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Skills available for India class X maths curriculum

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10.1 Commercial Mathematics

  • 10.1.i Compound Interest

  • 10.1.ii Sales Tax and Value Added Tax

  • 10.1.iii Banking

    • 10.1.iii.a Savings Bank Accounts. Types of accounts. Idea of savings Bank Account, computation of interest for a series of months.

    • 10.1.iii.b Recurring Deposit Accounts: computation of interest using the formula: SI = P (n(n+1))/(2 x 12) x r/100

  • 10.1.iv Shares and Dividends

    • 10.1.iv.a Face/Nominal Value, Market Value, Dividend, Rate of Dividend, Premium.

    • 10.1.iv.b Formulae

      • 10.1.iv.b.1 Income = number of shares × rate of dividend × FV.

      • 10.1.iv.b.2 Return = (Income / Investment) × 100.

10.2 Algebra

10.3 Geometry

  • 10.3.i Symmetry

    • 10.3.i.a Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamond-shaped figure.

    • 10.3.i.b Being given a figure, to draw its lines of symmetry. Being given part of one of the figures listed above to draw the rest of the figure based on the given lines of symmetry (neat recognizable free hand sketches acceptable).

  • 10.3.ii Similarity - Axioms of similarity of triangles. Basic theorem of proportionality.

  • 10.3.iii Loci

    • 10.3.iii.a The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.

    • 10.3.iii.b The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.

    • 10.3.iii.c The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

  • 10.3.iv Circles

    • 10.3.iv.a Chord Properties:

      • 10.3.iv.a.1 A straight line drawn from the center of a circle to bisect a chord which is not a diameter is at right angles to the chord.

      • 10.3.iv.a.2 The perpendicular to a chord from the center bisects the chord (without proof).

      • 10.3.iv.a.3 Equal chords are equidistant from the center.

      • 10.3.iv.a.4 Chords equidistant from the center are equal (without proof).

      • 10.3.iv.a.5 There is one and only one circle that passes through three given points not in a straight line.

    • 10.3.iv.b Arc and chord properties:

    • 10.3.iv.c Cyclic Properties:

    • 10.3.iv.d Tangent Properties:

      • 10.3.iv.d.1 The tangent at any point of a circle and the radius through the point are perpendicular to each other.

      • 10.3.iv.d.2 If two circles touch, the point of contact lies on the straight line joining their centers.

      • 10.3.iv.d.3 From any point outside a circle two tangents can be drawn and they are equal in length.

      • 10.3.iv.d.4 If a chord and a tangent intersect externally, then the product of the lengths of segments of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.

      • 10.3.iv.d.5 If a line touches a circle and from the point of contact, a chord is drawn, the angles between the tangent and the chord are respectively equal to the angles in the corresponding alternate segments.

  • 10.3.v Constructions

10.4 Mensuration

10.5 Trigonometry

  • 10.5.a Using Identities to solve/prove simple algebraic trigonometric expressions

    • 10.5.a.1 sin² A + cos² A = 1, 1 + tan² A = sec²A, 1+cot²A = cosec²A; 0 ≤ A ≤ 90°

  • 10.5.b Trigonometric ratios of complementary angles and direct application:

  • 10.5.c Heights and distances: Solving 2-D problems involving angles of elevation and depression using trigonometric tables.

10.6 Statistics

  • 10.6.1 Statistics – basic concepts, Histograms and Ogive, Mean, Median, Mode.

    • 10.6.1.a Graphical Representation. Histograms and ogives.

    • 10.6.1.b Computation of:

      • 10.6.1.b.1 Measures of Central Tendency: Mean, median, mode for raw and arrayed data. Mean, median class and modal class for grouped data. (both continuous and discontinuous).

      • 10.6.1.b.2 Mean by all 3 methods included:

        • 10.6.1.b.2.1 Direct: ∑fx/∑f

        • 10.6.1.b.2.2 Short-cut: A + ∑fx/∑f where d = x - A

        • 10.6.1.b.2.3 Step-deviation: A + ∑fx/∑f xi where t = x - A/i

10.7 Probability