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Machine Learning Foundations: exam pattern and behaviour

Computed from every MLF paper on the practice site (161 papers, 2455 questions), plus the pattern notes from your earlier study sessions.

What a paper looks like

Exam	Papers	Years	Typical marks	Typical no. of questions	Share of questions	Share of marks	Papers with a comprehension block
Quiz 1 weeks 1-4	53	2022-2026	40	15	MCQ 46% / MSQ 26% / SA 28%	MCQ 41% / MSQ 30% / SA 29%	79%
Quiz 2 weeks 5-8	53	2022-2026	40	15	MCQ 64% / MSQ 20% / SA 15%	MCQ 59% / MSQ 23% / SA 18%	100%
End Term all 12 weeks	55	2022-2026	40	14	MCQ 30% / MSQ 30% / SA 40%	MCQ 27% / MSQ 35% / SA 39%	96%

Some uploads on the source site merge two parallel sets, which is why a few papers show double marks. MCQ = one right option, MSQ = one or more right options (strict marking), SA = type the number.

Which weeks the papers lean on

Week topic	Quiz 1	Quiz 2	End Term
1. What is machine learning, and which maths do we need?	91%	33%	43%
2. Slopes, change and the steepest way up	100%	100%	98%
3. Vectors, matrices and the best-fit line	100%	67%	95%
4. The special directions of a matrix	100%	100%	100%
5. Symmetric matrices: the well-behaved ones	49%	100%	95%
6. SVD and PCA: squeezing data	45%	100%	69%
7. Finding the lowest point: gradient descent	26%	100%	83%
8. Bowls, not bumpy hills: convexity	2%	0%	93%
9. Optimising with rules: Lagrange and KKT	32%	0%	100%
10. Probability for machine learning	40%	100%	100%
11. The exponential family	13%	0%	57%
12. Estimating parameters, and EM	13%	0%	40%

Share of papers whose concept summary mentions the week's topic (keyword match, so treat it as a guide, not a count of questions).

How much repeats

Exam	Papers	Exam dates	Question slots	Different questions	Copies of each (average)	Different questions seen on 2+ exam dates
Quiz 1	53	11	792	169	4.7	2 (1%)
Quiz 2	53	10	768	135	5.7	3 (2%)
End Term	55	13	895	297	3.0	2 (1%)

Read this carefully. Within one exam date the parallel sets are drawn from the same pool, so each different question appears on several papers (the 'copies' column). Across different dates, questions with identical wording or identical figure files are rare. Matching here is exact, so a re-typed or re-cropped version counts as different; the real overlap in question type is much higher than this table can see. The takeaway: old papers teach you the types and stories that come back with new numbers, they are not a list of answers to memorise.

Questions that came back on a later exam date (exact match)

Exam dates it appeared on	Question (text-based ones)
4	Compute the sample covariance matrix C for the given dataset.	open
3	Which is the principal direction that is chosen for performing PCA?	open
2	Which of the following is/are supervised learning task(s)?	open
2	Choose the correct Primal optimization problem from the following.	open

What the history of past End Terms says (MLF)

Your earlier study sessions analysed 54 MLF End Term papers from 2022 to May 2026 (about 1,000 question slots, only 133 distinct stems once the parallel sets of the same exam date are collapsed). The pattern of what comes back, in tiers. (The counts below are slots: an item that sits in several parallel sets of one exam date is counted once per set.)

What the papers show

Tier 1: in almost every paper.

Linear programming word problems (comprehension sets): a story, then (a) the objective function (MCQ), (b) the constraints (MSQ), (c) the optimum (numeric). Recurring stories: TV sets with profits of Rs 510 and Rs 675 (seven times), products with labour and machine hours (eight times), hens and eggs, trucks vs vans, brownies vs cheesecake, a two-good consumer-utility problem (seven times).
KKT and Lagrange: "choose the correct primal optimisation problem" for the closest point to the origin (about 14 times), KKT true/false MSQs (about 12), complementary slackness, closest point on a circle or plane.
PCA: the "which of these is true about PCA?" MSQ (about 22 appearances), covariance of given points (about 11), projected variance.
Eigen puzzles: trace $=3$ , determinant $=2$ , one eigenvalue known (8 times); $\det((A^{-1})^T)$ from eigenvalues $1,\,0.5,\,0.25$ with answer 8 (7 times); real symmetric and positive definite MSQs.

What the papers show

Tier 2: very likely. Chebyshev with $\mu=70,\ \sigma=8$ , deviation 16 $\to0.25$ (8 times); the weak law of large numbers with exponential bulbs $\lambda=0.4$ , $n=50\to0.875$ (6 times); Markov bounds; linear approximation $L=ax+by+c$ at $(2,3)$ , find $a$ (21 times); gradient-descent statements and the first/second iteration; SVD and "unitary but not Hermitian" (6 times); MLE for a normal, exponential or discrete distribution; exponential, uniform and binomial story problems.

What the papers show

Tier 3: regular. Continuity and differentiability counts, convex functions and sets (including convex hull), the fencing problem (a farmer with 120 m or a gardener with 200 m), classification vs regression, two independent coin tosses.

The trend in 2025 to 2026 papers: more applied probability stories (exponential waiting times, uniform completion times, Markov bounds on ML-flavoured numbers, a spam classification story, a least-squares house-price fit) on top of the same LP / KKT / PCA / eigenvalue core. A typical recent paper: 1 LP comprehension block, 1 KKT/Lagrange block, 1 gradient-descent block, 2 to 3 PCA/covariance items, 2 to 3 eigen/matrix items, 2 to 3 probability-inequality/MLE/distribution items, 1 to 2 calculus items.

Quiz-by-quiz, from the concept summaries on this site

Quiz 1 (weeks 1 to 4): linear approximation (28 of 53 papers), least squares (22), loss functions (21), dimensionality reduction and clustering (20 each), eigenvalues (20), directional derivatives (14), projection matrices (13), partial derivatives (11).
Quiz 2 (weeks 5 to 8; counts are out of the 30 papers that have a summary): SVD (30 of 30), PCA (29), eigenvalues (29), gradient descent (25), covariance (23), quadratic forms (19), critical points (18), Hessian (17).
End Term (out of 42 summarised papers): Chebyshev (23), convex functions (21), Markov (20), gradient descent (17), KKT (14), MLE (14), convex sets (13), Hessian (13).

What this means for your preparation

Priority	Weeks	Why
Must be perfect	2, 3, 4, 6, 9	linear approximation, projection/least squares, eigen tricks, PCA/SVD, LP + KKT/Lagrange
High	5, 7, 8, 10	quadratic forms, gradient descent, convexity, the probability inequalities
Lighter	11, 12	the exponential family is never asked by name; MLE is; EM is not asked in MLF

The two four-mark closers of an End Term are usually a Lagrange multiplier problem and a least-squares problem: both are fixed recipes, so bank them first. Six rules from the earlier sessions that apply to every MLF question: (1) classify the question from its last sentence; (2) write the formula template before plugging numbers; (3) sanity-check (probabilities $\le1$ , variances $\ge0$ ); (4) in MSQs, "always" and "any" flags usually make an option false; (5) re-read the rounding instruction after you finish; (6) triage: do the LP comprehension sets first, integration proofs last.