Mathematics
Topics that carry the marks
The Mathematics section covers number system, HCF and LCM, fractions and decimals, ratio and proportion, percentages, profit and loss, simple and compound interest, average, time and work, speed and distance, mensuration of plane figures and solids, basic algebra (linear equations, exponents), geometry (angles, triangles, circles) and data handling.
Rules worth memorising
- For two numbers, HCF x LCM = product of the numbers.
- Profit percentage and loss percentage are calculated on cost price unless the question states otherwise.
- Simple interest = P x R x T / 100; compound amount = P(1 + R/100)^T.
- Area: triangle = half of base x height; circle = pi r squared; rectangle = length x breadth. Volume: cube = a cubed; cuboid = lbh; cylinder = pi r squared h.
Worked example
A trader marks an article 40% above cost price and then allows a 25% discount. Find his profit percentage. Let cost price = 100. Marked price = 140. Selling price after the 25% discount = 140 x 0.75 = 105. Profit = 5 on a cost of 100, so profit = 5%. The reasoning matters more than the answer: the mark-up is calculated on cost price while the discount is calculated on marked price, so the two percentages sit on different bases.
Traps that cost marks
- Average speed is total distance divided by total time, never the mean of the two speeds.
- Doubling the radius quadruples a circle's area, not doubles it.
- In compound interest the rate applies each year to the growing amount, not to the original principal.
- Leaving units unconverted (metres against centimetres) before substituting in a formula.