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🇮🇳 ICSE Class 9 · subject

ICSE Class 9 Mathematics Syllabus

The Mathematics syllabus for ICSE Class 9 in full: 1 chapter and 7 topics, every one listed below, plus 50 Mathematics flashcards with answers.

1Chapters
7Topics
50Flashcards

Mathematics syllabus: 1 chapter, 7 topics

Expand any chapter to see its topics and sub-topics.

  1. ICSE Class 9 Mathematics

     7 topics
    • Number System
    • Commercial Mathematics
    • Algebra
    • Geometry
    • Mensuration
    • Statistics
    • Trigonometry

ICSE Class 9 Mathematics flashcards — 50 questions with answers

  1. What is a rational number?

    A number that can be written in the form p/q where p and q are integers and q ≠ 0. Its decimal expansion is either terminating or non-terminating recurring.

  2. What is an irrational number, and give one example?

    A number that cannot be written as p/q (q ≠ 0); its decimal expansion is non-terminating and non-recurring. Example: √2 (or π).

  3. How do you rationalise the denominator of 1/(a + √b)?

    Multiply numerator and denominator by the conjugate (a − √b): 1/(a + √b) = (a − √b)/(a² − b).

  4. State the laws of exponents for aᵐ × aⁿ, aᵐ ÷ aⁿ, and (aᵐ)ⁿ.

    aᵐ × aⁿ = aᵐ⁺ⁿ; aᵐ ÷ aⁿ = aᵐ⁻ⁿ; (aᵐ)ⁿ = aᵐⁿ.

  5. What is the value of a⁰ (a ≠ 0) and a⁻ⁿ?

    a⁰ = 1 and a⁻ⁿ = 1/aⁿ.

  6. Express a⁽ᵐ/ⁿ⁾ in radical (surd) form.

    a^(m/n) = ⁿ√(aᵐ) = (ⁿ√a)ᵐ.

  7. What is the simple interest formula?

    S.I. = (P × R × T)/100, where P = principal, R = rate % per annum, T = time in years.

  8. What is the compound interest amount formula for annual compounding?

    A = P(1 + R/100)ⁿ, and C.I. = A − P, where n is the number of years.

  9. How is compound interest calculated when interest is compounded half-yearly?

    A = P(1 + R/200)^(2n), i.e. halve the rate and double the number of periods.

  10. What is the formula for the amount under depreciation at rate R% per year?

    A = P(1 − R/100)ⁿ, where P is the original value and n is the number of years.

  11. State the identity for (a + b)².

    (a + b)² = a² + 2ab + b².

  12. State the identity for (a − b)².

    (a − b)² = a² − 2ab + b².

  13. State the identity a² − b².

    a² − b² = (a + b)(a − b).

  14. State the expansion of (a + b)³.

    (a + b)³ = a³ + 3a²b + 3ab² + b³ = a³ + b³ + 3ab(a + b).

  15. State the expansion of (a − b)³.

    (a − b)³ = a³ − 3a²b + 3ab² − b³ = a³ − b³ − 3ab(a − b).

  16. State the identity for (a + b + c)².

    (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca.

  17. What is the factorisation formula for a³ + b³?

    a³ + b³ = (a + b)(a² − ab + b²).

  18. What is the factorisation formula for a³ − b³?

    a³ − b³ = (a − b)(a² + ab + b²).

  19. What does the Factor Theorem state?

    If p(x) is a polynomial and p(a) = 0, then (x − a) is a factor of p(x); conversely, if (x − a) is a factor, then p(a) = 0.

  20. What does the Remainder Theorem state?

    If a polynomial p(x) is divided by (x − a), the remainder is p(a).

Show the other 30 Mathematics flashcards

  1. What is the degree of a polynomial?

    The highest power of the variable in the polynomial. E.g. 3x⁴ − x + 2 has degree 4.

  2. What is the slope (gradient) of a line passing through points (x₁, y₁) and (x₂, y₂)?

    Slope m = (y₂ − y₁)/(x₂ − x₁).

