MBOSE Class X Mathematics

Chapters

1. Chapter 1 · Real Numbers

   Study this chapter

   How every whole number breaks down into primes, how that helps find HCF and LCM, and how to prove that numbers like the square root of 2 are irrational.

   • Fundamental Theorem of Arithmetic
   • Prime factorisation
   • HCF and LCM by prime factorisation
   • $\text{HCF} \times \text{LCM} =$ product of two numbers
   • Proofs that $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$ and expressions such as $3 + 2\sqrt{5}$ are irrational

2. Chapter 2 · Polynomials

   Study this chapter

   What the zeroes of a polynomial mean on a graph, how the zeroes of a quadratic are linked to its coefficients, and how to build a quadratic from them.

   • Linear, quadratic and cubic polynomials
   • Zeroes of a polynomial and their geometrical meaning
   • Relationship between the zeroes and the coefficients of a quadratic polynomial
   • Forming a quadratic polynomial from the sum and product of its zeroes

3. Chapter 3 · Pair of Linear Equations in Two Variables

   Study this chapter

   How two linear equations can be solved together, by drawing their lines on a graph or by substitution and elimination, and how to use them in word problems.

   • Pair of linear equations in two variables
   • Graphical method (intersecting, coincident and parallel lines)
   • Consistency through the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$, $\frac{c_1}{c_2}$
   • Algebraic solution by substitution and elimination
   • Word problems

4. Chapter 4 · Quadratic Equations

   Study this chapter

   Learn to spot, form and solve quadratic equations by factorisation or the quadratic formula, and use the discriminant to tell what kind of roots to expect.

   • Standard form $ax^2 + bx + c = 0$
   • Checking whether an equation is quadratic
   • Forming quadratic equations from situations
   • Roots
   • Solving by factorisation
   • The quadratic formula
   • Discriminant and nature of roots
   • Word problems

5. Chapter 5 · Arithmetic Progressions

   Study this chapter

   Number patterns that grow by the same step each time, and how to find any term or add up many terms quickly without listing them all.

   • Arithmetic progression
   • First term and common difference
   • General form
   • $n$th term
   • Finding terms and the number of terms
   • Sum of the first $n$ terms
   • Applications

6. Chapter 6 · Triangles

   Study this chapter

   When two triangles have the same shape but different sizes, how to prove they are similar, and how the Basic Proportionality Theorem helps solve problems.

   • Similar figures
   • Similarity of triangles
   • The Basic Proportionality Theorem (Thales) and its converse, with proofs
   • Criteria for similarity (AAA, AA, SSS, SAS)
   • Applications
   • Your exam can also ask basic triangle facts from earlier classes (types of triangles, perimeter, equilateral triangle formulas)

7. Chapter 10 · Circles

   Study this chapter

   What a tangent to a circle is, why it meets the radius at a right angle, and why the two tangents from an outside point are equal.

   • Tangent to a circle at a point
   • Theorem 10.1 (tangent ⊥ radius) and Theorem 10.2 (tangents from an external point are equal), with proofs
   • Number of tangents from a point
   • Applications

8. Chapter 11 · Areas Related to Circles

   Study this chapter

   Learn to find the area of a slice of a circle and the length of its curved edge, and to work out the areas of sectors and segments.

   • Area of a circle and circumference (revision)
   • Area of a sector and length of an arc
   • Area of a segment (minor and major)
   • Problems on sectors and segments with angles 60°, 90°, 120°

9. Chapter 12 · Surface Areas and Volumes

   Study this chapter

   How to find the surface area and volume of everyday objects made by joining two solids, such as a cone on a hemisphere or a cylinder.

   • Surface areas and volumes of cuboid, cube, cylinder, cone, sphere and hemisphere (revision)
   • Surface area and volume of combinations of any two of these solids

10. Chapter 7 · Coordinate Geometry

    Study this chapter

    Use coordinates to find the distance between two points, the point that divides a line in a given ratio, and the midpoint of a line segment.

    • Review of axes, quadrants and coordinates
    • Distance formula
    • Section formula (internal division)
    • Mid-point formula
    • Applications (collinearity, types of triangles and quadrilaterals, equidistant points)

11. Chapter 8 · Introduction to Trigonometry

    Study this chapter

    What sine, cosine and tangent mean in a right triangle, their values for special angles, and how to prove simple identities with them.

    • Trigonometric ratios of an acute angle of a right triangle
    • Existence and relations of the ratios
    • Values for 0°, 30°, 45°, 60° and 90°
    • The identity $\sin^2 A + \cos^2 A = 1$ and its two companions
    • Proving simple identities

12. Chapter 9 · Some Applications of Trigonometry

    Study this chapter

    Learn to work out the heights of towers and the widths of rivers without measuring them, using angles of elevation and depression.

    • Line of sight
    • Angles of elevation and depression
    • Simple problems on heights and distances (at most two right triangles; angles of 30°, 45°, 60°)

13. Chapter 13 · Statistics

    Study this chapter

    Learn to find the mean, median and mode of grouped data and use cumulative frequency to understand a large set of numbers.

    • Mean, median and mode of grouped data (bimodal situations avoided)
    • Cumulative frequency

14. Chapter 14 · Probability

    Study this chapter

    What the chance of an event really means, and how to calculate simple probabilities when tossing coins, rolling dice or drawing cards.

    • Classical definition of probability
    • Simple problems on finding the probability of an event