Calculus and Vectors

Short Questions

These questions are suitable for class warm ups or extensions at the end of the period.

This is divided by the major units of the Ontario Grade 12 Calculus and Vectors Course.

Fibonacci Sequence

The limit of the Fibonacci Sequence.

Leads to the golden ratio.

Solutions in the document.

Limit of the Fibonacci Sequence

Algebraic Derivatives

STEP Question from 2018

Working with function notation.

Solutions in the document.

Derivatives

These questions I have used as Thinking/Challenge questions on tests or as practice Thinking/Challenge questions (which every test should have).

Was always a lot of work trying to find these so I thought I would put these in one spot.

I have kept them in one big document for each unit, solutions at the end.

Limit Unit

If asked to find the slope of the tangent, they would be expected to use First Principles.

Limit Test Challenge Questions

Vectors on a Sphere

3D Vectors, Dot Product, Cross Product, Trigonometry

Taken from IB HL Paper 3, May 2025

Vectors on a Sphere

Division of Line Segments

Position Vectors, Intersection of Lines

Division of Line Segments

Coplanar, Volume of a Parallelepiped

Linear Combinations, Coplanar, Dot and Cross Product

Coplanar

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