Mathematics IB — Previous Year Papers
TGBIE IPE previous year questions for Maths IB — repeated topics and selected questions from recent exams to help you identify what appears every year.
Topics That Repeat Every Year
Every yearStraight Lines — finding concurrent lines or rhombus/square/parallelogram
Every yearPair of Lines — second degree equation factorisation or angle between lines
Every yearApplications — Maxima/Minima word problem or Rolle's/MVT
Every yearDifferentiation — implicit, parametric, or logarithmic differentiation LAQ
Almost every yearLimits — standard limit evaluation SAQs
Very frequentTangent and Normal — finding equations at a given point
Very frequent3D Geometry — section formula or direction cosines
FrequentLocus — translating geometric conditions to equations
Selected Questions from Past IPE Papers
IPE 2024 — Selected Questions
- 1.Find the equation of the straight line perpendicular to 5x − 2y = 7 and passing through the midpoint of the line joining (2,3) and (4,5). (4 marks)
- 2.Show that the equation 6x² − 5xy − 6y² = 0 represents two perpendicular lines. (4 marks)
- 3.Find the maximum value of f(x) = sin x + cos x. (2 marks)
- 4.Find the angle between the lines x + y + 1 = 0 and 2x − y + 3 = 0. (2 marks)
- 5.Show that the equation 2x² + 3xy − 2y² + 3x + y + 1 = 0 represents a pair of perpendicular straight lines. Find them. (7 marks)
- 6.Find the local extrema of f(x) = x³ − 12x. (7 marks)
IPE 2023 — Selected Questions
- 1.Verify Rolle's theorem for f(x) = x² − 1 on [−1, 1]. (4 marks)
- 2.If y = x·e^x, find y_n (nth derivative). (4 marks)
- 3.Evaluate: lim(x→0) (1 − cos mx)/(1 − cos nx). (2 marks)
- 4.Find the equation of straight lines passing through (1, 3) and (i) parallel (ii) perpendicular to 2x − 3y + 5 = 0. (4 marks)
- 5.If the distance between the lines 3x+4y = 9 and 6x+8y = 15 is d, find d. (2 marks)
- 6.Find the condition for the equation ax²+2hxy+by²+2gx+2fy+c=0 to represent a pair of straight lines. Apply it to show 2x²+xy−y²−5x−y+6=0 represents a pair of lines. (7 marks)