Final exam
Twenty questions from the whole course. Compare your score with your pretest and see how much you learned.
In this lesson you will learn
- How well you can use the ideas of the course without help
- How to measure what you learned with the normalized gain
- Which lessons to open again for the questions that you missed
At the start of the course, you did a pretest of 10 questions. Most of the questions were about lessons that you did not read yet. This final exam asks about the same ideas again, with new numbers, and it adds ten questions about the rest of the course. When you finish, you can compare the two scores and see how much you learned.
How to do the exam
The exam works best when it is hard. A test from memory makes the memory stronger, even when you get an answer wrong, if you read the feedback. Researchers call this retrieval practice. A second read of a lesson feels easier, but it does less.
Do the exam in these steps:
- Close your notes and the other lessons.
- Read each question, and calculate the numbers on paper.
- Select one answer. Then read the feedback, also for the answers that you got right.
- Write down the number of each question that you missed.
The first ten questions follow the order of the pretest. Question 1 here tests the same idea as question 1 of the pretest, and so on to question 10. Questions 11 to 20 follow the order of the modules.
The exam
Quiz · question 1 of 20
Final exam: 20 questions from the full course
1. You hold 3,000,000 of the 8,000,000 shares of a company. The company issues 2,000,000 new shares to an investor. What part of the company do you own now?
Measure your gain
A raw score does not tell you how much you learned. A learner who starts at 80% has only 20 points to gain, and a learner who starts at 20% has 80. The normalized gain solves this problem. It divides the points that you gained by the points that were open for you:
Normalized gain
= (after − before)
÷ (100% − before)
= (70% − 40%) ÷ (100% − 40%)
= 30% ÷ 60%
= 0.5
A gain of 0.5 means that you learned half of what you did not know. Richard Hake used this measure in 1998 for 62 physics courses and 6,542 students. Traditional lecture courses had an average gain of 0.23. Courses with active practice had an average gain of 0.48.
The calculator below reads your pretest and your final exam scores from this browser. If you did the tests on a different device, type the two scores.
Your progress
How much did you learn?
Compare your pretest with your final exam. The gain counts only the part that you did not know before.
An example. Do the pretest in the first lesson of the course to use your own score.
An example. Do the exam on this page to use your own score.
- Points open before
- 60
- 100 − pretest
- Points gained
- 30
- Final exam − pretest
- Normalized gain
- 0.50
- Points gained ÷ points open
- Pretest
- 40%
- Final exam
- 70%
Before the course, 60 points were open for you. You gained 30 of them, so your normalized gain is 0.50. You learned 50% of what you did not know.
In a 1998 study of 62 physics courses, Richard Hake found an average gain of 0.23 for traditional lecture courses and 0.48 for courses with active practice.
Work it out
A learner scores 30% on the pretest and 75% on the final exam. What is the normalized gain?
The learner gained 75 − 30 = 45 points. Before the course, 100 − 30 = 70 points were open. The gain is 45 ÷ 70 = 0.64.
Where to review
Each question tests one lesson. Find each question that you missed in this table, and open its lesson. Do the exercises of that lesson again, without the worked solution.
Keep what you learned
Memory decreases with time, and a review at the correct time makes the memory last longer. This is the idea behind spaced repetition. Cepeda and others (2008) did a study with more than 1,350 learners. For a test one year later, the best first review came after approximately 5% to 10% of that year. That is 18 to 37 days after you learn an idea.
Use this plan to keep the ideas of the course:
- Open the review deck now and do one set of cards.
- Do the exam again in approximately three weeks. Do not look at your old answers first.
- Before your next round, open the cheat sheet and the simulator with your own numbers.
Why does the exam use new numbers for the pretest ideas?
A question with the same numbers tests if you remember an answer. A question with new numbers tests if you can use the idea. Only the second skill helps you at a negotiation, when an investor gives you numbers that no lesson used.
Key takeaways
- 1.A test from memory, with feedback, keeps an idea longer than a second read of the lesson.
- 2.The normalized gain counts only the points that you did not have before. (after − before) ÷ (100% − before) lets you compare learners who start at different levels.
- 3.Each wrong answer points to one lesson. Open that lesson, do its exercises again, and then test yourself again a few days later.
- 4.For a test one year later, the best first review came approximately 18 to 37 days after the lesson (Cepeda and others, 2008).
Sources
- 1.Test-Enhanced Learning: Taking Memory Tests Improves Long-Term Retention. Roediger and Karpicke, Psychological Science 17(3), 2006.
- 2.Interactive-engagement versus traditional methods: A six-thousand-student survey. Hake, American Journal of Physics 66(1), 1998.
- 3.Spacing Effects in Learning: A Temporal Ridgeline of Optimal Retention. Cepeda and others, Psychological Science 19, 2008.
- 4.Improving Students' Learning With Effective Learning Techniques. Dunlosky and others, Psychological Science in the Public Interest 14(1), 2013.
- 5.26 U.S. Code § 1202, Partial exclusion for gain from certain small business stock. Cornell Legal Information Institute, 2026.
- 6.Filing a Form D notice. U.S. Securities and Exchange Commission, 2026-03-17.
- 7.The Y Combinator Standard Deal. Y Combinator, 2026.