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Measuring Massive Multitask Language Understanding

Dan Hendrycks
UC Berkeley

Collin Burns
Columbia University

Steven Basart
UChicago

Andy Zou
UC Berkeley

Mantas Mazeika
UIUC

Dawn Song
UC Berkeley

Jacob Steinhardt
UC Berkeley

ABSTRACT

We propose a new test to measure a text model’s multitask accuracy. The test
covers 57 tasks including elementary mathematics, US history, computer science,
law, and more. To attain high accuracy on this test, models must possess extensive
world knowledge and problem solving ability. We find that while most recent
models have near random-chance accuracy, the very largest GPT-3 model improves
over random chance by almost 20 percentage points on average. However, on every
one of the 57 tasks, the best models still need substantial improvements before
they can reach human-level accuracy. Models also have lopsided performance
and frequently do not know when they are wrong. Worse, they still have near-
random accuracy on some socially important subjects such as morality and law.
By comprehensively evaluating the breadth and depth of a model’s academic and
professional understanding, our test can be used to analyze models across many
tasks and to identify important shortcomings.

1

INTRODUCTION

Natural Language Processing (NLP) models have achieved superhuman performance on a number of
recently proposed benchmarks. However, these models are still well below human level performance
for language understanding as a whole, suggesting a disconnect between our benchmarks and the
actual capabilities of these models. The General Language Understanding Evaluation benchmark
(GLUE) (Wang et al., 2018) was introduced in 2018 to evaluate performance on a wide range of NLP
tasks, and top models achieved superhuman performance within a year. To address the shortcomings
of GLUE, researchers designed the SuperGLUE benchmark with more difficult tasks (Wang et al.,
2019). About a year since the release of SuperGLUE, performance is again essentially human-level
(Raffel et al., 2019). While these benchmarks evaluate linguistic skills more than overall language
understanding, an array of commonsense benchmarks have been proposed to measure basic reasoning
and everyday knowledge (Zellers et al., 2019; Huang et al., 2019; Bisk et al., 2019). However, these
recent benchmarks have similarly seen rapid progress (Khashabi et al., 2020). Overall, the near
human-level performance on these benchmarks suggests that they are not capturing important facets
of language understanding.

Transformer models have driven this recent progress by pretraining on massive text corpora, including
all of Wikipedia, thousands of books, and numerous websites. These models consequently see
extensive information about specialized topics, most of which is not assessed by existing NLP
benchmarks. It consequently remains an open question just how capable current language models are
at learning and applying knowledge from many domains.

To bridge the gap between the wide-ranging knowledge that models see during pretraining and the
existing measures of success, we introduce a new benchmark for assessing models across a diverse
set of subjects that humans learn. We design the benchmark to measure knowledge acquired during
pretraining by evaluating models exclusively in zero-shot and few-shot settings. This makes the
benchmark more challenging and more similar to how we evaluate humans. The benchmark covers
57 subjects across STEM, the humanities, the social sciences, and more. It ranges in difficulty
from an elementary level to an advanced professional level, and it tests both world knowledge and
problem solving ability. Subjects range from traditional areas, such as mathematics and history, to

1

(a) An example of few-shot learning and inference us-
ing GPT-3. The blue underlined bold text is the auto-
completed response from GPT-3, while the preceding
text is the user-inputted prompt. In this 2-shot learning
example, there are two instruction examples and one
initially incomplete example. On average, GPT-3 has
low accuracy on high school mathematics questions.

(b) Performance on a commonsense benchmark (Hel-
laSwag), a linguistic understanding benchmark (Super-
GLUE), and the massive multitask test. On previous
benchmarks, smaller models start well above random
chance levels and exhibit more continuous improve-
ments with model size increases, but on our test, GPT-3
moves beyond random chance with the largest model.

more specialized areas like law and ethics. The granularity and breadth of the subjects makes the
benchmark ideal for identifying a model’s blind spots.

We find that meaningful progress on our benchmark has only become possible in recent months.
In particular, models up to 13 billion parameters (Brown et al., 2020) achieve random chance
performance of 25% accuracy, but the 175 billion parameter GPT-3 model reaches a much higher
43.9% accuracy (see Figure 1b). On the other hand, unlike human professionals GPT-3 does not
excel at any single subject. Instead, we find that performance is lopsided, with GPT-3 having almost
70% accuracy for its best subject but near-random performance for several other subjects.

Our results indicate that while recent advances have been impressive, state-of-the-art models still
struggle at learning and applying knowledge from pretraining. The tasks with near-random accuracy
include calculation-heavy subjects such as physics and mathematics and subjects related to human
values such as law and morality. This second weakness is particularly concerning because it will
be important for future models to have a strong understanding of what is legal and what is ethical.
Worryingly, we also find that GPT-3 does not have an accurate sense of what it does or does not know
since its average confidence can be up to 24% off from its actual accuracy. We comprehensively
evaluate the breadth and depth of a model’s text understanding by covering numerous topics that
humans are incentivized to learn. Since our test consists in 57 tasks, it can be used to analyze
aggregate properties of models across tasks and to track important shortcomings. The test and code is
available at github.com/hendrycks/test.

