考試技巧

Doing well in your courses

a guide by Andrej Karpathy

Here is some advice I would give to younger students if they wish to do well in their undergraduate courses.

Having been tested for many years of my life (with pretty good results), here are some rules of thumb that I feel helped me:

GENERAL

All-nighters are not worth it.
Sleep does wonders. Optimal sleep time for me is around 7.5 hours, with an absolute minimum of around 4hrs.
It has happened to me several times that I was stuck on some problem for an hour in the night, but was able to solve it in 5 minutes in the morning. I feel like the brain “commits” a lot of shaky short-term memories to stable long-term memories during the night. I try to start studying for any big tests well in advance (several days), even if for short periods of time, to maximize the number of nights that my brain gets for the material.

Attend tutorials or review sessions.
Even if they are bad. The fact that they get you to think about the material is what counts. If its too boring, you can always work on something else. Remember that you can also try to attend a different tutorial with a different TA.

TESTS: PREPARATION

Considering the big picture and organisation is the key.
Create schedule of study, even if you dont stick to it. For me this usually involves getting an idea of everything I need to know and explicitly writing it down in terms of bullet points. Consider all points carefully and think about how long it will take you to get them down. If you don’t do this, there is a tendency to spend too much time on beginning of material and then skim through the (most important) later material due to lack of time.

Always try to look at previous tests BEFORE starting to study.
Especially if the past tests were written by the same professor. This will give you strong hints about how you should study. Every professor has a different evaluation style. Don’t actually attempt to complete the questions in the beginning, but take careful note of the type of questions.

Reading and understanding IS NOT the same as replicating the content.
Even I often make this mistake still: You read a formula/derivation/proof in the book and it makes perfect sense. Now close the book and try to write it down. You will find that this process is completely different and it will amaze you that many times you won’t actually be able to do this! Somehow the two things use different parts of the memory. Make it a point to make sure that you can actually write down the most important bits, and that you can re-derive them at will. Feynman famously knew this very well.

Always try to collaborate with others, but near the end.
Study alone first because in the early stages of studying others can only serve as a distraction. But near the end get together with others: they will often point out important pitfalls, bring up good issues, and sometimes give you an opportunity to teach. Which brings me to:

Don’t only hang out only with stronger students.
Weaker students will have you explain things to them and you will find that teaching the material helps A LOT with understanding.

Go to the prof before final exam at least once for office hours.
Even if you have no questions (make something up!) Profs will sometimes be willing to say more about a test in 1on1 basis (things they would not disclose in front of the entire class). Don’t expect it, but when this does happen, it helps a lot. Does this give you an unfair advantage over other students? Sometimes. It’s a little shady :slight_smile:
But in general it is a good idea to let the prof get to know you at least a little.

Study well in advance.
Did I mention this already? Maybe I should stress it again. The brain really needs time to absorb material. Things that looked hard become easier with time.
You want to alocate ~3 days for midterms, ~6 days for exams.

If things are going badly and you get too tired, in emergency situations, jug an energy drink.
They work. It’s just chemistry.

For things like math: Exercise > Reading.
It is good to study to the point where you are reasonably ready to start the exercises, but then fill in the gaps through doing exercises, especially if you have many available to you. The exercises will also make you go back and read things you don’t know.

Make yourself cheat sheet.
Even if you’re not allowed to bring it to the exam. Writing things down helps. What you want is to cram the entire course on 1 or more pages that you can in the end tile in front of you and say with high degree of confidence “This is exactly everything I must know”

Study in places where other people study as well, even if not the same thing.
This makes you feel bad when you are the one not studying. It works for me :slight_smile:
Places with a lot of background noise are bad and have a research-supported negative impact on learning. Libraries and Reading rooms work best.

TESTS: ON DAY OF

Optimal eating/drinking habit is: T-2 hours get coffee and food.
For me, Coffee or Food RIGHT before the test is ALWAYS bad
Coffee right before any potentially stressful situation is ALWAYS bad.
No coffee at all is bad.
I realize the coffee bit may be subjective to me, but its something to think about for yourself.

Study very intensely RIGHT before the test.
I see many people give up before the test and claim to “take a break”. Short term memory is a wonderful thing, don’t waste it! Study as intensely as possible right before the test. If you really feel you must take a break, take it about an hour before the test, but make sure you study really hard 30-45 minutes before the test.

DURING THE TEST

Always use pencil for tests.
You want to be able to erase your garbage “solutions”

Look over all questions very briefly before start.
A mere 1-3 second glance per question is good enough. Just absorb all key words, and get idea of the size of the entire test.

