Home › School Maths › Class 9

Class 9 Maths — 14 skills

Everything a Class 9 child (ages 14–15) practises in BeadBop School Maths, aligned to NCERT. Each skill below has a one-line explanation and sample questions with answers — practise them free in the app with step-by-step help.

Practise Class 9 maths free हिंदी में

Class 1 · Class 2 · Class 3 · Class 4 · Class 5 · Class 6 · Class 7

Numbers

Rational and irrational numbers

A rational number can be written as p/q; its decimal either ends or repeats. A recurring decimal like 0.4545… = 45/99 = 5/11, while √2 never ends or repeats, so it is irrational.

Builds on: Add rational numbers

Try it:

  1. Which fraction has a terminating decimal expansion? → 1/8
  2. Write 0.9777… (only the 7 repeats) as a fraction in simplest form. → 44/45

Exponents and rationalising surds

a^(p/q) means take the q-th root, then raise to the power p: 8^(2/3) = 2² = 4. To rationalise 1/(√a − √b), multiply top and bottom by √a + √b.

Builds on: Exponents and powers, Rational and irrational numbers

Try it:

  1. Rationalise the denominator: 1/(√13 + √5) → (√13 − √5)/8
  2. Evaluate 8 2/3 . → 4

Algebra

Polynomials and remainder theorem

The degree is the highest power of x. To find p(a), put x = a. Remainder theorem: dividing p(x) by (x − a) leaves remainder p(a).

Builds on: Evaluate algebraic expressions, Multiply and divide integers

Try it:

  1. Find the remainder when −4x 2 − 9x + 8 is divided by (x + 2). → 10
  2. Find the remainder when −3x 3 + 6x 2 + 7x − 9 is divided by (x − 3). → −15

Factorising polynomials

For ax² + bx + c find two numbers that multiply to a × c and add to b, then split the middle term: x² + 5x + 6 = (x + 2)(x + 3). Factor theorem: (x − a) is a factor when p(a) = 0.

Builds on: Polynomials and remainder theorem, Factorisation

Try it:

  1. If (x + 2) is a factor of x 3 − x 2 + 8x + k, find k. → 28
  2. Factorise: 3x 2 − 4x − 4 → (x − 2)(3x + 2)

Linear equations in two variables

A point (x, y) is a solution of ax + by = c if putting in its x and y makes both sides equal. Substitute the point, then solve for the unknown.

Builds on: Two-step equations, Coordinate geometry

Try it:

  1. Which point is a solution of −3x − y = 11? → (−4, 1)
  2. Find k if x = 2, y = 4 is a solution of kx + 6y = 28. → 2

Shapes & patterns

Coordinate geometry

In (x, y), x is the abscissa and y the ordinate. Signs give the quadrant: (+,+) I, (−,+) II, (−,−) III, (+,−) IV. A point with y = 0 lies on the x-axis.

Builds on: Add and subtract integers

Try it:

  1. What is the ordinate of the point (−2, −7)? → −7
  2. In which quadrant does the point (−5, 8) lie? → Quadrant II

Lines and angles

Vertically opposite angles are equal; a linear pair adds to 180°. With parallel lines cut by a transversal, corresponding and alternate angles are equal, and co-interior angles add to 180°.

Builds on: Complementary and supplementary angles

Try it:

  1. Two parallel lines are cut by a transversal. One angle is 26°. Find its corresponding angle (in degrees). → 26
  2. Two angles form a linear pair and are in the ratio 1 : 2. Find the larger angle (in degrees). → 120

Triangles and congruence

Angles of a triangle add to 180°. In an isosceles triangle the angles opposite the equal sides are equal. Two triangles are congruent by SSS, SAS, ASA/AAS or RHS.

Builds on: Lines and angles, Exterior angle of a triangle

Try it:

  1. In an isosceles triangle the angle between the two equal sides is 60°. Find each base angle (in degrees). → 60
  2. Each base angle of an isosceles triangle is 55°. Find the third angle (in degrees). → 70

Quadrilaterals and mid-point theorem

In a parallelogram, opposite angles are equal and adjacent angles add to 180°. Mid-point theorem: the segment joining the mid-points of two sides of a triangle is parallel to the third side and half as long.

Builds on: Triangles and congruence

Try it:

  1. In parallelogram ABCD, ∠A = 86°. Find ∠B (in degrees). → 94
  2. In parallelogram ABCD, ∠A = 130°. Find ∠B (in degrees). → 50

Angles in circles

The angle at the centre is twice the angle at the circumference on the same arc. Angles in the same segment are equal. Opposite angles of a cyclic quadrilateral add up to 180°.

Builds on: Triangles and congruence

Try it:

  1. A, B, C, D lie on a circle, with C and D on the same side of chord AB. If ∠ACB = 79°, find ∠ADB (in degrees). → 79
  2. ABCD is a cyclic quadrilateral with ∠D = 62°. Find ∠B (in degrees). → 118

Measurement

Heron's formula

Find s = (a + b + c) ÷ 2, then area = √(s(s − a)(s − b)(s − c)). For sides 5, 5, 6: s = 8, area = √(8 × 3 × 3 × 2) = 12.

Builds on: Perimeter of polygons, Pythagoras theorem

Try it:

  1. Use Heron's formula to find the area of a triangle with sides 24 cm, 13 cm and 13 cm (in cm²). → 60
  2. Use Heron's formula to find the area of a triangle with sides 10 cm, 12 cm and 10 cm (in cm²). → 48

Cone, sphere and hemisphere

Sphere: area 4πr², volume (4/3)πr³. Hemisphere: curved area 2πr², total 3πr², volume (2/3)πr³. Cone: curved area πrl, volume (1/3)πr²h, with l² = r² + h².

Builds on: Circumference and area of a circle, Heron's formula

Try it:

  1. Find the volume of a cone with radius 5 cm and height 12 cm (in cm³, in terms of π). → 100π
  2. A cone has radius 9 cm and height 12 cm. Find its slant height (in cm). → 15

Data handling

Mean, median and mode

Mean = total ÷ count (for a table, Σfx ÷ Σf). Median = middle value after sorting (average the two middle values if the count is even). Mode = most frequent value.

Builds on: Median and mode, Mean and range

Try it:

  1. Marks 10, 12, 14, 45 were scored by 2, 3, 6, 3 students respectively. What is the mode ? → 14
  2. Marks 3, 10, 11, 60 were scored by 5, 7, 2, 8 students respectively. What is the mode ? → 60

Experimental probability

Experimental probability = number of times the event happened ÷ total number of trials. If a coin shows heads 45 times in 100 tosses, P(head) = 45/100 = 9/20.

Builds on: Simple probability, Mean, median and mode

Try it:

  1. Out of 250 bulbs tested, 21 were defective. What is the experimental probability that a bulb is not defective ? → 229/250
  2. A coin is tossed 60 times and shows heads 30 times. What is the experimental probability of getting a tail ? (simplest form) → 1/2

Questions parents ask

What maths does a Class 9 child learn?

In Class 9 (ages 14–15) BeadBop covers 14 skills: Rational and irrational numbers, Exponents and rationalising surds, Polynomials and remainder theorem, Factorising polynomials, Coordinate geometry, Linear equations in two variables, Lines and angles, Triangles and congruence, Quadrilaterals and mid-point theorem, Angles in circles, Heron's formula, Cone, sphere and hemisphere, Mean, median and mode, Experimental probability.

How can my child practise Class 9 maths at home?

Start with the free starting-point check in BeadBop. It recommends the right skill, explains it step by step and gives practice that adapts to your child.

Find your child’s starting point — free