Foundation Exam: A Statistical Analysis

The Foundation Exam has been a core part of UCF’s Computer Science Bachelor’s program since 1998. Initially, the exam consisted of questions related to the following classes:
- Computer Science I
- Introduction to Discrete Structures

Since Fall 2016, the exam stopped having questions about Discrete Structures, as a result, there are more questions related to Computer Science I (12 questions in total).
More importantly, since Summer 2015, information about the performance of the students on each exam has been made publicly available in the UCF's Previous Foundation Exams Website. Thanks to that information, we can see how difficult the Foundation Exam is and what to expect before taking it, as well as pointing out some interesting patterns that will show us more details about the exam itself.

PASSING LINE
The passing line is simple: any student with a total average score that is equal or bigger to the passing line will pass the Foundation Exam, on the other hand, any student that has less average score than the passing line will fail the exam.
With that being said, here is a graph showing the passing line of each exam since Summer 2015.

After looking at the graph, we can conclude that the passing line is always between 50% and 70%, no matter what the exam average is. The most common passing line to find is 55%, but it is also important to be prepared for the less common 60% and 65%.
Furthermore, we can see in the graph that there are a couple of outliers: 50% and 70%, being the lowest and highest passing lines, respectively.

Highest Passing Line: 70% - Summer 2017.

Lowest Passing Line: 50% - Summer 2016 (included Discrete Structures questions); - Spring 2025.

Here is another graph, showing how the passing line varies over the years:

Once again, we can see how the exam's passing line mostly stays between 55% and 60%, and how some years seem "easier" than others (lower passing lines).

Highest passing lines in a year: 2017 - 60%, 70%, 55%.

The lowest passing lines in a year can be seen in any year with 55%, 55%, 60%.

A very frequent statement between students is "The Summer exam is harder than Spring and Fall", which is something debatable because the difficulty of the exams depend on multiple factors, specially the topics in the exam itself and what kind of questions appear on it, but we can give ourselves an idea of how hard the exam is by looking at the passing line.

Spring Average Passing Line: 56.5%

Summer Average Passing Line: 59.3%

Fall Average Passing Line: 55.8%

If we are talking exclusively about passing lines, then it is true: the Summer exam is harder than the Spring and Fall ones.

The Summer exam has higher average passing lines than the other two exams, but it also has the highest average passing rates. On the next section below, I will be showing the data of the Foundation Exam's passing rates.

PASSING RATES

The passing rate is the most discussed concern about the Foundation Exam. Every exam is hard for some and easy for others, which is why so many students pass (or fail) on their first, second or third try. The next graph shows the passing rate for each exam since 2015:

This graph is interesting, it looks like there is not a lot of consistency between exams, in some cases the passing rates go from under 45% to over 50%, and in other cases they go from over 50% to under 45%. Out of the 31 exams analyzed above, 17 of them had a passing rate above 50% (more than half the students passed their respective exam).

Highest Passing Rate: 65.30% - Spring 2020.

Lowest Passing Rate: 39.8% - Fall 2015 (included Discrete Structures questions).
Lowest Passing Rate: 40.30% - Spring 2017 (only Data Structures and Algorithms questions).

Here is another graph, showing how the passing rate varies over the years:

From the graph above we can see that there is no clear or constant passing rate, instead, it has a very unpredictable timeline. One of the most important points to note is that since Spring 2017, the passing rates have only been under 45% twice (Spring 2018 and Fall 2021).

Biggest passing rate increase between exams: Spring 2017 (42%) -> (62.40%) Summer 2017.
*22.40% increase.

Biggest passing rate decrease between exams (ignoring 2020): Summer 2023 (61.50%) -> (49.70%) Fall 2023.
*11.80% decrease.

Earlier I mentioned that, despite having the highest average passing lines, the Summer Foundation Exam also has the highest passing rates. Here are the averages for each term:

Spring Average Passing Rate: 49.26%

Summer Average Passing Rate: 52.47%

Fall Average Passing Rate: 50.33%

With all this information we can also find a very important statistic about the Foundation Exam:

AVERAGE PASSING RATE OF THE FOUNDATION EXAM (SINCE 2015): 50.69%

The number might seem surprising, but it makes sense, since most tests have an average passing rate of around 50%, as we just saw on the graphs above.

Note: The average passing rate does not mean that 50.69% unique people that take the exam end up passing it (students get 3 chances, and the data does not tell if the student passed on the first, second or third try). Instead, the 50.69% simply shows the average passing rate of the exam over the years.

That concludes the "Exam Stats" tab. There is one more important thing to talk about: Topics of the Foundation Exam, which I explain in the "Topics Stats" tab on the upper-right corner.

As previously mentioned on the "Exam Stats" tab, the Foundation Exam consisted of Data Structures, Algorithms, and Discrete Structures questions. Since Fall 2016, the exam consists of 12 Data Structures and Algorithms questions, based on topics seen on COP-3502C (Computer Science I).

There are many topics taught on COP-3502C, and they can be classified as:

- Algorithm Analysis
- AVL Trees
- Backtracking (not in the Exam since Fall 2021)
- Base Conversion
- Binary Trees
- Bitwise Operators
- Dynamic Memory Allocation (in C)
- Hash Tables
- Heaps
- Linked Lists
- Queues
- Recurrence Relation
- Recursion
- Sorting
- Stacks
- Summation
- Tries

Currently, there are 17 topics in total for an exam of 12 questions. The next graph shows how many appearances each topic has on the Foundation Exam since 1998. Note: the questions published on the "Previous Foundation Exams" website did not include an "official" topic on the questions until Fall 2008, meaning that every Foundation Exam until then had questions which topics were enumerated but not classified. Example: 1) question... instead of 1) (Sorting). Due to this, I will show two graphs: one showing data since 1998 (topics of the questions classified by me until Fall 2008), and another one showing data since Fall 2008 (topics of the questions already classified on the exam).

