Study review companion with self-test flashcards

*(Abridged — Steps 1, 2 and 6 shown.)* **Step 1 — Skill tree** ``` Foundations (must come first) ├─ Vectors: notation, addition, scaling, dot product [low] ├─ Matrices as data vs. matrices as transformations [low] └─ Matrix multiplication, transpose, inverse [medium] Core ├─ Linear independence, span, basis, rank (needs: vectors, matmul) [medium] ├─ Orthogonality and projection (needs: dot product) [medium] └─ Solving Ax = b; l

**LAYER 1 — Explain Like I'm 5** Imagine you have a favourite toy car. You love it exactly as it is, but you want it to sparkle. So you put it inside a clear box covered in glitter. The car hasn't changed at all — it's the same car — but now every time someone looks at it, they see glitter too. A decorator is that glitter box: it wraps something up without changing what's inside. --- **LAYER 2 — The Real Explanation** *What it is:* a decorator is a function that takes another function as inp

*(This sample picks up after the two check-in questions, where the learner said they are comfortable with basic probability but have never used Bayes' theorem in practice.)* **For a 10-year-old — the lost puppy** You think your puppy is probably asleep under the bed, because that's where she usually is. Then you hear a crunching noise from the kitchen. You don't throw away everything you knew about her — you just become a lot less sure about the bed and a lot more sure about the kitchen. *How

**Explanation** Every cell is wrapped in a thin boundary called the cell membrane. It is not a solid wall — it is more like a flexible skin with tiny gaps and doorways in it. Some things slip through those gaps on their own, and other things are too big or the wrong shape and have to be let in deliberately. That difference is the whole idea: the membrane decides what gets in and out, which is how a cell stays different on the inside from the water around it. Diffusion is the name for the "slip

Hi! I'm your AI-Tutor, and I'm glad to help you with anything you're curious about. So — photosynthesis, at high school level, and you already know that plants use sunlight to make food but the chemical steps are the fuzzy part. That's honestly the perfect place to start, because "sunlight makes food" is the right intuition; we just need to make it concrete. Let me set up one idea before I ask you anything. Think of photosynthesis as a recipe. Sunlight is the oven — it supplies the energy. But

Thanks for sharing this — and for being clear about the goal, which makes the feedback much easier to aim. You are broadly on track. The argument exists and a reader can follow it. What is holding it back is that the claim is doing less work than it could. **What is working** Your opening move is a good one. "The scheme was announced as a solution to overcrowding, and overcrowding got worse" sets up a gap between promise and outcome, which is exactly the shape a critical essay wants. You also