Commercial Mathematics
(i) Compound Interest
(a) As a repeated Simple Interest computation with a growing Principal. Use of this in computing Amount over a 2 or 3-year period. Relation between Amount and CI.
(b) Use of formula A = P (1+ r /100 )n. Finding CI from the relation CI = A – P.
Interest compounded half-yearly included.
Using the formula to find one quantity given different combinations of A, P, r, n, CI and SI;difference between CI and SI type included.
Rate of growth and depreciation.
Note: Paying back in equal installments, being given rate of interest and installment amount, not included.
(ii) Sales Tax and Value Added Tax Computation of tax including problems involving mark-ups, discounts, list-price, profit, loss, basic/cost price including inverse cases.
(iii) Banking
(a) Savings Bank Accounts: computation of interest for a series of months.
(b) Recurring Deposit Accounts: computation of interest using the formula: SI = P (n (n+1)/2) rt / 100.
(iv) Shares and Dividends
Note: Brokerage and fractional shares not included.
(a) Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium.
(b) Formulae
Income = number of shares × rate of dividend × FV.
Return = (Income / Investment) ×100.
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Algebra
(i) Linear Inequations Linear Inequations in one unknown for x ? N, Z, R. Solving -
(ii) HCF and LCM of polynomials by factorization.
(iii) Quadratic Equations
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Geometry
(i) Symmetry
(ii) Similarity
(iii) Loci
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Mensuration
Circle: Area and Perimeter. Direct application problems including Inner and Outer area types.
Three-dimensional solids including right circular cone and sphere: Area (total surface and curved surface) and Volume.
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Trigonometry
Proof of and using Identities to solve/prove simple algebraic trigonometric expressions
sin2A + cos2 A = 1 ,1 + tan2A = sec2A ,1+cot2A = cosec2A; 0 ? A ? 90°
Trigonometric ratios of complementary angles and direct application:
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Statistics
Graphical Representation: For grouped data (both continuous and discontinuous)
histograms, frequency polygons and ogives. Finding the mode from the histogram, the upper and lower Quartiles from the ogive, the median from the ogive.
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