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Class 11 Maths — 15 skills

Everything a Class 11 child (ages 16–17) 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.

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Algebra

Sets and Venn diagrams

n(A ∪ B) = n(A) + n(B) − n(A ∩ B): subtract the overlap because it was counted twice. A set with n elements has 2ⁿ subsets.

Builds on: Mean and range

Try it:

  1. In a group of 39 students, every student likes tea or coffee (or both). 12 like tea and 33 like coffee. How many like both ? → 6
  2. In a group of 42 students, every student likes tea or coffee (or both). 30 like tea and 29 like coffee. How many like both ? → 17

Relations and functions

If n(A) = m and n(B) = n, there are 2^(mn) relations from A to B. For f∘g, work from the inside: (f∘g)(x) = f(g(x)).

Builds on: Sets and Venn diagrams, Evaluate algebraic expressions

Try it:

  1. What is the domain of f(x) = 1/(x − 4)? → ℝ − {4}
  2. A has 2 elements and B has 2 elements. How many relations are there from A to B? → 16

Complex numbers

Treat i like a letter, then replace i² by −1: (2 + i)(3 − i) = 6 − 2i + 3i − i² = 7 + i. The modulus of a + bi is √(a² + b²).

Builds on: Multiply and divide integers, Algebraic identities

Try it:

  1. Simplify i 68 . → 1
  2. Write the conjugate of −3 − 6i. → −3 + 6i

Linear inequalities

Solve like an equation, but when you multiply or divide by a NEGATIVE number, flip the sign: −2x < 6 → x > −3.

Builds on: Two-step equations

Try it:

  1. Solve −7x + 12 > −37 for real x. Which interval is the solution set? → (−∞, 7)
  2. Solve 3x − 2 ≥ −26 for real x. Which interval is the solution set? → [−8, ∞)

Binomial theorem

The general term of (a + b)ⁿ is Tᵣ₊₁ = ⁿCᵣ aⁿ⁻ʳ bʳ. There are n + 1 terms; if n is even the middle term is term n/2 + 1.

Builds on: Permutations and combinations, Algebraic identities

Try it:

  1. Find the coefficient of the middle term in the expansion of (x − 3)⁶. → −540
  2. Find the sum of all the coefficients in the expansion of (2x + 2)⁶. → 4096

Sequences and series (GP)

In a GP each term is r times the last: aₙ = a·rⁿ⁻¹ and Sₙ = a(rⁿ − 1)/(r − 1). For two numbers, AM = (a + b)/2 and GM = √(ab).

Builds on: Arithmetic progressions

Try it:

  1. Find the geometric mean (GM) of 1 and 25. → 5
  2. Find the 6th term of the GP 5, −15, 45, … → −1215

Trigonometry

Trigonometric functions

π radians = 180°, so multiply degrees by π/180. For allied angles, find the reference angle and use ASTC (All, Sin, Tan, Cos positive in quadrants I–IV): sin 210° = −sin 30° = −1/2.

Builds on: Trigonometric ratios

Try it:

  1. Find the value of tan 225°. → 1
  2. Convert 2π/5 radians to degrees. → 72°

Data handling

Permutations and combinations

Order matters → permutation ⁿPᵣ = n!/(n − r)!. Order does not matter → combination ⁿCᵣ = n!/(r!(n − r)!). Example: ⁵P₂ = 20, ⁵C₂ = 10.

Builds on: Sets and Venn diagrams

Try it:

  1. In how many ways can a team of 2 be chosen from 7 players? → 21
  2. In how many ways can a team of 4 be chosen from 6 players? → 15

Mean deviation and variance

Find the mean x̄ first. Mean deviation = Σ|x − x̄| ÷ n. Variance = Σ(x − x̄)² ÷ n, and standard deviation = √variance.

Builds on: Mean, mode and median of grouped data, Mean and range

Try it:

  1. Find the standard deviation of: 13, 8, 8, 14, 16, 19. → 4
  2. Find the mean deviation about the mean of: 39, 37, 32, 40, 42. → 2.8

Probability of events

P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and P(not A) = 1 − P(A). Example: P(A) = 1/2, P(B) = 1/3, P(A ∩ B) = 1/6 → P(A ∪ B) = 2/3.

Builds on: Probability with cards, dice and coins, Sets and Venn diagrams

Try it:

  1. P(A) = 1/3, P(B) = 1/4 and P(A ∩ B) = 1/6. Find P(neither A nor B). → 7/12
  2. P(A) = 1/5, P(B) = 1/3 and P(A ∩ B) = 1/15. Find P(A ∪ B). → 7/15

Shapes & patterns

Straight lines

Slope m = (y₂ − y₁)/(x₂ − x₁); point–slope form y − y₁ = m(x − x₁). Distance from (x₁, y₁) to ax + by + c = 0 is |ax₁ + by₁ + c|/√(a² + b²).

Builds on: Distance, section and mid-point, Linear equations in two variables

Try it:

  1. Find the equation of the line with slope −3 passing through (−4, −6). → y = −3x − 18
  2. Find the distance of the point (−5, 2) from the line 12x + 5y + 14 = 0. → 36/13

Conic sections

Circle (x − h)² + (y − k)² = r²: centre (h, k), radius r. Parabola y² = 4ax: focus (a, 0), latus rectum 4a. Ellipse x²/a² + y²/b² = 1 (a > b): c² = a² − b², e = c/a.

Builds on: Straight lines, Coordinate geometry

Try it:

  1. Find the length of the latus rectum of the ellipse x²/25 + y²/16 = 1. → 32/5
  2. Find the radius of the circle x² + y² + 6x − 6y + 14 = 0. → 2

Introduction to 3D geometry

Distance between two points in space: √((x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²). The signs of (x, y, z) tell you the octant.

Builds on: Distance, section and mid-point, Pythagoras theorem

Try it:

  1. Find the distance between the points (−2, −4, −5) and (−13, 6, −7). → 15
  2. In which octant does the point (−7, 8, −2) lie? → VI

Calculus

Limits

First try putting x = a. If you get 0/0, factorise and cancel (x − a). Standard results: lim (xⁿ − aⁿ)/(x − a) = naⁿ⁻¹ and lim (sin x)/x = 1 as x → 0.

Builds on: Factorising polynomials, Trigonometric ratios

Try it:

  1. Evaluate lim x→2 (x² − 4)/(x − 2). → 4
  2. Evaluate lim x→−2 (−3x² − x + 2). → −8

Derivatives

Power rule: d/dx(xⁿ) = nxⁿ⁻¹, and constants multiply through: d/dx(5x³) = 15x². The derivative is lim h→0 [f(x + h) − f(x)]/h.

Builds on: Limits

Try it:

  1. If f(x) = −2x³ − 4x² + 9x − 1, find f′(−1). → 11
  2. Find d/dx (−6x⁷). → −42x⁶

Questions parents ask

What maths does a Class 11 child learn?

In Class 11 (ages 16–17) BeadBop covers 15 skills: Sets and Venn diagrams, Relations and functions, Trigonometric functions, Complex numbers, Linear inequalities, Permutations and combinations, Binomial theorem, Sequences and series (GP), Straight lines, Conic sections, Introduction to 3D geometry, Limits, Derivatives, Mean deviation and variance, Probability of events.

How can my child practise Class 11 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.

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