.
- SI = PRT/100; CI = P(1 + R/100)^T - P.
- Ratio, average, time-work, and speed = distance/time.
Mensuration
- Rectangle: area lb, perimeter 2(l+b).
- Circle: area πr², circumference 2πr.
- Cylinder: volume πr²h, curved surface 2πrh, total surface 2πr(r+h).
- Cone: volume (1/3)πr²h; sphere: (4/3)πr³.
Worked example
A trader marks an article 25% above cost and gives a 20% discount. Find the profit percentage. Let CP = 100. MP = 125. Discount = 20% of 125 = 25. SP = 100. Profit = 0%. The common error is taking 20% of CP, which gives a false 5% profit. Answer: no profit, no loss.
Traps
- Applying discount on cost price instead of marked price.
- Mixing SI and CI for multi-year sums.
- Using diameter in place of radius.
- Forgetting to convert cm to m before area or volume.
- Ignoring that successive percentage changes do not simply add.