Mathematics IA — Revision Checklist
All 10 chapters of Maths IA broken into checkable items, prioritised by TGBIE exam weight. Tick off each item as you revise — this list covers everything that appears in SAQ and LAQ sections.
Ch. 3 Matrices — High Weight
High- Types of matrices: row, column, square, diagonal, scalar, identity, zero, symmetric, skew-symmetric, orthogonal
- Matrix multiplication: order rule — (m×n)(n×p) = (m×p); verify by hand
- Transpose properties: (Aᵀ)ᵀ = A; (AB)ᵀ = BᵀAᵀ — prove these
- Determinant of 2×2 and 3×3 — expansion along any row or column
- Adjoint and inverse: A⁻¹ = (1/|A|)·adj A — memorise and apply
- Rank: find using row-echelon form; know when system is consistent/inconsistent
- Solving simultaneous equations using Cramer's rule and inverse method
Ch. 4 & 5 Vectors — High Weight
High- Types of vectors: zero, unit, collinear, coplanar, like, unlike — definitions
- Scalar multiplication and triangle law of addition
- Component form: a⃗ = a₁i + a₂j + a₃k; |a⃗| = √(a₁²+a₂²+a₃²)
- Section formula (internal and external) — apply to 3D coordinate problems
- Dot product: a⃗·b⃗ = |a⃗||b⃗|cosθ — find angle between vectors
- Cross product: direction by right-hand rule; |a⃗×b⃗| = |a⃗||b⃗|sinθ
- Scalar triple product [a⃗ b⃗ c⃗]: value, coplanarity condition = 0
- Area of triangle = ½|a⃗×b⃗|; area of parallelogram = |a⃗×b⃗|
Ch. 6 Trigonometry up to Transformations — High Weight
High- Compound angle formulas: sin(A±B), cos(A±B), tan(A±B) — know all 6
- Double angle: sin2A, cos2A (all 3 forms), tan2A
- Triple angle: sin3A = 3sinA − 4sin³A; cos3A = 4cos³A − 3cosA
- Half-angle: sinA = 2sin(A/2)cos(A/2); cosA = cos²(A/2) − sin²(A/2)
- Sum to product: sinC + sinD = 2sin((C+D)/2)cos((C−D)/2) — all 4 formulas
- Product to sum: 2sinAcosB = sin(A+B) + sin(A−B) — all 4 forms
- Values at 30°, 45°, 60°, 90° — including sin, cos, tan, cosec, sec, cot
Ch. 7 Trigonometric Equations — Medium Weight
Medium- Principal solution vs general solution — know the difference
- General solution: sinθ = sinα ⟹ θ = nπ + (−1)ⁿα
- General solution: cosθ = cosα ⟹ θ = 2nπ ± α
- General solution: tanθ = tanα ⟹ θ = nπ + α
- Solve equations like 2cos²θ − √3cosθ = 0 by factorisation
Ch. 8 & 9 Inverse Trig & Hyperbolic — Medium Weight
Medium- Domain and range of sin⁻¹, cos⁻¹, tan⁻¹ — memorise restrictions
- sin⁻¹(x) + cos⁻¹(x) = π/2; tan⁻¹(x) + cot⁻¹(x) = π/2
- tan⁻¹(x) + tan⁻¹(y) formula — condition xy < 1
- 2tan⁻¹(x) = sin⁻¹, cos⁻¹, tan⁻¹ equivalents
- cosh²x − sinh²x = 1 (hyperbolic identity)
- Addition formulas for sinh and cosh
- Inverse hyperbolic in logarithmic form — sinh⁻¹(x) = ln(x + √(x²+1))
Ch. 1 & 2 Functions & Induction — Medium Weight
Medium- Types of functions: one-one (injective), onto (surjective), bijective
- Inverse function exists only if f is a bijection
- fog ≠ gof in general — verify with examples
- Mathematical induction: base case, assume P(k), prove P(k+1)
- Induction on divisibility: show expression divisible by some integer
Ch. 10 Properties of Triangles — High Weight (LAQ)
High- Sine rule: a/sinA = b/sinB = c/sinC = 2R — apply to find sides/angles
- Cosine rule: cosA = (b²+c²−a²)/(2bc) — derive and apply
- Half-angle formulas for sin(A/2), cos(A/2), tan(A/2) in terms of s
- Heron's formula: Δ = √(s(s−a)(s−b)(s−c)) — calculate area
- In-radius r = Δ/s; Circum-radius R = abc/4Δ
- Ex-radii: r₁ = Δ/(s−a) and so on — know all three
- Problem type: given two sides and included angle — find remaining elements