Helped by prompts from his father, the nine-year-old detailed an apparent £7 billion black hole in spending estimates for HS2 - a claim later contested by Government lawyers.
Questioned over his personal mathematical ability, Alex responded: "I got 93 per cent in my last maths test and was top of the class in three quarters of my classes."
The young campaigner warned that a proposed temporary road would be far harder to cycle a bike on - "it will have to go up and down hills, through farmers' fields and there would have to gates to stop sheeps and cows getting out" - and warned that the next generation trains would be too noisy.
Alex criticised the response from HS2 managers to concerns raised his submission - "I don't think they actually bothered to read what I said" - and mocked their map-reading abilities.
"If you gave me a map and told me to look for two places it might take me a while but I know I'd do better in finding them than the HS2 people did," the youngster said.
He finished: "I wrote my petition because I didn't think the HS2 people were very good at maths and I didn't think they were very good at knowing where things were. I genuinely didn't think they were good at anything.
"I would say that they have proved me right, but it really is worse than I thought. I am still willing to help them with their maths if they want."
James Strachan QC, representing the Department for Transport, thanked Alex for the "very kind" offer of help but declined, saying that "the devil was in the detail".
Robert Syms, a Conservative MP, commended the youngster's evidence, adding: "Safe trip back to the Midlands."