SYLLABUS:
Commercial Mathematics
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GST: computation including discount, profit/loss, list price & inverse problems
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Banking: Recurring Deposit interest & maturity calculations
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Shares & Dividends: face value, market value, dividend income & returns
2. Algebra
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Linear Inequations (one variable): solve algebraically, set notation, number-line graphing
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Quadratic Equations: nature of roots (Δ >0, =0, <0); solve via factorisation and formula; simple applications
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Ratio & Proportion: including continued proportion, mean proportion, componendo/dividendo techniques
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Factor & Remainder Theorems: check divisibility, factorisation of polynomials up to degree 3
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Matrices: 2×2 matrices—addition, subtraction, multiplication; identity and null matrices
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Arithmetic & Geometric Progressions: nᵗʰ term, sum of n terms, applications
3. Co‑ordinate Geometry
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Reflections across lines x=0, y=0, x=a, y=a and the origin; invariant points
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Equation of a straight line: slope-intercept (y = mx + c) and two-point form; slope as tan θ; parallel/perpendicular conditions
4. Geometry
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Similarity: SSS, SAS, AA, Basic Proportionality Theorem, area ratios; simple applications
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Loci: locus of points at fixed distances, equidistant from lines/points
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Circles:
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Angle properties: angle in a segment, semicircle, circle centre
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Cyclic quadrilateral properties
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Tangents & secants theorems, tangent-chord properties
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Constructions: tangents from a point, inscribing/circumscribing circles on triangles and hexagons
5. Mensuration
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Surface area and volume of cylinder, cone, sphere (incl. hemisphere)
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Combination of solids, including volume-by-melting-and-recasting; no frustum problems
6. Trigonometry
Trigonometric identities: sin²A + cos²A = 1; 1 + tan²A = sec²A; 1 + cot²A = cosec²A
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Heights & distances: 2‑D problems using trig ratios and tables (using θ between 0–90°)
7. Statistics
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Central tendency (mean, median, mode) for both raw and grouped data
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Graphical representations: histograms, less-than ogives; determine quartiles, median, mode, IQR
8. Probability
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Random experiments, sample space, events, theoretical probability for simple events
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