Mathematics
Mathematics tests arithmetic, algebra, geometry, mensuration, trigonometry and data interpretation. The JE paper rewards clean method and unit discipline more than long calculation.
Core rules
- BODMAS: brackets, orders, division/multiplication, addition/subtraction.
- Percentage change = (change/original) × 100. Successive changes multiply: a% then b% gives a + b + ab/100.
- Average = sum/count. Simple interest = PRT/100; compound amount = P(1+R/100)^T.
- Time-speed-distance: distance = speed × time; for a train crossing a pole, distance = train length; crossing a platform, distance = train + platform.
- Mensuration: circle area πr², circumference 2πr; cylinder volume πr²h; rectangle area lb.
Worked example
A 120 m train runs at 54 km/h. How long does it take to cross a pole? Convert speed: 54 × 5/18 = 15 m/s. Distance is the train's own length, 120 m. Time = 120/15 = 8 s. If it crosses a 180 m platform, distance becomes 120 + 180 = 300 m and time = 20 s.
Traps
Do not mix km/h and m/s. In compound interest, interest is added each period; simple interest is not. A is 20% more than B means A = 1.2B, not A = B + 20. In mensuration, check whether the question asks for curved surface area or total surface area. For percentages, the base changes after each successive change.