ICSE Class 10 Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in ICSE Class 10, not a summary of it.

1. 1

   ICSE Mathematics

   5 topics

   • Commercial Mathematics
   • Algebra
   • Geometry
   • Mensuration
   • Statistics

Mathematics flashcards for ICSE Class 10

21 of 50 cards from the Mathematics deck — real questions with worked answers.

1. In Compound Interest, what is the formula for the amount A when interest is compounded annually for n years at rate R% on principal P?

   A = P(1 + R/100)^n. Compound Interest = A − P.

2. How do you compute compound interest when it is compounded half-yearly at R% per annum for n years?

   Use A = P(1 + (R/2)/100)^(2n); i.e. halve the rate and double the number of conversion periods. CI = A − P.

3. What is the formula for the value of an article after n years if it depreciates at R% per annum?

   Depreciated value = P(1 − R/100)^n, where P is the original cost.

4. How is GST (Goods and Services Tax) split, and how is it calculated on intra-state sale of an article of value V at rate r%?

   For intra-state sale, GST = CGST + SGST, each at r/2%. Total GST = V × r/100. For inter-state sale, IGST = V × r/100 is charged instead.

5. In GST, what is Input Tax Credit (ITC) and how does it determine a dealer's net GST payable?

   ITC is the GST a dealer already paid on purchases. Net GST payable = Output GST (on sales) − Input GST (on purchases / ITC).

6. What is the maturity value formula for a Recurring Deposit of monthly instalment P for n months at R% per annum simple interest?

   Interest I = P × [n(n+1)/2] × (R/100) × (1/12); Maturity Value = P×n + I.

7. For shares: define Nominal (Face) Value, Market Value, and Dividend.

   Nominal/Face Value (NV) is the printed value of a share. Market Value (MV) is the price it trades at. Dividend is the profit paid per share, calculated as a percentage of the FACE value, not the market value.

8. How do you find the annual income and the rate of return (yield) from shares?

   Income = Number of shares × Face value × Dividend%. Number of shares = Investment ÷ Market value. Yield% = (Annual income ÷ Investment) × 100.

9. State the quadratic formula for solving ax² + bx + c = 0.

   x = [−b ± √(b² − 4ac)] / (2a), valid for a ≠ 0.

10. What does the discriminant D = b² − 4ac tell you about the roots of a quadratic equation?

    If D > 0: two distinct real roots; if D = 0: two equal (real, coincident) roots; if D < 0: no real roots (roots are imaginary).

11. State the Factor Theorem and the Remainder Theorem for a polynomial p(x).

    Remainder Theorem: when p(x) is divided by (x − a), the remainder is p(a). Factor Theorem: (x − a) is a factor of p(x) if and only if p(a) = 0.

12. What is the condition for two ratios a:b and c:d to be in proportion, and what are the means and extremes?

    They are in proportion if a:b :: c:d, i.e. a/b = c/d, equivalently ad = bc (product of extremes a, d = product of means b, c).

13. Define the third proportional, fourth proportional, and mean proportional.

    Fourth proportional of a, b, c is x where a:b = c:x. Third proportional of a, b is x where a:b = b:x. Mean proportional of a and b is √(ab).

14. State the law of componendo and dividendo for a/b = c/d.

    If a/b = c/d, then (a + b)/(a − b) = (c + d)/(c − d).

15. What is the order of a matrix, and when can two matrices A and B be multiplied?

    Order is rows × columns (m × n). A (m×n) and B (p×q) can be multiplied as AB only if n = p; the product has order m × q.

16. What is the identity matrix and the additive identity (zero matrix) in matrix algebra?

    The identity matrix I has 1s on the main diagonal and 0s elsewhere, satisfying AI = IA = A. The zero (null) matrix O has all entries 0, satisfying A + O = A.

17. State the formula for the nth term of an Arithmetic Progression (AP) with first term a and common difference d.

    aₙ = a + (n − 1)d.

18. State the two formulas for the sum of the first n terms of an AP.

    Sₙ = n/2 [2a + (n − 1)d], or equivalently Sₙ = n/2 (a + l) where l is the last term.

19. State the nth term and sum formulas for a Geometric Progression (GP) with first term a and common ratio r.

    nth term aₙ = arⁿ⁻¹. Sum Sₙ = a(rⁿ − 1)/(r − 1) for r > 1, or a(1 − rⁿ)/(1 − r) for r < 1.

20. How do you solve a pair of linear equations in two variables by the method of cross-multiplication?

    For a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0: x/(b₁c₂ − b₂c₁) = y/(c₁a₂ − c₂a₁) = 1/(a₁b₂ − a₂b₁).

21. State the distance formula between points (x₁, y₁) and (x₂, y₂).

    Distance = √[(x₂ − x₁)² + (y₂ − y₁)²].

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