On test, do easy questions first.
Do not allow yourself to get stuck on something too long. Come back to it later. I skip questions all the time… Sometimes I can complete as little as 30% of the test on my first pass. Some questions somehow become much easier once you’re “warmed up”, I can’t explain it.

Always try to be neat on the test.
Surprisingly few people actually realize this obvious fact: A human being will mark your test. A sad human being gives low marks. I suspected this as undergrad student and confirmed it strongly when I was TAing and actually marking.

Always BOX IN/CIRCLE the answer
Especially when there is derivation around it. This allows the marker to give you a quick check mark for full marks and move on. Get in the mindset of a marker.

NEVER. EVER. EVER. Leave test early.
You made a silly mistake (I guarantee it), find it and fix it. If you can’t find it, try harder until time runs out. If you are VERY certain of no mistakes, work on making test more legible and easier to mark. Erase garbage, box in answers, add steps to proofs, etc.
I have no other way of putting this-- people who leave tests early are stupid. This is a clear example of a situation where potential benefits completely outweigh the cost.

Communicate with the marker.
Show the marker that you know more than what you put down. Ok you can’t do a particular step, but make it clear that you know how to proceed if you did. Don’t be afraid to leave notes when necessary. Believe it or not the markers often end up trying to find you more marks-- make it easy for them.

Consider number of points per question.
Many tests will tell you how many marks every question is worth. This can give you very strong hints when you are doing something wrong. It also gives you strong hints at what questions you should be working on. It is, of course, silly to spend too much time on questions worth little marks that are still relatively hard for you.

If there are <5 minutes left and you are still stuck on some question, STOP.
Your time is better spent re-reading all questions and making absolutely sure you did not miss any secondary
questions, and that you answered everything. You wouldn’t believe how many silly marks people lose this way.

Congratulations if you got all the way here! Now that you are here, here’s my last (very important advice). It is something that I wish someone had told me when I was an undergraduate.

Undergrads tend to have tunnel vision about their classes. They want to get good grades, etc. The crucial fact to realize is that noone will care about your grades, unless they are bad. For example, I always used to say that the smartest student will get 85% in all of his courses. This way, you end up with somewhere around 4.0 score, but you did not over-study, and you did not under-study.

Your time is a precious, limited resource. Get to a point where you don’t screw up on a test and then switch your attention to much more important endeavors. What are they?

Getting actual, real-world experience, working on real code base, projects or problems outside of silly course exercises is extremely imporant. Professors/People who know you and can write you a good reference letter saying that you have initiative, passion and drive are extremely important. Are you thinking of applying to jobs? Get a summer internship. Are you thinking of pursuing graduate school? Get research experience! Sign up for whatever programs your school offers. Or reach out to a professor/graduate student asking to get involved on a research project you like. This might work if they think you’re driven and motivated enough. Do not underestimate the importance of this: A well-known professor who writes in their recommendation letter that you are driven, motivated and independent thinker completely dwarfs anything else, especially petty things like grades. It also helps a lot if you squeeze in at least one paper before you apply. Also, you should be aware that the biggest pet peeve from their side are over-excited undergrad students who sign up for a project, meet a few times, ask many questions, and then suddenly give up and disappear after all that time investment from the graduate student’s or professor’s side. Do not be this person (it damages your reputation) and do not give any indication that you might be.

Other than research projects, get involved with some group of people on side projects or better, start your own from scratch. Contribute to Open Source, make/improve a library. Get out there and create (or help create) something cool. Document it well. Blog about it. These are the things people will care about a few years down the road. Your grades? They are an annoyance you have to deal with along the way. Use your time well and good luck.

Last edited by @suen 2025-10-21T02:56:26Z

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@Creative
翻譯,信雅達。

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@Creative

翻譯已完成,力求信、雅、達:

課程制勝指南:Andrej Karpathy的應試策略與建議

這是一份我為希望在大學課程中取得佳績的年輕學子準備的建議。

憑藉多年應試(且結果頗佳)的經驗,以下是我認為對我有所助益的幾條原則:

總則(GENERAL)

通宵熬夜絕非良策。
睡眠能創造奇蹟。對我而言,最佳睡眠時間約為7.5小時,底線也至少要有4小時。我曾多次在夜間被某個問題困擾一小時,但第二天早上卻能在五分鐘內迎刃而解。我感覺大腦在夜間將許多不穩定的短期記憶固化為穩定的長期記憶。我會提前數天(即使每次學習時間很短)開始為大型考試做準備,以確保我的大腦有足夠的夜晚來消化材料。

