Subject-Specific Content: Mathematics
What this section tests
Part D carries 75 questions - the largest block in the paper - and is set at roughly intermediate-to-degree standard. It rewards formula fluency and speed rather than lengthy derivation. Candidates opting for Physical Sciences, Biological Sciences, Social Studies or English sit an equivalent paper in that subject, but the mathematics paper is the most widely taken, so it is used here as the model.
Core areas
- Arithmetic: percentages, profit and loss, simple and compound interest, ratio and proportion, time–work, time–distance, averages, mixtures and alligation.
- Algebra: quadratic discriminant, sum and product of roots, AP and GP sums, surds and indices, remainder theorem, partial fractions.
- Geometry: Pythagoras, congruence and similarity (areas scale as the square of corresponding sides), circle theorems - angle in a semicircle is 90°, tangent is perpendicular to the radius, alternate segment theorem.
- Mensuration, trigonometry, coordinate geometry: standard volumes and surface areas, identities, distance and section formulae, slope conditions for parallel and perpendicular lines.
- Statistics and probability: mean, median, mode for grouped data; classical probability with and/or rules.
Worked example
A ₹500 item carries successive discounts of 20% and 10%. Successive percentages never add. Multiply the factors: 500 × 0.80 × 0.90 = ₹360, so the equivalent single discount is 28%, not 30%. The shortcut is a + b + ab/100 with both values negative: −20 − 10 + 2 = −28.
Traps that cost marks
- Adding successive percentage changes instead of multiplying factors.
- Forgetting unit conversion in mensuration (cm to m, litres to cubic centimetres).
- Dropping the negative root of a quadratic, or dividing by a variable that may be zero.
- Using the diameter where the radius is required, and vice versa.
- Answering 'how much more' questions with the absolute value instead of the difference.
Key points
- Successive percentage changes multiply as factors; never add them.
- Equivalent discount of 20% and 10% is 28%.
- Equal roots mean the discriminant b² − 4ac = 0.
- Areas of similar figures scale with the square of the side ratio.
- Angle in a semicircle is 90°; tangent meets radius at 90°.
- Convert all units before substituting into mensuration formulae.