Mathematics: Algebra, Geometry and Trigonometry
Mathematics in AP POLYCET checks Class 10 arithmetic, algebra, geometry, trigonometry and data handling through objective questions. Because options are numerical, a correct method must be finished with exact substitution and a quick reasonableness check.
Core rules and formulas
- Real numbers: use Euclid’s division lemma for HCF; for two positive integers, HCF × LCM = product of the numbers.
- Quadratic equations: for ax² + bx + c = 0, roots satisfy α + β = −b/a and αβ = c/a; discriminant D = b² − 4ac tells whether roots are real, equal or imaginary.
- Arithmetic progressions: nth term = a + (n − 1)d; sum of n terms = n/2[2a + (n − 1)d].
- Trigonometry: sin²θ + cos²θ = 1; know sin, cos and tan at 0°, 30°, 45°, 60° and 90°.
- Similar triangles: areas are in the ratio of the squares of corresponding sides.
- Mensuration: keep radius, height and slant height in the same unit before substituting.
Worked example: solve 2x² − 7x + 3 = 0. Factor: 2x² − 6x − x + 3 = (2x − 1)(x − 3) = 0, so x = 1/2 or x = 3. Check with coefficients: sum = 7/2 and product = 3/2, matching −b/a and c/a. This confirms both roots.
Traps that cost marks
- Cancelling a variable that may be zero, losing a valid root.
- Using diameter as radius in circle, cylinder or cone problems.
- Mixing degree and radian mode; AP POLYCET standard-angle questions use degrees.
- Counting terms in an AP from 0 instead of 1.
- Leaving answers in wrong units (cm² vs m²).