務必參加輔導課或複習環節。
即使課程品質不佳,僅是逼迫你去思考材料這一事實就彌足珍貴。如果課程太過枯燥,你也可以做些其他事情。請記住,你可以嘗試參加不同助教(TA)主持的輔導課。

考試:準備階段(TESTS: PREPARATION)

綜觀全局和規劃組織是成功的關鍵。
制定學習時間表,即使你不一定完全遵守。對我來說,這通常包括了解所有需要掌握的知識點,並以項目符號明確地寫下來。仔細考慮所有要點,並估計掌握它們所需的時間。如果不這樣做,你傾向於將過多時間花在早期材料上,最後因為時間不足而草草瀏覽(往往是最重要的)後期內容。

開始學習前,務必先查看歷年試卷。
特別是如果過去的試卷是由同一位教授出題。這能為你的學習方式提供強烈的提示。每位教授的評估風格都不同。一開始不要試圖完成題目,而是仔細記下問題的類型。

閱讀理解不等同於內容重現。
即使是我,也經常犯這個錯誤:你在書中讀到一個公式、推導或證明,它看起來完全合乎情理。但現在請合上書,試著把它寫下來。你會發現這個過程完全不同,很多時候你會驚訝地發現自己根本寫不出來!這兩種行為似乎利用了記憶的不同部分。請確保你能隨心所欲地寫下並重新推導出最重要的內容。費曼(Feynman)對此深有體悟。

合作學習,但需接近尾聲時。
先獨自學習,因為在學習的早期階段,他人只會讓你分心。但臨近考試時,再與他人聚集:他們通常能指出重要的陷阱,提出好的問題,有時也給你提供教學的機會。這就引出了下一點:

不要只與強者為伍。
較弱的同學會讓你向他們解釋問題,你會發現「教學相長」對於理解材料有巨大的幫助。

期末考前至少去一次教授的辦公時間。
即使你沒有任何問題(可以編造一個!)教授有時更願意在私下一對一地透露有關考試的更多信息(這些信息他們不會在全班面前公開)。不要抱持期待,但一旦發生,將大有幫助。這是否給你帶來了不公平的優勢?有時是的。這確實有點「不光明」:slight_smile: 但總體而言,讓教授至少對你有所了解是個好主意。

提前充分學習。
我是否已經提過這點了?也許我該再次強調。大腦確實需要時間來吸收材料。隨著時間的推移,那些看起來困難的東西會變得更容易。你應該為期中考分配約3天,為期末考分配約6天的時間。

如果狀態不佳,感到過度疲倦,在緊急情況下,不妨灌下一瓶能量飲料。
它們是有效的。這就是化學作用。

對於數學等科目:練習優先於閱讀。
學習到讓你準備好開始練習的程度是好的,但之後主要應通過做練習來填補知識空白,特別是當你有很多習題可供使用時。練習也會促使你回過頭去閱讀你不了解的內容。

製作自己的「小抄」(cheat sheet)。
即使考試不允許帶進去。寫下來這個過程本身就有幫助。你需要將整個課程濃縮在一頁或多頁紙上,最終你能將它們鋪在你面前,並充滿信心地說:「這正是我必須知道的一切。」

在其他人也在學習的地方學習,即使他們學習的科目不同。
這會讓你成為那個不學習的人時感到愧疚。對我來說,這很奏效 :slight_smile: 有大量背景噪音的地方很糟糕,並有研究證實會對學習產生負面影響。圖書館和閱覽室是最好的選擇。

考試:當日(TESTS: ON DAY OF)

最佳飲食習慣是:考前2小時攝入咖啡和食物。
對我來說,考前立刻喝咖啡或吃東西總是不好的。在任何潛在壓力情境前立刻喝咖啡總是不好的。完全不喝咖啡也是不好的。我意識到咖啡這部分可能因人而異,但值得你為自己思考一下。

考前應非常集中地學習。
我看到許多人在考試前放棄學習,聲稱要「休息一下」。短期記憶是一件美妙的東西,不要浪費它!在考試前盡可能集中精力學習。如果你真的覺得需要休息,可以在考前一小時休息,但要確保在考前30到45分鐘內努力學習。

考試期間(DURING THE TEST)

