Ib Math Aa Hl Exam Questionbank May 2026

She set down her pen. The screen glowed with the green checkmark of the official answer. Seven out of seven. A perfect paper.

She checked the solution bank. Correct. A tiny, fragile smile. ib math aa hl exam questionbank

Prove by mathematical induction that for all n ∈ ℤ⁺, Σ_{k=1}^n (k * k!) = (n+1)! – 1. She set down her pen

Maya laughed. It was almost elegant. The base case: n=1, 1 1! = 1, and (2)! – 1 = 1. True. The inductive step: Assume true for n. Then add (n+1) (n+1)! to both sides. Left becomes sum to n+1. Right becomes (n+1)! – 1 + (n+1)*(n+1)! = (n+1)!(1 + n + 1) – 1 = (n+2)! – 1. Done. A perfect paper

At 4:47 AM, she reached Question 9. The final one. The “challenge” problem.

The second question was a nightmare dressed in vectors. Line L1 passes through (1,2,3) with direction (2, -1, 2). L2 is given by (x-3)/2 = (y+1)/1 = (z-4)/-2. Find the shortest distance between L1 and L2. Maya groaned. This was the kind of problem that separated the 6s from the 7s. She sketched the cross product of the direction vectors, found a vector connecting the two lines, and then did the scalar projection. Her arithmetic was shaky—she forgot a negative sign halfway through, had to erase four lines, and nearly threw her pencil across the room.