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Mathematics Worksheet
🤖 Machine Learning Mathematics
SCORE___ / 20
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After this worksheet you can
Apply the gradient-descent update rule.Understand the role of the learning rate.Connect loss minimization to training.Recognise overfitting from train/test gaps.📚 Quick Recap
Machine learning relies on a handful of core mathematical ideas from linear algebra, calculus, and statistics — understanding these foundations demystifies how models actually learn from data.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1w = 10, learning rate 0.2, gradient 5. The update gives:
2w = 2, learning rate 0.05, gradient −8. The update gives:
3A learning rate that is too low causes:
4Training aims to ___ the loss function:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Update rule: w ← w − η × .
6w = 10, η = 0.2, gradient 5 ⇒ new w = .
7w = 10, learning rate 0.2, gradient 5. Find the updated parameter.
8w = 2, learning rate 0.05, gradient −8. Find the updated parameter.
9What happens if the learning rate is set too low?
🚀 Section C · Challenge ● CHALLENGE 5
10What is the goal of training in terms of the loss function?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-A 3-B 4-B | 5 gradient 6 9 7 = 10 − 1 = 9 8 = 2 + 0.4 = 2.4 9 = Training becomes very slow | 10 = To minimize the loss