CBSE Class 9 and 10 Maths: revision path with simulations

The CBSE Mathematics (041) syllabus for Classes 9 and 10 in order, following the new Class 9 units and the Class 10 NCERT chapters. Each topic links to simulations you can drag and explore, and the Class 10 topics are the ones assessed in the board exam.

39 topics · 43 simulations

Class 9

Rational numbers on the number line; density IX Unit I Number System
- Rational numbers on a number line – comparing and zooming in
Decimal expansions of rational numbers IX Unit I Number System
- Rational numbers on a number line – comparing and zooming in
Irrational numbers, proof of irrationality, square root spiral IX Unit I Number System
- Square Roots on the Number Line – Construction and Approximation
Polynomials, degree, terms and coefficients IX Unit II Introduction to Polynomials
- Polynomials in one variable – graphs, values and roots
Linear growth and decay; slope and y-intercept of y = ax + b IX Unit II Introduction to Polynomials
- Graphing lines – slope and y-intercept
- Linear functions – graphs and the equation ax + b = 0
Explicit and recursive rules of sequences IX Unit II Sequences and Progressions
- Sequences from patterns – difference tables, the nth term and recurrence relations
Arithmetic progressions; sum of the first n natural numbers IX Unit II Sequences and Progressions
- Arithmetic and geometric sequences – simple and compound interest
Geometric progressions, fractals and the Tower of Hanoi IX Unit II Sequences and Progressions
- Arithmetic and geometric sequences – simple and compound interest
- Sequences from patterns – difference tables, the nth term and recurrence relations
Visualising identities with geometric models IX Unit II Exploring Algebraic Identities
- Algebraic Identities – Cut and Rearrange
Factorising quadratics with algebra tiles IX Unit II Exploring Algebraic Identities
- Area model algebra – expanding and factorising
Simplifying rational expressions IX Unit II Exploring Algebraic Identities
- The fraction (ax + b)/(cx + d): domain and graph
Graph of a linear equation in two variables IX Unit II Linear Equations in Two Variables
- Equation balance – linear equations in two variables
- Graphing lines – slope and y-intercept
Pair of linear equations: graphical solution, consistency, substitution and elimination IX Unit II Linear Equations in Two Variables
- Systems of Two Linear Equations – Solving Graphically
Distance and midpoint; collinearity and right-angle checks IX Unit III Coordinate Geometry
- Lines and circles in the coordinate plane
- Coordinate Plane – Four Quadrants, Reflections and Distances
Linear pairs, vertically opposite angles, parallel lines and transversals IX Unit IV Lines and Angles
- Parallel Lines and a Transversal – Alternate and Corresponding Angles
- Angle facts – angles at a point, parallel lines, triangle and polygon angle sums
SAS, SSS, ASA, RHS, AAS; isosceles triangle properties IX Unit IV Triangles: Congruence Theorems
- Constructing triangles with a compass – congruence criteria
Parallelogram theorems, mid-point theorem, medians in ratio 2:1 IX Unit IV 4-gons (Quadrilaterals)
- Quadrilateral explorer – identifying special quadrilaterals
- Thales' theorem – parallel lines in a triangle
Chords, angles subtended by arcs, cyclic quadrilaterals, circumcircle IX Unit IV Circles
- Circle theorems explorer – drag points, measure angles
- Circumscribed and inscribed circles of triangles and regular polygons
- Circles – chords and tangents
Circumference, π, arc length and sector area IX Unit V Area and Perimeter
- Circumference and area of a circle – roll a wheel, rearrange sectors
Heron's formula and Brahmagupta's formula IX Unit V Area and Perimeter
- Law of Cosines, Law of Sines, and triangle area
Cuboid, cylinder, cone, pyramid and sphere IX Unit V Surface Area and Volume
- Cylinder, cone, and sphere – surface area and volume
- Cylinder, cone, sphere, prism and pyramid in 3D – nets and cross-sections
- Regular pyramids – triangular and square base
Graphs of data, stacked bar graphs, weighted average, mean, median, mode IX Unit VI Statistics
- Summary statistics of a data set – dragging data points
- Data charts – bar, line, and pie from the same table
Randomness, probability scale and empirical probability IX Unit VI Introduction to Probability
- Experimental probability from repeated marble draws
- Dice and coin tosses – experimental probability
Theoretical probability, sample spaces, tree diagrams and tables IX Unit VI Introduction to Probability
- Classical probability: sample space and events
- Rolling two dice – sample space and probability
- Addition and Multiplication Rules of Probability with Venn and Tree Diagrams

Class 10

Fundamental Theorem of Arithmetic; HCF and LCM Exam topicX Ch 1 Real Numbers
- Sieve of Eratosthenes – finding prime numbers
Proofs of irrationality of √2, √3, √5 Exam topicX Ch 1 Real Numbers
- Square Roots on the Number Line – Construction and Approximation
Zeros of a polynomial; relation between zeros and coefficients of a quadratic Exam topicX Ch 2 Polynomials
- Polynomials in one variable – graphs, values and roots
- Graphing quadratics – coefficients, vertex form, focus and directrix
Graphical method, consistency, algebraic conditions and solution methods Exam topicX Ch 3 Pair of Linear Equations in Two Variables
- Systems of Two Linear Equations – Solving Graphically
Factorisation, quadratic formula and nature of roots Exam topicX Ch 4 Quadratic Equations
- Parabola y = ax² and quadratic equations
- Graphing quadratics – coefficients, vertex form, focus and directrix
nth term and sum of n terms Exam topicX Ch 5 Arithmetic Progressions
- Arithmetic and geometric sequences – simple and compound interest
Similar triangles, basic proportionality theorem and similarity criteria Exam topicX Ch 6 Triangles
- Thales' theorem – parallel lines in a triangle
- Similar triangles – measuring height with shadows
Distance formula and section formula Exam topicX Ch 7 Coordinate Geometry
- Lines and circles in the coordinate plane
Trigonometric ratios, standard angles and identities Exam topicX Ch 8 Introduction to Trigonometry
- Trig ratios of an acute angle – measuring height with elevation angle
- Unit circle and the sine, cosine, tangent graphs
Heights and distances; angles of elevation and depression Exam topicX Ch 9 Some Applications of Trigonometry
- Trig ratios of an acute angle – measuring height with elevation angle
- Bearings and navigation – journeys, return bearings, angles of elevation and depression
Tangent perpendicular to radius; equal tangents from an external point Exam topicX Ch 10 Circles
- Circles – chords and tangents
Area of sectors and segments Exam topicX Ch 11 Areas Related to Circles
- Circumference and area of a circle – roll a wheel, rearrange sectors
Surface areas and volumes of combinations of solids Exam topicX Ch 12 Surface Areas and Volumes
- Cylinder, cone, and sphere – surface area and volume
- Cylinder, cone, sphere, prism and pyramid in 3D – nets and cross-sections
Mean (direct, assumed mean, step deviation), median and mode of grouped data Exam topicX Ch 13 Statistics
- Mean, median and mode of grouped data
- Grouped frequency table and relative frequency chart
Classical probability Exam topicX Ch 14 Probability
- Classical probability: sample space and events
- Rolling two dice – sample space and probability

Topics follow the published curriculum; the mapping to simulations is by Simulic. Simulic is not affiliated with CBSE or NCERT.