考試務必使用鉛筆。
你需要能夠擦除你那些「垃圾解法」。

開始前,快速瀏覽所有考題。
每道題僅需1到3秒的掃視即可。吸收所有關鍵詞,並對整個試卷的篇幅有個概念。

在試卷上,先做簡單的題目。
不要讓自己長時間卡在某個問題上。稍後再回過頭來處理。我會一直跳過問題…有時我在第一次過目時只能完成30%的試卷。一旦你「熱身」完畢,有些問題不知何故會變得容易得多,這點我也無法解釋。

試卷務必保持整潔。
令人驚訝的是,很少人真正意識到這個顯而易見的事實:閱卷的是一個人類。一個心情不佳的人類會打低分。我在本科時就懷疑這一點,而在擔任助教並實際批改試卷時得到了強烈證實。

永遠將答案用方框或圓圈標註。
特別是當周圍有推導過程時。這能讓閱卷者快速給你一個滿分的勾,然後繼續下一題。請站在閱卷人的角度思考。

絕不。絕對不。提前交卷。
你一定犯了一個愚蠢的錯誤(我保證),去找到並修正它。如果你找不到,就努力尋找,直到時間用完。如果你非常確定沒有錯誤,那就努力讓試卷更清晰、更容易批改。擦除多餘的內容,將答案框起來,給證明添加步驟等。我不知道該怎麼表達——提前交卷的人是愚蠢的。這是一個潛在收益完全大於成本的明確例子。

與閱卷人「溝通」。
向閱卷人表明你所知道的超過你寫下來的內容。好吧,你無法完成某個特定的步驟,但要清楚地表明,如果你能做到,你知道如何繼續。必要時不要害怕留下註釋。信不信由你,閱卷者通常會努力幫你多找些分數——讓他們輕鬆一點。

考慮每道題的分值。
許多試卷會告訴你每道題值多少分。當你做錯事時,這可以給你非常強烈的提示。它也能強烈暗示你應該把精力放在哪些問題上。將過多時間花在你覺得相對困難、但分值又很低的問題上,顯然是愚蠢的。

如果剩下不到5分鐘,而你仍被某些問題卡住,請停止。
你最好把時間花在重新閱讀所有問題,並百分之百確定自己沒有錯過任何次要問題,並且所有問題都已回答。你不會相信有多少人以這種方式丟失了愚蠢的分數。

如果你堅持讀到這裡,恭喜你!現在你已經到了這裡,這是我的最後一個(非常重要的)建議。這是我希望在我讀本科時有人能告訴我的事情。

本科生往往對他們的課程有「隧道視野」。他們想獲得好成績等等。但需要意識到的關鍵事實是,除非你的成績很差,否則沒有人在乎你的分數。例如,我常說,最聰明的學生會在所有課程中獲得85%的成績。這樣,你最終的總成績仍接近滿分(4.0),但你既沒有「過度學習」,也沒有「學習不足」。

你的時間是寶貴且有限的資源。 達到一個你在考試中不會搞砸的程度,然後將注意力轉向更為重要的追求。這些追求是什麼?

獲得實際的、真實世界的經驗,在課程練習之外,從事真實的代碼庫、項目或問題,這極為重要。能了解你、並能寫出強有力推薦信(信中稱讚你有主動性、熱情和衝勁)的教授/專業人士至關重要。你在考慮找工作嗎?去獲得暑期實習。你在考慮讀研究生嗎?去獲得研究經驗!報名參加學校提供的任何項目。或者主動聯繫你喜歡的教授或研究生,請求參與他們的研究項目。如果你表現出足夠的動力和積極性,這可能會奏效。不要低估這一點的重要性:一位知名的教授在他的推薦信中寫道你富有衝勁、積極主動且是一個獨立思考者,這完全碾壓其他一切,尤其是像成績這樣瑣碎的事情。如果你在申請前能擠出一篇論文,也會大有幫助。此外,你應該意識到,教授們最討厭的是那種過度興奮的本科生——他們報名參加項目,見了幾次面,問了很多問題,然後在導師或研究生成本投入時間後,突然放棄並消失。不要成為這種人(這會損害你的聲譽),也不要給出任何你可能是這種人的暗示。

除了研究項目之外,還可以與一群人一起參與副業項目,或者,最好是從頭開始創建自己的項目。為開源(Open Source)做貢獻,創建/改進一個庫。走出去,創造(或幫助創造)一些很酷的東西。做好文檔記錄。寫博客分享。這些才是幾年後人們會在乎的事。你的成績?不過是你前行路上必須應對的煩惱罷了。善用你的時間,祝你好運。

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真题+清醒+考试中把卷子上的字当做你知识储备+烧香

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魔!术!技!巧!

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2592。。。

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