Mathematics: Arithmetic, Algebra and Geometry Essentials
What you must know
The mathematics section rewards speed and accuracy on standard types. Focus on:
- Number system: place value, HCF and LCM, divisibility rules for 2, 3, 4, 5, 6, 8, 9 and 11.
- Percentages, profit and loss: profit% = (profit/cost price) × 100; discount is always on the marked price.
- Ratio and proportion: keep units consistent before forming ratios.
- Average: average = sum of values / number of values; remember the shortcut for consecutive numbers.
- Simple and compound interest: SI = P × R × T / 100.
- Time, speed and distance: also trains and boats-and-streams.
- Algebra: simplification, linear equations in one variable, identities such as (a+b)² = a² + 2ab + b².
- Mensuration: area and perimeter of rectangle, square, triangle and circle; volume of cube, cuboid and cylinder.
Traps to watch
- Percentage change: a 20% increase followed by a 20% decrease does not return to the original value.
- Profit on cost price, discount on marked price - mixing these up is the most common error.
- Unit mismatch in speed problems (metres and kilometres).
- Average of averages: you cannot average two averages unless the group sizes are equal.
Rule of thumb
Estimate the answer before calculating. If your computed value is far from the estimate, recheck the setup.
Worked example: An article bought for ₹400 is sold for ₹460. Profit = 60. Profit% = (60/400) × 100 = 15%.