Class 10 Mathematics

Chapters

1. 1Real NumbersLesson: Real Numbers · 15 sections · chapter quiz

   Every lock-and-key code, every fraction in its lowest terms and every 'divide equally' problem rests on one fact: whole numbers are built from primes in exactly one way.

   • • I can state the Fundamental Theorem of Arithmetic and write any composite number as a product of primes.
   • • I can find HCF and LCM from prime factorisations and use HCF × LCM = a × b for two numbers.
   • • I can prove that √2, √3, √5 and numbers like 3 + 2√5 are irrational.
2. 2PolynomialsLesson: Polynomials · 15 sections · chapter quiz

   The path of a thrown ball, the profit of a small shop and the shape of a bridge arch are all described by polynomials. Where such a curve meets the x-axis tells us when the ball lands or when profit becomes zero.

   • • I can find the zeros of a polynomial from its graph and algebraically.
   • • I can state and verify the relationship between the zeros and coefficients of a quadratic polynomial.
   • • I can build a quadratic polynomial from the sum and product of its zeros.
3. 3Pair of Linear Equations in Two VariablesLesson: Pair of Linear Equations in Two Variables · 15 sections · chapter quiz

   Two tickets for adults and three for children cost ₹850; one adult and two children cost ₹500. Two unknowns, two facts — a pair of linear equations finds both prices.

   • • I can represent a pair of linear equations graphically and interpret the solution.
   • • I can decide consistency using the ratios of coefficients.
   • • I can solve pairs of equations by substitution and elimination and use them to model real situations.
4. 4Quadratic EquationsLesson: Quadratic Equations · 15 sections · chapter quiz

   A rectangular garden's length is 3 m more than its width and its area is 40 m². Finding the width leads to x(x + 3) = 40 — a quadratic equation.

   • • I can write quadratic equations in standard form ax² + bx + c = 0, a ≠ 0.
   • • I can solve quadratic equations by factorisation and by the quadratic formula.
   • • I can use the discriminant to decide the nature of roots and solve real-life problems.
5. 5Arithmetic ProgressionsLesson: Arithmetic Progressions · 15 sections · chapter quiz

   Saving ₹100 in the first month and ₹20 more every month after, or seats in an auditorium increasing by 2 per row — these lists grow by a fixed step. They are arithmetic progressions (APs).

   • • I can recognise an arithmetic progression and find its common difference.
   • • I can derive and use the nth term aₙ = a + (n − 1)d.
   • • I can derive and use Sₙ = n/2 [2a + (n − 1)d] to solve daily-life problems.
6. 6Triangles: SimilarityLesson: Triangles: Similarity · 15 sections · chapter quiz

   A photograph enlarged on a phone, a map and the real city, the shadow of a pole and of a tower — shapes that have the same form but different sizes are similar. Similar triangles let us measure heights we cannot climb.

   • • I can distinguish similar figures from congruent figures with examples and counter-examples.
   • • I can prove the Basic Proportionality Theorem (Thales) and use its converse.
   • • I can use the AAA, SSS and SAS similarity criteria to solve problems.
7. 7Coordinate GeometryLesson: Coordinate Geometry · 15 sections · chapter quiz

   A city planner wants a bus stop exactly between two schools, or one-third of the way along a road. Coordinates answer 'how far' and 'where exactly' with simple formulae.

   • • I can find the distance between two points using the distance formula.
   • • I can derive and use the section formula for internal division.
   • • I can use these formulae to test shapes and find unknown points.
8. 8Introduction to TrigonometryLesson: Introduction to Trigonometry · 15 sections · chapter quiz

   How tall is a tree you cannot climb? How steep is a ramp? Trigonometry ('triangle measurement') links the angles of a right triangle to the ratios of its sides.

   • • I can define the six trigonometric ratios of an acute angle and explain why they are well defined.
   • • I can find the values of the ratios at 0°, 30°, 45°, 60° and 90°.
   • • I can prove sin²A + cos²A = 1 and use simple identities and ratio relationships.
9. 9Some Applications of TrigonometryLesson: Some Applications of Trigonometry · 15 sections · chapter quiz

   Surveyors find the height of a hill, sailors judge distance to a lighthouse, and fire-fighters choose ladder angles — all without measuring the height directly.

   • • I can identify the line of sight, angle of elevation and angle of depression.
   • • I can draw a correct diagram for a heights-and-distances problem.
   • • I can solve problems with at most two right triangles using 30°, 45° and 60°.
10. 10Circles: TangentsLesson: Circles: Tangents · 15 sections · chapter quiz

    A bicycle wheel touches the road at exactly one point; a belt over two pulleys touches each pulley along tangents. Tangents describe where straight lines just touch circles.

    • • I can describe secants and tangents and the number of tangents from a point.
    • • I can prove that the tangent at a point is perpendicular to the radius through it.
    • • I can prove that the tangents from an external point are equal and apply this.
11. 11Areas Related to CirclesLesson: Areas Related to Circles · 15 sections · chapter quiz

    A pizza slice, the area a car's wiper cleans, a fan blade's sweep — these are sectors. Gardens, logos and window designs often combine circles, sectors and triangles.

    • • I can derive and use formulae for the area and arc length of a sector.
    • • I can find the area of a segment for central angles 60°, 90° and 120°.
    • • I can solve problems on areas and perimeters of combinations involving sectors.
12. 12Surface Areas and VolumesLesson: Surface Areas and Volumes · 15 sections · chapter quiz

    An ice-cream cone with a scoop on top, a capsule, a tent with a cylindrical base, a toy top — everyday objects are often two simple solids joined together.

    • • I can visualise solids made by combining two of: cube, cuboid, sphere, hemisphere, cylinder, cone.
    • • I can find the total surface area of a combined solid by adding only visible surfaces.
    • • I can find the volume of a combined solid by adding or subtracting volumes.
13. 13StatisticsLesson: Statistics · 15 sections · chapter quiz

    A school wants to know the 'typical' marks of 200 students, a shop the most common shoe size, a city the middle income. Grouped data and averages turn long lists into decisions.

    • • I can find the mean of grouped data by the direct, assumed-mean and step-deviation methods.
    • • I can find the mode of grouped data using the modal class formula.
    • • I can find the median of grouped data using cumulative frequency and interpret all three measures.
14. 14ProbabilityLesson: Probability · 15 sections · chapter quiz

    Weather forecasts say '70% chance of rain'; a board game asks for a six. Probability measures how likely an event is, from impossible (0) to certain (1).

    • • I can state the classical (theoretical) definition of probability for equally likely outcomes.
    • • I can find probabilities of simple events with coins, dice, cards and everyday situations.
    • • I can use P(E) + P(not E) = 1 and recognise impossible and sure events.