Mathematics Class 10 ICSE CISCE Topics and Syllabus

• Concept of Compound Interest 
  • Compound Interest as a Repeated Simple Interest Computation with a Growing Principal 
  • Use of Compound Interest in Computing Amount Over a Period of 2 Or 3-years 
• 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.

(a) Compound interest as a repeated Simple Interest computation with a growing Principal. Use of this in computing Amount over a period of 2 or 3-years.

(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.

• Shares and Dividends Examples 
• Shares and Dividends 

  (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.

  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. Note: Brokerage and fractional shares not included

• Introduction to Banking 
• Computation of Interest 
  • Computation of interest for a series of months
  • Recurring Deposit Accounts:- computation of interest using the formula
• Bank 
  • Bank
  • Types of bank account

(a) Savings Bank Accounts.

Types of accounts. Idea of savings Bank Account, computation of interest for a series of months.

(b) Recurring Deposit Accounts: computation of interest using the formula:

• Sales Tax, Value Added Tax, and Good and Services Tax 
• Computation of Tax 

  Computation of tax including problems involving discounts, list-price, profit, loss, basic/cost price including inverse cases

  • List Price 
  • Basic/Cost Price Including Inverse Cases. 
  • Selling Price 
  • Dealer 
• Concept of Discount 
• Concepts of Cost Price, Selling Price, Total Cost Price, and Profit and Loss, Discount, Overhead Expenses and GST 
• Goods and Service Tax (Gst) 
• Gst Tax Calculation 
• Input Tax Credit (Itc) 

• Co-ordinates Expressed as (x,y) 
• Distance Formula 
• Section Formula 
• The Mid-point of a Line Segment (Mid-point Formula) 

Co-ordinates expressed as (x,y) Distance between two points, section, and Midpoint formula, Concept of slope, equation of a line, Various forms of straight lines.

(a) Distance formula.

(b) Section and Mid-point formula (Internal section only, co-ordinates of the centroid of a triangle included).

• Quadratic Equations 
  •  Introduction and Standard Form of a Quadratic Equation - ax² + bx + c = 0, (a ≠ 0)
• Solutions of Quadratic Equations by Factorization 
• Nature of Roots 
  • Nature of Roots Based on Discriminant
  • two distinct real roots, two equal real roots, no real roots
  • Solutions of Quadratic Equations by Using Quadratic Formula and Nature of Roots

  • Two distinct real roots if b² – 4ac > 0

  • Two equal real roots if b² – 4ac = 0

  • No real roots if b² – 4ac < 0

(a) Quadratic equations in one unknown. Solving by:

• Factorisation.
• Formula.

(b) Nature of roots,

Two distinct real roots if b² – 4ac > 0

Two equal real roots if b² – 4ac = 0

No real roots if b² – 4ac < 0

(c) Solving problems

• Factor Theorem 
• Remainder Theorem 
• Factorising a Polynomial Completely After Obtaining One Factor by Factor Theorem 

  Note: f (x) not to exceed degree 3

(a) Factor Theorem.

(b) Remainder Theorem.

(c) Factorising a polynomial completely after obtaining one factor by factor theorem.

Note: f (x) not to exceed degree 3.

• Concept of Proportion 
  • Proportion
  • Continued or mean proportion
  • Proportionality law
• Componendo and Dividendo Properties 
• Alternendo and Invertendo Properties 
• Direct Applications 
• Concept of Ratio 

(a) Duplicate, triplicate, sub-duplicate, sub-triplicate, compounded ratios.

(b) Continued proportion, mean proportion

(c) Componendo and dividendo, alternendo and invertendo properties.

(d) Direct applications.

• Linear Inequations in One Variable 
  • For x ∈ N , W, Z, R
• Solving Algebraically and Writing the Solution in Set Notation Form 
• Representation of Solution on the Number Line 

Linear Inequations in one unknown for x _E N, W, Z, R. Solving

• Algebraically and writing the solution in set notation form.
• Representation of solution on the number line.

