Mathematics
High-yield topics
Prepare number system, HCF-LCM, percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, pipes, speed-distance-time, boats, mixtures, algebra, linear equations, geometry of triangles and circles, mensuration, basic trigonometry and statistics. Maintain a formula sheet and solve a mixed set daily so that you can choose the fastest method under time pressure.
Traps
Successive percentage changes are multiplicative, not additive. Profit percentage is calculated on cost price unless stated otherwise. In average problems, adding a value changes both the total and the count. In time and work, individual rates add; in pipes, inlets add and outlets subtract. Compound interest differs from simple interest from the second period onward. Geometry questions often hide a unit mismatch between cm and m. Read whether the question asks for percentage or percentage points.
Worked example
Two successive discounts of 20% and 10% give a single equivalent discount of 1 - (0.8 x 0.9) = 1 - 0.72 = 0.28, that is 28%, not 30%. Rule of thumb: convert every successive change into a multiplier, multiply the multipliers, and never simply add percentages. For equations, verify the answer by substitution.