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

### CISCE Class 10 Mathematics Course Structure 2023-2024 With Marking Scheme

# | Unit/Topic | Weightage |
---|---|---|

I | Commercial Mathematics | |

1 | Compound Interest | |

2 | Shares and Dividends | |

3 | Banking | |

4 | Gst (Goods and Services Tax) | |

II | Algebra | |

1 | Co-ordinate Geometry Distance and Section Formula | |

2 | Quadratic Equations | |

3 | Factorization | |

4 | Ratio and Proportion | |

5 | Linear Inequations | |

6 | Arithmetic Progression | |

7 | Geometric Progression | |

8 | Matrices | |

9 | Reflection | |

10 | Co-ordinate Geometry Equation of a Line | |

III | Geometry | |

1 | Loci | |

2 | Circles | |

3 | Constructions | |

4 | Symmetry | |

5 | Similarity | |

IV | Mensuration | |

V | Trigonometry | |

VI | Statistics | |

VII | Probability | |

Total | - |

## Syllabus

### CISCE Class 10 Mathematics Syllabus for Commercial Mathematics

- Concept of Compound Interest
- 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

- 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)

### CISCE Class 10 Mathematics Syllabus for Algebra

- 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
- Standard Form of a Quadratic Equation

- Solutions of Quadratic Equations by Factorization
- Nature of Roots of a Quadratic Equation

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

- Factorisation.
- Formula.

(b) Nature of roots,

Two distinct real roots if b^{2} – 4ac > 0

Two equal real roots if b^{2} – 4ac = 0

No real roots if b^{2} – 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
- Slopes of X-axis, Y-axis and lines parallel to axes.
- Slope of line – using ratio in trigonometry
- Slope of Parallel Lines

- 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-y
_{1}) = m(x-x_{1})

- (y-y
- 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-y_{1}) = m(x-x_{1})

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

- 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
**Tangent theorem:**A 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)
- Properties of Congruent Chords
- 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
- 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.

### CISCE Class 10 Mathematics Syllabus for Mensuration

- Circumference of a Circle
- Circle - Direct Application Problems Including Inner and Outer Area
- Surface Area of a Right Circular Cone
- Surface Area of a Sphere
- Surface area of a sphere
- Hemisphere
- Hollow Hemisphere

- Volume of a Cylinder
- Volume of a Combination of Solids
- Surface Area of Cylinder
- Right Circular Cylinder
- Hollow Cylinder

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

- Trigonometric Ratios of Complementary Angles
- Trigonometric Identities
- Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
- Trigonometry

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

sin^{2} A + cos^{2} A = 1

1 + tan^{2} A = sec^{2} A

1+cot^{2} A = cosec^{2} A; 0< A<90^{0}

(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

- Median of Grouped Data
- Ogives (Cumulative Frequency Graphs)
- Concepts of Statistics
- Graphical Representation of Data as Histograms
- Construction of a histogram for continuous frequency distribution
- Construction of histogram for discontinuous frequency distribution.

- Graphical Representation of Ogives
- Finding the Mode from the Histogram
- Finding the Mode from the Upper Quartile
- Finding the Mode from the Lower Quartile
- Finding the Median, upper quartile, lower quartile from the Ogive
- Calculation of Lower, Upper, Inter, Semi-Inter Quartile Range
- Concept of Median
- Mean of Grouped Data
- Mean of Ungrouped Data
- Median of Ungrouped Data
- Mode of Ungrouped Data
- Mode of Grouped Data
- Mean of Continuous Distribution

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

- Basic Ideas of Probability
- Probability - A Theoretical Approach
- Classical Definition of Probability
- Type of Event - Impossible and Sure Or Certain
- assume that all the experiments have equally likely outcomes, impossible event, sure event or a certain event, complementary events,

- Sample Space
- Type of Event - Complementry
- Simple Problems on Single Events
Not using set notation

- Random Experiments

- 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)