Mathematics · Grade 12

Precalculus

Functions, vectors, complex numbers and the ideas that open calculus.

Taught byMarcus Ellery · Ivana Petrović

5units
20lessons
17–18typical age
Common Corestandards

Units

Unit 1: Functions and transformationsStandards: F-BF.A.1, F-BF.B.3–4 · 4 lessons
1. Composition of functions
2. Inverse functions
3. Transformations of graphs
4. Piecewise functions
Unit 2: Trigonometry in depthStandards: F-TF.A.3–4, F-TF.C.9 · 4 lessons
1. Special angles and symmetry
2. Trigonometric identities
3. Sum and difference formulas
4. Solving trigonometric equations
Unit 3: Vectors and complex numbersStandards: N-VM.A.1–3, N-VM.B.4–5, N-CN.B.4–6 · 4 lessons
1. Vectors and magnitude
2. Adding and scaling vectors
3. Complex numbers in polar form
4. Operations on the complex plane
Unit 4: Matrices, sequences and seriesStandards: N-VM.C.6–12, F-IF.A.3, A-SSE.B.4 · 4 lessons
1. Matrix operations
2. Matrices as transformations
3. Sequences and series
4. Sums of geometric series
Unit 5: Rates of change and conic sectionsStandards: F-IF.B.6, F-IF.C.7d, G-GPE.A.2–3 · 4 lessons
1. Average rate of change
2. Limits as an idea
3. Asymptotes of rational functions
4. Parabolas, ellipses and hyperbolas

Who teaches you

Every lesson has a named AI teacher and a mentor who keeps you on track. Both are AI, and every screen says so.

AI Super Professor · MathematicsMarcus Ellery
I start from what you already understand and make every new idea grow out of it. A rule is never just given: you see why it works, try it on a small case, then use it on a real problem. When you are stuck, I ask a smaller question instead of showing the answer.
- Algebra
- Geometry and proof
- Data and probability
Mathematics is not about numbers or computations. It is about understanding.
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AI Super Mentor · MathematicsIvana Petrović
I do not teach the lessons; Marcus does. I look at your week with you: what you finished, where you struggled, and what one change would help most. Then we write a short plan you can keep.
- Study plans
- Habits
- Maths in real life
The best way to understand a concept is to teach it. The second best is to apply it.
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How lessons run

Each topic is one Live class lesson in four steps: warm-up, explain, try it, check. The AI tutor gives hints, not answers, and waits for the learner to think.