Mathematics
Mathematics in the Bihar Polytechnic entrance tests algebra, trigonometry, coordinate geometry, mensuration and elementary statistics. Most marks come from direct formula use, so write the formula before substituting.
Algebra
- For ax² + bx + c = 0, roots = [−b ± √(b²−4ac)]/(2a); sum = −b/a; product = c/a.
- Discriminant D = b²−4ac: D > 0 gives two distinct real roots, D = 0 equal roots, D < 0 no real roots.
- Factorise by splitting the middle term when integer factors exist.
Trigonometry and coordinate geometry
- sin²θ + cos²θ = 1; tanθ = sinθ/cosθ. Learn standard values at 0°, 30°, 45°, 60° and 90°.
- Distance between (x₁,y₁) and (x₂,y₂) is √[(x₂−x₁)² + (y₂−y₁)²]; midpoint coordinates are the averages of the corresponding coordinates.
Mensuration
- Circle: area πr², circumference 2πr. Triangle: area ½ × base × height. Cylinder: volume πr²h. Sphere: volume (4/3)πr³.
- Convert all lengths to the same unit before calculating.
Worked example
Solve x² − 5x + 6 = 0. Split −5 as −2 −3: x² − 2x − 3x + 6 = 0. Group: x(x−2) − 3(x−2) = 0, so (x−2)(x−3) = 0. Therefore x = 2 or x = 3. Check: sum 2+3 = 5 = −(−5)/1; product 2×3 = 6 = 6/1.
Traps
- A quadratic normally has two roots; do not drop the negative root.
- In the distance formula, subtract coordinates before squaring; reversing the order is harmless, but forgetting to square is not.
- Check whether the question gives radius or diameter. Using diameter as radius is a common mensuration error.
- In trigonometry, check whether the calculator or question is in degrees or radians.