CBSE Class 10 Mathematics Syllabus

Mathematics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Mathematics in CBSE Class 10, not a summary of it.

1. 1

   Real Numbers

   4 topics

   • Euclid's Division Lemma
   • Fundamental Theorem of Arithmetic
   • Revisiting Irrational Numbers
   • Revisiting Rational Numbers and Their Decimal Expansions
2. 2

   Polynomials

   3 topics

   • Geometrical Meaning of the Zeroes of a Polynomial
   • Relationship between Zeroes and Coefficients of Polynomial
   • Division Algorithm for Polynomials
3. 3

   Pair of Linear Equations in Two Variables

   3 topics

   • Graphical Method of Solution of a Pair of Linear Equations
   • Algebraic Methods of Solving a Pair of Linear Equations
   • Equations Reducible to a Pair of Linear Equations in Two Variables
4. 4

   Quadratic Equations

   3 topics

   • Introduction to Quadratic Equations
   • Method of Completing the Square
   • Nature of Roots
5. 5

   Arithmetic Progressions

   3 topics

   • Introduction to Arithmetic Progression
   • nth Term of an AP
   • Sum of First n Terms of an AP
6. 6

   Triangles

   3 topics

   • Similar Figures
   • Criteria for Similarity of Triangles
   • Areas of Similar Triangles
7. 7

   Coordinate Geometry

   3 topics

   • Distance Formula
   • Section Formula
   • Area of a Triangle
8. 8

   Introduction to Trigonometry

   3 topics

   • Trigonometric Ratios
   • Trigonometric Ratios of Some Specific Angles
   • Trigonometric Ratios of Complementary Angles
9. 9

   Some Applications of Trigonometry

   1 topic

   • Heights and Distances
10. 10

    Circles

    2 topics

    • Tangent to a Circle
    • Number of Tangents from a Point on a Circle
11. 11

    Constructions

    2 topics

    • Division of a Line Segment
    • Construction of Tangents to a Circle
12. 12

    Areas Related to Circles

    3 topics

    • Perimeter and Area of a Circle
    • Areas of Sector and Segment of a Circle
    • Areas of Combinations of Plane Figures
13. 13

    Surface Areas and Volumes

    4 topics

    • Surface Area of a Combination of Solids
    • Volume of a Combination of Solids
    • Conversion of Solid from One Shape to Another
    • Frustum of a Cone
14. 14

    Statistics

    4 topics

    • Mean of Grouped Data
    • Mode of Grouped Data
    • Median of Grouped Data
    • Graphical Representation of Cumulative Frequency Distribution
15. 15

    Probability

    3 topics

    • Classical Definition of Probability
    • Types of Events
    • Probability – A Theoretical Approach

Mathematics flashcards for CBSE Class 10

21 of 78 cards from the Mathematics deck — real questions with worked answers.

1. State Euclid's Division Lemma.

   For any two positive integers a and b, there exist unique whole numbers q and r such that a = bq + r, where 0 ≤ r < b.

2. State the Fundamental Theorem of Arithmetic.

   Every composite number can be expressed (factorised) as a product of primes, and this factorisation is unique, apart from the order in which the prime factors occur.

3. For two positive integers a and b, how are HCF and LCM related to the numbers themselves?

   HCF(a, b) × LCM(a, b) = a × b.

4. How can you prove √2 is irrational using the Fundamental Theorem of Arithmetic?

   Assume √2 = p/q (p, q coprime). Then 2q² = p², so 2 divides p², hence 2 divides p; writing p = 2c gives 2 divides q² too, so 2 divides q. This contradicts p, q being coprime, so √2 is irrational.

5. What is the condition on the denominator q for a rational number p/q (in lowest terms) to have a terminating decimal expansion?

   The prime factorisation of q must be of the form 2^n × 5^m, where n and m are non-negative integers.

6. When does a rational number p/q (in lowest terms) have a non-terminating repeating decimal expansion?

   When the denominator q has at least one prime factor other than 2 or 5.

7. What does the zero of a polynomial p(x) represent geometrically?

   A zero of p(x) is the x-coordinate of a point where the graph of y = p(x) intersects (cuts) the x-axis.

8. How many zeroes can a polynomial of degree n have, and what does this mean for its graph?

   A polynomial of degree n has at most n zeroes, so its graph can intersect the x-axis at most n times.

9. For a quadratic polynomial ax² + bx + c with zeroes α and β, what are the sum and product of zeroes?

   Sum of zeroes α + β = −b/a; Product of zeroes αβ = c/a.

10. For a cubic polynomial ax³ + bx² + cx + d with zeroes α, β, γ, state the three relationships between zeroes and coefficients.

    α + β + γ = −b/a; αβ + βγ + γα = c/a; αβγ = −d/a.

11. State the Division Algorithm for polynomials.

    For polynomials p(x) and g(x) ≠ 0, there exist unique polynomials q(x) and r(x) such that p(x) = g(x)·q(x) + r(x), where r(x) = 0 or degree of r(x) < degree of g(x).

12. In the graphical method, what does the point of intersection of two lines representing a pair of linear equations give?

    It gives the unique solution (the values of x and y) that satisfy both equations simultaneously.

13. For a pair of linear equations a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, what condition gives a unique solution (consistent, intersecting lines)?

    a₁/a₂ ≠ b₁/b₂.

14. For a pair of linear equations, what condition gives infinitely many solutions (consistent, coincident lines)?

    a₁/a₂ = b₁/b₂ = c₁/c₂.

15. For a pair of linear equations, what condition gives no solution (inconsistent, parallel lines)?

    a₁/a₂ = b₁/b₂ ≠ c₁/c₂.

16. Name the three algebraic methods for solving a pair of linear equations in two variables.

    Substitution method, Elimination method, and Cross-multiplication method.

17. In the cross-multiplication method for a₁x+b₁y+c₁=0 and a₂x+b₂y+c₂=0, what is the formula for x and y?

    x/(b₁c₂−b₂c₁) = y/(c₁a₂−c₂a₁) = 1/(a₁b₂−a₂b₁).

18. How are equations like 2/x + 3/y = 13 reduced to a pair of linear equations?

    By substituting 1/x = u and 1/y = v, converting them into linear equations in u and v, which are then solved and back-substituted to find x and y.

19. What is the standard (general) form of a quadratic equation?

    ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0.

20. What is the quadratic formula for the roots of ax² + bx + c = 0?

    x = (−b ± √(b² − 4ac)) / (2a).

21. Describe the method of completing the square to solve ax² + bx + c = 0.

    Make the coefficient of x² equal to 1, add and subtract the square of half the coefficient of x to form a perfect square (x + b/2a)², then take the square root and solve for x.

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