Mathematics IA — Exam Writing Tips
How to write Maths IA answers that score full marks in the TGBIE 1st Year exam — section-by-section presentation tips for proofs, vectors, matrices, and trigonometry.
General Exam Strategy
- 1Maths IA paper: Section A (SAQs — 2 marks each), Section B (SAQs — 4 marks each), Section C (LAQs — 7 marks each). Attempt all sections in order.
- 2Read the full paper in the first 10 minutes. Star the questions you are most confident about — attempt those first within each section.
- 3Never leave a question blank. Even a partially correct setup earns partial marks. Write the formula, substitute values, and attempt a result.
- 4Carry over answers clearly. If Q.5 result is used in Q.6, state: 'Using result from Q.5, ...'
- 5For trigonometric identity proofs: always write LHS and RHS separately, never cross-multiply. Work from one side to the other.
Matrices — How to Write
- 1Always write the order of the matrix (e.g., A is a 3×3 matrix) before starting any operation.
- 2For inverse: write A⁻¹ = (1/|A|) · adj(A), then compute |A|, then compute adj(A) step-by-step.
- 3For Cramer's rule: set up determinants Δ, Δ₁, Δ₂, Δ₃ clearly with column substitutions. Show all expansions.
- 4Rank: write each row-operation step on a new line with the operation in the margin (e.g., R₂ → R₂ − 2R₁).
- 5State: 'Since |A| ≠ 0, A is non-singular and A⁻¹ exists.' This earns a mark even in multi-mark questions.
Vectors — How to Write
- 1Always write vectors with arrow notation (a⃗) or bold. In written exams underline the vector symbol.
- 2For dot product angle problems: write the formula, substitute values, simplify, then take inverse cosine.
- 3For coplanarity: compute [a⃗ b⃗ c⃗] = 0 using the determinant. Write the 3×3 determinant explicitly.
- 4For area of triangle: show |a⃗×b⃗| computation step-by-step, then halve it.
- 5Scalar triple product: expand the determinant clearly. Show each multiplication and subtraction step.
Trigonometric Identities — How to Write
- 1For proof questions: write LHS = ... (first line), then work step-by-step to arrive at RHS. End with 'LHS = RHS. Hence proved.'
- 2For finding the value of expressions like sin75°: write sin(45°+30°), expand using compound angle formula, substitute standard values.
- 3When proving sum-to-product identities: use the formulas as a tool — don't re-derive them.
- 4For multiple angle problems: use cos2A and sin2A as building blocks — don't skip steps.
- 5Trigonometric equation solutions: always express the general solution clearly. If the range is given (e.g., 0 to 2π), list specific solutions.
Properties of Triangles — How to Write
- 1State which rule you are using (Sine rule / Cosine rule / Half-angle formula) before applying it.
- 2For 'prove' questions involving r, R, r₁ etc.: start from the definition (Δ = rs), then substitute.
- 3Heron's formula: compute s first, then s−a, s−b, s−c. Show all four values before computing the root.
- 4If asked to find an angle: use cosine rule, simplify to get cosA, then write A = cos⁻¹(value) in degrees.
- 5For area problems: verify your answer is positive. Area is always positive.