Madhyama Class X Mathematics: Algebra, Trigonometry, and Statistics
What the Class X paper tests
The BSE Odisha Madhyama Class X mathematics paper extends the Class IX base into real numbers, polynomials, pairs of linear equations, quadratic equations, arithmetic progressions, similar triangles, coordinate geometry, trigonometry, circles, areas related to circles, surface areas and volumes, statistics, and probability. Expect multi-step problems that combine algebra with geometry or mensuration.
Core rules
- Real numbers: Euclid’s division algorithm gives HCF; HCF × LCM = product of two positive integers.
- Quadratics: for ax²+bx+c=0, D = b²−4ac; roots = (−b ± √D)/2a. D>0: two distinct real roots; D=0: equal roots; D<0: no real roots.
- AP: a_n = a+(n−1)d; S_n = n/2[2a+(n−1)d].
- Similar triangles: AA, SSS, SAS similarity; basic proportionality theorem.
- Trigonometry: sin²θ + cos²θ = 1; standard angles 0°, 30°, 45°, 60°, 90°.
- Circles: tangent is perpendicular to radius at point of contact; sector area = (θ/360)πr².
Worked example
Solve x²−5x+6=0.
- Identify a=1, b=−5, c=6.
- D = (−5)²−4(1)(6) = 25−24 = 1.
- x = (5 ± √1)/2 = (5 ± 1)/2.
- Roots: x=3 and x=2. Check: 3²−5(3)+6 = 9−15+6 = 0; 2²−5(2)+6 = 4−10+6 = 0.
Traps
Forgetting the ± in the quadratic formula; cancelling x from x²=5x and losing x=0; using n instead of n−1 in the AP nth term; confusing similarity ratio with area ratio (areas scale as the square of the ratio); using the wrong trigonometric ratio after identifying the sides; and applying the median formula with frequencies rather than cumulative frequencies.