# Mathematics Class 10 ICSE CISCE Topics and Syllabus

CISCE Syllabus For Class 10 Mathematics: Knowing the Syllabus is very important for the students of Class 10. Shaalaa has also provided a list of topics that every student needs to understand.

The CISCE Class 10 Mathematics syllabus for the academic year 2023-2024 is based on the Board's guidelines. Students should read the Class 10 Mathematics Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the CISCE Class 10 Mathematics Syllabus pdf 2023-2024. They will also receive a complete practical syllabus for Class 10 Mathematics in addition to this.

## CISCE Class 10 Mathematics Revised Syllabus

CISCE Class 10 Mathematics and their Unit wise marks distribution

## Syllabus

### CISCE Class 10 Mathematics Syllabus for Commercial Mathematics

1 Compound Interest

(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.

2 Shares and Dividends
• 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
3 Banking

(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:

### CISCE Class 10 Mathematics Syllabus for Algebra

1 Co-ordinate Geometry Distance and Section 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).

(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

3 Factorization

(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.

4 Ratio and Proportion

(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.

5 Linear Inequations

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.
6 Arithmetic Progression
• Finding their General term.
• Finding Sum of their first ‘n’ terms.
• Simple Applications.
7 Geometric Progression
• Finding their General term.
• Finding Sum of their first ‘n’ terms.
• Simple Applications.
8 Matrices

(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.
9 Reflection

(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

10 Co-ordinate Geometry Equation of a Line

(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.

### CISCE Class 10 Mathematics Syllabus for Geometry

1 Loci
• 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.

2 Circles

(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.

3 Constructions

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

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

4 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).

5 Similarity

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.

### CISCE Class 10 Mathematics Syllabus for Mensuration

Area and circumference of circle, Area and volume of solids – cone, sphere.

(a) Circle: Area and Circumference. Direct application problems including Inner and Outer area..

(b) Three-dimensional solids - right circular cone and sphere: Area (total surface and curved surface) and Volume. Direct application problems including cost, Inner and Outer volume and melting and recasting method to find the volume or surface area of a new solid. Combination of two solids included.

Note: Frustum is not included.

Areas of sectors of circles other than quartercircle and semicircle are not included.

### CISCE Class 10 Mathematics Syllabus for Trigonometry

(a) Using Identities to solve/prove simple algebraic trigonometric expressions.

sin2 A + cos2 A = 1

1 + tan2 A = sec2 A

1+cot2 A = cosec2 A; 0< A<900

(b) Trigonometric ratios of complementary angles and direct application:

sin A = cos(90 - A),cos A = sin(90 – A)

tan A = cot (90 – A), cot A = tan (90- A)

sec A = cosec (90 – A), cosec A = sec(90 – A)

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

Note: Cases involving more than two right angled triangles excluded.

### CISCE Class 10 Mathematics Syllabus for Statistics

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

(a) Graphical Representation. Histograms and ogives.

Finding the mode from the histogram, the upper quartile, lower Quartile and median from the ogive.

Calculation of inter Quartile range.

(b) Computation of:

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).

### CISCE Class 10 Mathematics Syllabus for Probability

• Random experiments
• Sample space
• Events
• Definition of probability
• Simple problems on single events (tossing of one or two coins, throwing a die and selecting a student from a group)