There are many many references in the slides I presented. They may serve you as a round-map if any of the technique will be useful for the future. I understand that your time for the exam preparation is limited.

I thus compiled a carefully curated list of references. I tried my best to keep it short

1. minimal - The references in bold gives you steepest learning curve and provides the very basics.
2. recommended - The references in the normal text should make you somewhat more familiar with the topic. 
3. (*)advanced - The references in italics are interesting for the students specifically interested in the topic. These are not required.
4. VIDEO - There are many excellent sources online that can help you to jump into the topic quickly. I list those that I found useful. These are not required.

Also, the knowledge of R will not be mandatory for the exam. Candidate who is familiar with the minimal and the recommended sources can expect an excellent grade. This list is very far from being complete or comprehensive and it also reflects my view on what is important and, at the same time, how to learn in a fastest possible manner.

Linear regression:

(I assume familiarity with chapters 1-4 in Faraway, Julian J. Linear models with R. Chapman and Hall/CRC, 2004.)

Maximum likelihood:

Lanot, Gauthier. "Maximum likelihood and economic modeling." IZA World of Labor 326 (2017).

Chapter 10.1 - 10.8 in https://www.ssc.wisc.edu/~bhansen/probability/ [this resource used to be free, it is not anymore, I will look for some suitable free alternative]

(*)Chapter 10.9 - 10.20 in https://www.ssc.wisc.edu/~bhansen/probability/

VIDEO: Very non-technical exposition (6mins) https://www.youtube.com/watch?v=XepXtl9YKwc

Bootstrap:

Kennedy, Peter E. "Bootstrapping student understanding of what is going on in econometrics." The Journal of Economic Education 32.2 (2001): 110-123.

VIDEO: Very non-technical exposition (10mins) https://www.youtube.com/watch?v=Xz0x-8-cgaQ

Graphical causal models:

Sections 1-3.1 Hünermund, Paul, and Elias Bareinboim. "Causal Inference and Data Fusion in Econometrics." arXiv preprint arXiv:1912.09104 (2019).

Chapter 3 in https://mixtape.scunning.com/

Sections 3.2 and further Hünermund, Paul, and Elias Bareinboim. "Causal Inference and Data Fusion in Econometrics." arXiv preprint arXiv:1912.09104 (2019).

Cinelli, Carlos, Andrew Forney, and Judea Pearl. "A crash course in good and bad controls." Available at SSRN 3689437 (2020).

VIDEO: Paul Hunnermund presents his Data Fusion paper https://www.youtube.com/watch?v=GtpnWQ9uTL8

Randomization and Selection on observables:

Chapters 4 and 5 in https://mixtape.scunning.com/

Duflo, Esther, Rachel Glennerster, and Michael Kremer. "Using randomization in development economics research: A toolkit." Handbook of development economics 4 (2007): 3895-3962.

LaLonde, Robert J. "Evaluating the econometric evaluations of training programs with experimental data." The American economic review (1986): 604-620.

Dehejia, Rajeev H., and Sadek Wahba. "Propensity score-matching methods for nonexperimental causal studies." Review of Economics and statistics 84.1 (2002): 151-161.

(*)Imbens, Guido W. "Matching methods in practice: Three examples." Journal of Human Resources 50.2 (2015): 373-419.

Instrumental variables:

Chapter 7 in https://mixtape.scunning.com/

Chapter 4 in Angrist, Joshua D., and Jörn-Steffen Pischke. Mostly harmless econometrics. Princeton university press, 2008.

Angrist, Joshua D., Guido W. Imbens, and Donald B. Rubin. "Identification of causal effects using instrumental variables." Journal of the American statistical Association 91.434 (1996): 444-455.

Regression Discontinuity Design:

Chapter 6 in Angrist, Joshua D., and Jörn-Steffen Pischke. Mostly harmless econometrics. Princeton university press, 2008.

Chapter 6 in https://mixtape.scunning.com/

Chapter 21 in https://www.ssc.wisc.edu/~bhansen/econometrics/

Difference-in-differences:

Chapter 9 in https://mixtape.scunning.com/

Chapter 18 in https://www.ssc.wisc.edu/~bhansen/econometrics/

Bertrand, Marianne, Esther Duflo, and Sendhil Mullainathan. "How much should we trust differences-in-differences estimates?." The Quarterly journal of economics 119.1 (2004): 249-275.

VIDEO: Brady Neal - Lecture 9 https://www.youtube.com/playlist?list=PLoazKTcS0RzZ1SUgeOgc6SWt51gfT80N0

(*)VIDEO: List of recent advances here https://taylorjwright.github.io/did-reading-group/

VIDEO: Excellent 9minutes explainer what is wrong with TWFE. https://www.youtube.com/watch?v=hu2nDbnpALA

Synthetic control methods:

Abadie, Alberto. "Using synthetic controls: Feasibility, data requirements, and methodological aspects." Journal of Economic Literature 59.2 (2021): 391-425.

Abadie, Alberto, Alexis Diamond, and Jens Hainmueller. "Synthetic control methods for comparative case studies: Estimating the effect of California’s tobacco control program." Journal of the American statistical Association 105.490 (2010): 493-505.

Chapter 10 in https://mixtape.scunning.com/

VIDEO: First 50minutes of NBER Summer Institute lectures https://www.youtube.com/watch?v=T2p9Wg650bY

Machine learning essentials:

Varian, Hal R. "Big data: New tricks for econometrics." Journal of Economic Perspectives 28.2 (2014): 3-28.

(*)VIDEO: Victor Chernozhukov on Double maching learning https://www.youtube.com/watch?v=eHOjmyoPCFU

(**)Chernozhukov, Victor, et al. "Double/debiased machine learning for treatment and structural parameters." The Econometrics Journal 21.1 (2018): C1-C68.

EXAMPLE of an exam from 2021

You asked for an example of what is expected on the exam. Below you may find the first exam from Fall semester 2021. This may help you to be calibrate your efforts.

I will not post a solution to this exam. But if you will send me your solutions I will do my best to correct it within some reasonable time.