TG POLYCET Mathematics: Formulas, Speed and Sign Discipline
TG POLYCET Mathematics follows the Telangana SSC syllabus and tests speed with fundamental algebra, geometry, trigonometry, mensuration, statistics and probability. There is no calculus. Because the paper is OMR-based and time-bound, formula recall and sign discipline decide many marks.
Core rules
- Real numbers: for positive integers a and b, HCF(a,b) × LCM(a,b) = a × b; Euclid's lemma is a = bq + r, 0 ≤ r < b.
- Quadratics: for ax² + bx + c = 0, D = b² − 4ac. D > 0 gives two distinct real roots, D = 0 equal roots, D < 0 no real roots. Sum = −b/a, product = c/a.
- AP: nth term a + (n−1)d, sum n/2[2a + (n−1)d]. GP: nth term ar^(n−1), sum a(r^n − 1)/(r − 1) for r ≠ 1.
- Coordinate geometry: distance √[(x₂−x₁)² + (y₂−y₁)²], midpoint ((x₁+x₂)/2, (y₁+y₂)/2), section formula for ratio m:n.
- Trigonometry: sin²θ + cos²θ = 1, tanθ = sinθ/cosθ, and standard angles 0°, 30°, 45°, 60°, 90°.
- Mensuration: cylinder volume πr²h; cone volume (1/3)πr²h; sphere volume (4/3)πr³; cylinder CSA 2πrh.
- Probability: P(E) = favourable outcomes / total outcomes, with 0 ≤ P(E) ≤ 1.
Worked example
Solve 2x² − 7x + 3 = 0. Here a = 2, b = −7, c = 3, so D = 49 − 24 = 25. Since D > 0, the roots are real and distinct: x = [7 ± √25]/(2×2) = (7 ± 5)/4. Thus x = 12/4 = 3 or x = 2/4 = 1/2. Check: sum 3 + 1/2 = 7/2 = −b/a; product 3 × 1/2 = 3/2 = c/a. Both match.
Traps
Dropping the negative sign when b is negative; using n instead of n−1 in AP sums; mixing curved surface area with total surface area; forgetting unit conversion in mensuration; treating 'at least one' as a single favourable case. In trigonometry, sin(A+B) is not sinA + sinB.