And now, the official count of topics appearances on the Foundation Exam.

There is not a big difference between the two graphs because most topics (especially on the right half of the graph) started appearing on the Foundation Exam around 2016. Algorithm analysis is the topic with the most appearances since it appears twice in almost every Foundation Exam.

As mentioned before, a few topics started appearing around 2016, more specifically Dynamic Memory Allocation (in C), Bitwise Operator, and Tries; as expected, Dynamic Memory Allocation (in C) has appeared in every single Foundation Exam since then.

On the "Exam Stats" tab I discussed about the inconsistent passing rates of the Foundation Exam, which directly depend on how students perform on each question, so it is a good idea to check which topic has the best and worst average score. The next graph will show the average score of each topic on the Foundation Exam:

It seems like students perform the best on Dynamic Memory Allocation questions, which is expected since it is the most essential topic in COP-3502C, on the contrary, Bitwise Operators questions look like the hardest part of the Foundation Exam, and it could be argued that it is pulling the passing rate down.

On a more positive note, the average score for 12 out of 17 topics in the exam is above 50%, meaning that most students are getting at least half credit for those kinds of questions.

Certainly, there are some questions that are more complicated than others, despite being of the same topic, and the average scores for these questions prove that. The next graph shows the highest-average questions for each topic, in other words, the single question of each topic where students got the best scores. We can see that some specific questions were understood by most students, hence their high averages. Surprisingly, Recurrence Relations, which is a non-coding topic, has a high of 58.80%, so a lot of students have struggled with those kind of math-based questions.

The question with the highest average is a Queues question from Fall 2018, where students got an average score of 96%. Here it is:

Most queues questions consist of coding or filling the boxes, but this one is different, consisting of analyzing a situation and how to apply queues. Despite having a question with such a high average, the passing rate of the Fall 2018 Foundation Exam was not out of the ordinary: 51.20%.

On the contrary, there are some questions with really low average scores. The next graph shows them:
Those are the questions (of each topic) where students struggled the most, unfortunately, the average scores of those questions are so low that they do not even beat the 50% mark, in other words, these are arguably the hardest questions of the Foundation Exam.

There is one very unnerving piece of information in that graph: the lowest-average question of Algorithm Analysis is 9.8%, meaning that most students had a very low score on this question. The worst part about it? It happened twice in two completely different Foundation Exams.


These two questions have the lowest-average score in a Foundation Exam since 2015, and they negatively affected the passing rate of both exams, but not as bad as other exams with lower passing rates.

Passing rate of Fall 2021 Foundation Exam (left): 44.6% (6th lowest since 2015).

Passing rate of Summer 2025 Foundation Exam (right): 45.5% (8th lowest since 2015).

Despite having such low averages, both exams had a Top Average Score of 50 out of 50, meaning that at least one student got their respective question 100% correct.

The Foundation Exam's topics vary each semester, but currently, there are a few topics that are almost guaranteed to appear in future exams (they have appeared in every exam since Fall 2016), these are:

- Algorithm Analysis (2 questions).
- Binary Trees.
- Dynamic Memory Allocation.
- Linked Lists
- Recursion
- Sorting

The 5 questions remaining should be based on the following topics:

- AVL Trees.
- Base Conversion.
- Bitwise Operators
- Hash Tables
- Heaps
- Queues
- Recurrence Relations
- Stacks
- Summation
- Tries

Up next, I'll show a side-by-side comparison of the "Easiest" and "Hardest" Foundation Exams in terms of average scores of each topic.


That concludes the "Topics Stats" tab. I wrote a short conclusion in the "Conclusion & Thoughts" tab, on the upper right corner.

In conclusion, all topics featured in the Foundation Exam must be studied and understood enough to perform well in the exam, and after analyzing the pattern of the last few exams, it is expected to see around 50% of students passing it (with the rest of students failing it). There can be a lot of explanations on why people pass or fail the exam, but the reality is that a lot of people take the exam without being fully prepared for it.

There are other skills not related to the exam that must be learned before the exam, for example: time management and stress control, as well as knowing how to calm your nerves. It is common to hear students talking about getting nervous and forgetting things during the exam. There's 12 questions in the exam and you have 2 hours in total to answer them, so students should allocate 10 minnutes for each question. Obviously, questions such as Base Conversion or Summation can be finished quicker if done correctly, so those extra minutes gained should be applied to harder topics such as Bitwise Operators or Tries (harder and most time-consuming questions).

Besides, it is important to have an open mind before taking the exam, since there is a high chance of the exam's passing line being 55% or 60%, as well as a passing rate being between 45% and 52%.

The best resources I can recommend to study for the FE:

- Passthefoundationexam: Best website to practice past Foundation Exams or specific topics from the exam.

- KnightHacks' Youtube Channel: Best videos on YouTube to review topics featured in the Foundation Exam.

-UCF's Previous Foundation Exams Website: Best website to pick and choose which exams you want to practice.

This is the end of the project. Thank you for reading this!

If you have any question, please send me a direct message or reply to my intial post.