• Arithmetic Progression - Finding Their General Term 
• Arithmetic Progression - Finding Sum of Their First ‘N’ Terms. 
• Simple Applications of Arithmetic Progression 

• Finding their General term.
• Finding Sum of their first ‘n’ terms.
• Simple Applications.

• Geometric Progression - Finding Their General Term. 
• Geometric Progression - Finding Sum of Their First ‘N’ Terms 
• Simple Applications - Geometric Progression 

• Finding their General term.
• Finding Sum of their first ‘n’ terms.
• Simple Applications.

• Introduction to Matrices 

  (a) Order of a matrix. Row and column matrices.

  (b) Compatibility for addition and multiplication.

  (c) Null and Identity matrices.

• Addition and Subtraction of Matrices 
• Multiplication of Matrix 

  Multiplication of a 2*2 matrix by

  • a non-zero rational number
  • a matrix
• Matrices Examples 

(a) Order of a matrix. Row and column matrices.

(b) Compatibility for addition and multiplication.

(c) Null and Identity matrices.

(d) Addition and subtraction of 2*2 matrices.

(e) Multiplication of a 2*2 matrix by

• a non-zero rational number
• a matrix.

• Reflection Examples 
• Reflection Concept 

  (a) Reflection of a point in a line:-

  • x=0, y =0, x= a, y=a, the origin.

  (b) Reflection of a point in the origin.

  (c) Invariant points.

• Reflection of a Point in a Line 

  x=0, y =0, x= a, y=a, the origin.

• Reflection of a Point in the Origin. 
• Invariant Points. 

(a) Reflection of a point in a line:

x=0, y =0, x= a, y=a, the origin.

(b) Reflection of a point in the origin.

(c) Invariant points.F

• Slope of a Line 
• Concept of Slope 
• Equation of a Line 
• Various Forms of Straight Lines 
• General Equation of a Line 
• Slope – Intercept Form 
  • y = mx+c
• Two - Point Form 
  • (y-y₁) = m(x-x₁)
• Geometric Understanding of ‘m’ as Slope Or Gradient Or tanθ Where θ Is the Angle the Line Makes with the Positive Direction of the x Axis 
• Geometric Understanding of c as the y-intercept Or the Ordinate of the Point Where the Line Intercepts the y Axis Or the Point on the Line Where x=0 
• Conditions for Two Lines to Be Parallel Or Perpendicular 
• Simple Applications of All Co-ordinate Geometry. 

(c) Equation of a line:

Slope –intercept form y = mx+c

Two- point form (y-y₁) = m(x-x₁)

Geometric understanding of ‘m’ as slope/ gradient/ tanθ where θ is the angle the line makes with the positive direction of the x axis.

Geometric understanding of c as the y-intercept/the ordinate of the point where the line intercepts the y axis/ the point on the line where x=0.

Conditions for two lines to be parallel or perpendicular. Simple applications of all of the above.

• Introduction of Loci 
  • Definition
  • Meaning
• Loci Examples 
• Constructions Under Loci 
• Theorems Based on Loci 

  (a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.

  (b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.

  (c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

Loci :- Definition, meaning, Theorems based on Loci.

(a) The locus of a point equidistant from a fixed point is a circle with the fixed point as centre.

(b) The locus of a point equidistant from two interacting lines is the bisector of the angles between the lines.

(c) The locus of a point equidistant from two given points is the perpendicular bisector of the line joining the points.

• Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles 
• Areas of Sector and Segment of a Circle 
  • Area of the Sector and Circular Segment
  • Length of an Arc
• Tangent Properties - 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 
• Tangent Properties - 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 
• Tangent to a Circle 

  Theorem - The tangent at any point of a circle is perpendicular to the radius through the point of contact.

