Mathematics IA — Previous Year Papers
TGBIE IPE previous year questions for Maths IA — repeated topics and selected questions from recent exams. Use these to identify what comes up every year.
Topics That Repeat Every Year
Every yearMatrices — Solution of 3 equations (Cramer's or inverse method)
Every yearVectors — Scalar triple product / Volume of parallelepiped
Every yearProperties of Triangles — r, R, r₁, r₂, r₃ relationships
Every yearTrigonometry — Prove identity involving multiple angles
Almost every yearMathematical Induction — Sum formula or divisibility
Almost every yearFunctions — Bijection and inverse
Very frequentVectors — Area of triangle or parallelogram
Very frequentInverse Trigonometric — Sum formula proof
Very frequentTrigonometric Equations — General solution
FrequentHyperbolic Functions — Definition and addition formula
Selected Questions from Past IPE Papers
IPE 2024 — Selected Questions
- 1.Find A⁻¹ for A = [[1,0,0],[2,3,4],[5,−6,x]] for a particular x. (7 marks)
- 2.Find the volume of the tetrahedron with coterminous edges i+j, j+k, k+i. (4 marks)
- 3.Prove that cos²(π/4 − θ) − sin²(π/4 − θ) = sin2θ. (2 marks)
- 4.If A+B+C = π, prove that sin2A + sin2B + sin2C = 4sinA·sinB·sinC. (7 marks)
- 5.In ΔABC, if tanA/2 : tanB/2 : tanC/2 = 1:1:1, prove the triangle is equilateral. (4 marks)
IPE 2023 — Selected Questions
- 1.Solve: 2x + 3y + 5z = 28, x + y − z = −2, 3x − y − z = 2 using matrices. (7 marks)
- 2.Show that [a⃗+b⃗ b⃗+c⃗ c⃗+a⃗] = 2[a⃗ b⃗ c⃗]. (4 marks)
- 3.Prove that sin(n+1)θ·sin(n−1)θ + cos(n+1)θ·cos(n−1)θ = cos2θ. (2 marks)
- 4.In ΔABC prove: (r₁−r)(r₂−r)(r₃−r) = 4Rr². (7 marks)
- 5.Find the general solution of sinθ + √3·cosθ = √2. (4 marks)