  3. What is the distance between two points (x₁, y₁) and (x₂, y₂)?

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

  4. State the condition for a system of linear equations to have a unique solution graphically.

    The two lines intersect at exactly one point (they are non-parallel; different slopes).

  5. State the Pythagoras Theorem.

    In a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: c² = a² + b².

  6. What are the conditions for two triangles to be congruent (list the criteria)?

    SSS, SAS, ASA, AAS, and RHS (for right-angled triangles).

  7. State the Mid-Point Theorem.

    The line segment joining the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.

  8. What is the sum of the interior angles of a polygon with n sides?

    (n − 2) × 180°.

  9. What is the sum of the exterior angles of any convex polygon?

    360°, regardless of the number of sides.

  10. State the angle sum property of a triangle.

    The sum of the three interior angles of a triangle is 180°.

  11. What are the key properties of a parallelogram?

    Opposite sides are equal and parallel, opposite angles are equal, and the diagonals bisect each other.

  12. How does a rhombus differ from a parallelogram?

    A rhombus is a parallelogram with all four sides equal, and its diagonals bisect each other at right angles.

  13. What is the area of a triangle given base b and height h?

    Area = ½ × b × h.

  14. State Heron's formula for the area of a triangle with sides a, b, c.

    Area = √[s(s−a)(s−b)(s−c)], where s = (a + b + c)/2 is the semi-perimeter.

  15. What is the area of an equilateral triangle of side a?

    Area = (√3/4)a².

  16. What is the area and circumference of a circle of radius r?

    Area = πr²; Circumference = 2πr.

  17. What is the area of a trapezium with parallel sides a and b and height h?

    Area = ½ × (a + b) × h.

  18. What is the curved surface area and total surface area of a right circular cylinder?

    CSA = 2πrh; TSA = 2πr(h + r).

  19. What is the volume of a right circular cylinder?

    Volume = πr²h.

  20. What is the area of a rectangle and its diagonal?

    Area = length × breadth; Diagonal = √(l² + b²).

  21. How do you find the mean of ungrouped data?

    Mean = (sum of all observations)/(number of observations) = Σx / n.

  22. What is the median of a data set, and how is it found?

    The middle value when data is arranged in order. For n odd it is the ((n+1)/2)th term; for n even it is the average of the (n/2)th and (n/2 + 1)th terms.

  23. What is the mode of a data set?

    The observation that occurs most frequently in the data.

  24. What is the range of a data set?

    Range = largest observation − smallest observation.

  25. Define the six trigonometric ratios in terms of a right triangle.

    sin θ = opp/hyp, cos θ = adj/hyp, tan θ = opp/adj, cosec θ = hyp/opp, sec θ = hyp/adj, cot θ = adj/opp.

  26. State the fundamental trigonometric identity relating sin and cos.

    sin²θ + cos²θ = 1.

  27. State the identity involving sec and tan.

    sec²θ − tan²θ = 1, i.e. 1 + tan²θ = sec²θ.

  28. State the identity involving cosec and cot.

    cosec²θ − cot²θ = 1, i.e. 1 + cot²θ = cosec²θ.

  29. Give the values of sin, cos, and tan for 0°, 30°, 45°, 60°, and 90°.

    sin: 0, ½, 1/√2, √3/2, 1. cos: 1, √3/2, 1/√2, ½, 0. tan: 0, 1/√3, 1, √3, undefined.

  30. What are the reciprocal relationships among the trigonometric ratios?

    cosec θ = 1/sin θ; sec θ = 1/cos θ; cot θ = 1/tan θ; and tan θ = sin θ/cos θ.

ICSE Class 9 Mathematics FAQ

What is in the ICSE Class 9 Mathematics syllabus?

ICSE Class 9 Mathematics is split into 1 chapter: ICSE Class 9 Mathematics. Together they contain 7 topics.

How many chapters are in ICSE Class 9 Mathematics?

1 chapter, containing 7 topics.

Are there flashcards for ICSE Class 9 Mathematics?

Yes — a 50-card Mathematics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.