NCERT Class 10 Maths
Class 10 Maths: Mathematics chapter-wise practice
At this level most marks are lost in small steps: a sign that flips, a formula half remembered, a unit left out. Questions are grouped by topic so your child can go deep on one idea at a time, and every solution is written out the way a teacher would want it in the exam copy.
- 14 chapters
- 677 practice questions
Mathematics
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Chapter 1 Real Numbers
Use prime factorisation to reason about HCF, LCM and divisibility. Build contradiction proofs for familiar irrational numbers such as $\sqrt{2}$ and $\sqrt{3}$.
Topics: Prime factorisation and uniqueness, Divisibility from prime factors, HCF and LCM of two integers, HCF and LCM of three integers, Meeting and cycle problems, Irrationality by contradiction, Irrational expressions
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Chapter 2 Polynomials
Connect zeroes of polynomials with graph intersections and coefficients. Use sums and products of zeroes to factor, verify and build quadratic polynomials.
Topics: Degree, value and zero of a polynomial, Geometrical meaning of zeroes, Maximum number of zeroes, Quadratic zeroes and coefficients, Constructing quadratic polynomials, Cubic zeroes and coefficients
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Chapter 3 Pair of Linear Equations in Two Variables
Represent two unknown quantities by a pair of linear equations. Decide whether the pair has one solution, no solution or infinitely many solutions, and solve by graph, substitution or elimination.
Topics: Forming a pair from a situation, Graphical solution, Consistency and ratio test, Substitution method, Elimination method, Word problems with pairs, Dependent and inconsistent cases
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Chapter 4 Quadratic Equations
Turn real situations into quadratic equations, solve by factorisation, and use the discriminant to decide the nature of roots. Practise choosing meaningful roots in word problems.
Topics: Standard form and identification, Modelling quadratic situations, Roots and verification, Solving by factorisation, Word problems after factorisation, Discriminant and nature of roots, Quadratic formula and applications
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Chapter 5 Arithmetic Progressions
Recognise arithmetic progressions, find their nth terms, add their first n terms, and use them in salary, savings, rows and race problems.
Topics: Recognising arithmetic progressions, First term, common difference and form, nth term formula, Missing terms and term tests, Sum of first n terms, Applications of AP, Arithmetic mean and optional patterns
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Chapter 6 Triangles
Understand similar figures and similar triangles, use Basic Proportionality Theorem and apply AA, SSS and SAS similarity in proofs and measurement problems.
Topics: Similar figures and scale factor, Similarity of polygons, Triangle similarity and correspondence, Basic Proportionality Theorem, Converse of BPT, AA, SSS and SAS similarity, Applications of similarity
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Chapter 7 Coordinate Geometry
Use coordinates to find distances, test shapes and collinearity, and locate points that divide a line segment in a given ratio.
Topics: Coordinate axes and ordered pairs, Distances on axes and from origin, Distance formula, Classifying triangles and quadrilaterals, Equidistant points and loci, Section formula, Midpoint, trisection and applications
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Chapter 8 Introduction to Trigonometry
Define trigonometric ratios in right triangles, use standard-angle values, and prove identities using sin, cos, tan, sec, cosec and cot.
Topics: Right-triangle sides relative to an angle, Six trigonometric ratios, Reciprocal and quotient relations, Ratios from one known ratio, Specific angles 0°, 30°, 45°, 60°, 90°, Evaluating expressions and solving angle pairs, Trigonometric identities
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Chapter 9 Some Applications of Trigonometry
Use trigonometric ratios to find heights and distances from angles of elevation and depression. The chapter turns real scenes such as towers, bridges, ladders and shadows into right-triangle models.
Topics: Line of sight and angles, Right-triangle model, Single-angle height and distance, Observer height and extra parts, Two-angle problems, Depression and multi-object applications
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Chapter 10 Circles
Study tangents to circles, the radius-tangent perpendicular theorem, and equal tangents from an external point. The chapter uses clean geometry proofs and right-triangle calculations.
Topics: Lines and circles, Tangent-radius perpendicular, Number of tangents, Equal tangents theorem, Tangent length calculations, Tangential figures and angle results
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Chapter 11 Areas Related to Circles
Find arc lengths, areas of sectors, and areas of segments of circles. The chapter applies these ideas to clocks, grazing fields, brooches, umbrellas, wipers and warning lights.
Topics: Sectors and segments, Arc length, Sector area, Segment area, Major regions and complements, Applications and units
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Chapter 12 Surface Areas and Volumes
Break real objects such as capsules, tents, toy rockets, glasses and scooped wood into familiar solids. Then choose the visible surface areas or add/subtract volumes carefully with units.
Topics: Recognising combined solids, Exposed and hidden surfaces, Surface area calculations, Volume of combined solids, Capacity, displacement and units, NCERT application problems, Board presentation and estimation
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Chapter 13 Statistics
Extend mean, median and mode from ungrouped data to grouped frequency distributions. Use class marks, cumulative frequencies and suitable formulae to interpret real data tables.
Topics: Grouped data and class marks, Mean of grouped data, Mode of grouped data, Median of grouped data, Cumulative frequency distributions, Continuous classes and ogive readiness, Interpreting and presenting results
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Chapter 14 Probability
Use equally likely outcomes to compute theoretical probability. Count favourable outcomes carefully for coins, dice, cards, bags, complements and everyday chance situations.
Topics: Random experiments and equally likely outcomes, Theoretical probability formula, Elementary, sure and impossible events, Complementary events, Sample spaces for coins, dice and cards, Applications with real objects, Board reasoning and fallacy checks
Where does the study time go?
In Classes 9 and 10 many children leave home early and come back late after school and coaching. Self-study gets pushed into the last hour of the night, when they are too tired to think clearly. What helps most is knowing exactly which topics deserve that hour.
Tuition is fine, and plenty of children need it. But a tutor with eight or ten children in one batch cannot sit with each of them, and cannot always keep track of what the school did that week. Sometimes the tuition follows its own order of chapters, the child ends up juggling two plans for the same subject, and the confusion shows up in the next test.
NoTuition.in gives that small window some shape: the chapter your child is doing in school, a short activity, practice that explains every mistake, and a clear view for you of what needs work.
Practise Class 10 Maths the way the book teaches it
The free plan opens one full chapter in every subject, so you can see how your child gets on before you pay anything.