Mathematics: Arithmetic, Algebra and Geometry
What the paper tests
Expect arithmetic (ratio, percentage, profit and loss, average, time-work, speed-distance), algebra (simplification, linear and quadratic equations, indices, logarithms), and geometry and mensuration (triangles, circles, areas and volumes), with a little number theory and statistics. Speed matters, so learn standard results rather than deriving everything.
Concepts to master
Percentage change = (change/original) x 100, always measured from the original. For successive changes, multiply factors: a 20% rise then a 10% fall gives 1.2 x 0.9 = 1.08, an 8% net rise. Profit percentage is calculated on cost price unless stated otherwise. For time and work, convert days to rates: if A finishes in 12 days and B in 18, their combined rate is 1/12 + 1/18 = 5/36, so together they take 36/5 days. In algebra, factorise quadratics by finding two numbers whose product is the constant term and whose sum is the middle coefficient. In mensuration, remember area of a circle, circumference, and volume of cylinder and sphere.
Traps
Mixing cost price and selling price as the base of a percentage; forgetting unit conversion (metres to centimetres, minutes to hours); assuming a 25% increase cancels a 25% decrease (it does not); and misreading "average of first n natural numbers", which is (n+1)/2.
Rule of thumb
Write the given quantities with units before calculating, and check whether the answer is plausible in size. In ratio problems, assign a variable to the common multiplier.
Worked example
A shopkeeper buys an item for 400 and sells at 500. Profit = 100, so profit percent = 100/400 x 100 = 25%.