• Number of Tangents from a Point on a Circle 

  Theorem - The Length of Two Tangent Segments Drawn from a Point Outside the Circle Are Equal

• Chord Properties - 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 
• Chord Properties - the Perpendicular to a Chord from the Center Bisects the Chord (Without Proof) 
• Theorem: Equal chords of a circle are equidistant from the centre. 
• Converse: The chords of a circle which are equidistant from the centre are equal. 
• Chord Properties - There is One and Only One Circle that Passes Through Three Given Points Not in a Straight Line 
• Arc and Chord Properties - the Angle that an Arc of a Circle Subtends at the Center is Double that Which It Subtends at Any Point on the Remaining Part of the Circle 
• Theorem: Angles in the Same Segment of a Circle Are Equal. 
• Arc and Chord Properties - Angle in a Semi-circle is a Right Angle 
• Arc and Chord Properties - If Two Arcs Subtend Equal Angles at the Center, They Are Equal, and Its Converse 
• Arc and Chord Properties - If Two Chords Are Equal, They Cut off Equal Arcs, and Its Converse (Without Proof) 
• Arc and Chord Properties - If Two Chords Intersect Internally Or Externally Then the Product of the Lengths of the Segments Are Equal 
• Cyclic Properties 
  • Opposite Angles of a Cyclic Quadrilateral Are Supplementary
  • The Exterior Angle of a Cyclic Quadrilateral is Equal to the Opposite Interior Angle (Without Proof)
• Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers 

(a) Chord Properties:

• 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.
• The perpendicular to a chord from the center bisects the chord (without proof).
• Equal chords are equidistant from the center.
• Chords equidistant from the center are equal (without proof).
• There is one and only one circle that passes through three given points not in a straight line.

(b) Arc and chord properties:-

• The angle that an arc of a circle subtends at the center is double that which it subtends at any point on the remaining part of the circle.
• Angles in the same segment of a circle are equal (without proof).
• Angle in a semi-circle is a right angle.
• If two arcs subtend equal angles at the center, they are equal, and its converse.
• If two chords are equal, they cut off equal arcs, and its converse (without proof).
• If two chords intersect internally or externally then the product of the lengths of the segments are equal.

(c) Cyclic Properties:

• Opposite angles of a cyclic quadrilateral are supplementary.
• The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle (without proof).

(d) Tangent Properties:

• The tangent at any point of a circle and the radius through the point are perpendicular to each other.
• If two circles touch, the point of contact lies on the straight line joining their centers.
• From any point outside a circle two tangents can be drawn and they are equal in length.
• 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.
• 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.

Note: Proofs of the theorems given above are to be taught unless specified otherwise.

• Circumscribing and Inscribing a Circle on a Regular Hexagon 
• Circumscribing and Inscribing a Circle on a Triangle 
• Construction of Tangents to a Circle 
  • Construction of Tangent to the Circle from the Point Out Side the Circle
  • To construct the tangents to a circle from a point outside it
• Circumference of a Circle 
• Circumscribing and Inscribing Circle on a Quadrilateral 

(a) Construction of tangents to a circle from an external point.

(b) Circumscribing and inscribing a circle on a triangle and a regular hexagon.

• Concept of Symmetry 
• Concept of Lines Symmetry 
  • Figures with one Line of Symmetry
  • Figures with two Line of Symmetry
  • Figures with more Line of Symmetry

(a) Lines of symmetry of an isosceles triangle, equilateral triangle, rhombus, square, rectangle, pentagon, hexagon, octagon (all regular) and diamondshaped figure.

(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).

• Similarity of Triangles 
• Similarity Triangle Theorem 

  If in a two triangles corresponding angles are equal then their corresponding sides are in same ratio hence two triangle are similar

• Axioms of Similarity of Triangles 
• Areas of Similar Triangles Are Proportional to the Squares on Corresponding Sides 

Axioms of similarity of triangles. Basic theorem of proportionality.

(a) Areas of similar triangles are proportional to the squares on corresponding sides.

(b) Direct applications based on the above including applications to maps and models.