2 RELATED WORK

Pretraining. The dominant paradigm in NLP is to pretrain large models on massive text corpora
including educational books and websites. In the process, these models are exposed to information
about a wide range of topics. Petroni et al. (2019) found that recent models learn enough information
from pretraining that they can serve as knowledge bases. However, no prior work has comprehensively
measured the knowledge models have across many real-world domains.

Until recently, researchers primarily used fine-tuned models on downstream tasks (Devlin et al., 2019).
However, larger pretrained models like GPT-3 (Brown et al., 2020) have made it possible to achieve
competitive performance without fine-tuning by using few-shot learning, which removes the need for
a large fine-tuning set. With the advent of strong zero-shot and few-shot learning, it is now possible
to curate a diverse set of tasks for evaluation and remove the possibility of models on “spurious cues”
(Geirhos et al., 2020; Hendrycks et al., 2019b) in a dataset to achieve high performance.

2

Few Shot Prompt and Predicted AnswerHow many numbers are in the list 25, 26, ..., 100?(A) 75 (B) 76 (C) 22 (D) 23Answer: BCompute i+i2+i3+···+i258+i259.(A) -1 (B) 1 (C) i (D) -iAnswer: AIf 4 daps = 7 yaps, and 5 yaps = 3 baps,how many daps equal 42 baps?(A) 28 (B) 21 (C) 40 (D) 30Answer: C␣The following are multiple choice questionsabout high school mathematics.SmallMediumLargeX-LargeModel Size2030405060708090Performance (%)GPT-3 Few Shot Test PerformanceCommonsenseLinguisticsKnowledge (Ours)Benchmarks. Many recent benchmarks aim to assess a model’s general world knowledge and basic
reasoning ability by testing its “commonsense.” A number of commonsense benchmarks have been
proposed in the past year, but recent models are already nearing human-level performance on several
of these, including HellaSwag (Zellers et al., 2019), Physical IQA (Bisk et al., 2019), and CosmosQA
(Huang et al., 2019). By design, these datasets assess abilities that almost every child has. In contrast,
we include harder specialized subjects that people must study to learn.

Some researchers have suggested that the future of NLP evaluation should focus on Natural Language
Generation (NLG) (Zellers et al., 2020), an idea that reaches back to the Turing Test (Turing, 1950).
However, NLG is notoriously difficult to evaluate and lacks a standard metric (Sai et al., 2020).
Consequently, we instead create a simple-to-evaluate test that measures classification accuracy on
multiple choice questions.

While several question answering benchmarks exist, they are comparatively limited in scope. Most
either cover easy topics like grade school subjects for which models can already achieve strong
performance (Clark et al., 2018; Khot et al., 2019; Mihaylov et al., 2018; Clark et al., 2019), or
are focused on linguistic understanding in the form of reading comprehension (Lai et al., 2017;
Richardson et al., 2013). In contrast, we include a wide range of difficult subjects that go far beyond
linguistic understanding.

3 A MULTITASK TEST

We create a massive multitask test consisting of multiple-choice questions from various branches of
knowledge. The test spans subjects in the humanities, social sciences, hard sciences, and other areas
that are important for some people to learn. There are 57 tasks in total, which is also the number
of Atari games (Bellemare et al., 2013), all of which are listed in Appendix B. The questions in
the dataset were manually collected by graduate and undergraduate students from freely available
sources online. These include practice questions for tests such as the Graduate Record Examination
and the United States Medical Licensing Examination. It also includes questions designed for
undergraduate courses and questions designed for readers of Oxford University Press books. Some
tasks cover a subject, like psychology, but at a specific level of difficulty, such as “Elementary,”
“High School,” “College,” or “Professional.” For example, the “Professional Psychology” task draws
on questions from freely available practice questions for the Examination for Professional Practice
in Psychology, while the “High School Psychology” task has questions like those from Advanced
Placement Psychology examinations.

We collected 15908 questions in total, which we split into a few-shot development set, a validation
set, and a test set. The few-shot development set has 5 questions per subject, the validation set may
be used for selecting hyperparameters and is made of 1543 questions, and the test set has 14080
questions. Each subject contains 100 test examples at the minimum, which is longer than most exams
designed to assess people.

Since our test aggregates different subjects and several levels of difficulty, we measure more than
straightforward commonsense or narrow linguistic understanding. Instead, we measure arbitrary
real-world text understanding. Since models are pretrained on the Internet, this enables us to test how
well they can extract useful knowledge from massive corpora. To succeed at our test, future models
should be well-rounded, possess extensive world knowledge, and develop expert-level problem
solving ability. These properties make the test likely to be an enduring and informative goalpost.

3.1 HUMANITIES

The humanities is a group of disciplines that make use of qualitative analysis and analytic methods
rather than scientific empirical methods. Branches of the humanities include law, philosophy, history,
and so on (Appendix B). Mastering these subjects requires a variety of skills. For example, legal
understanding requires knowledge of how to apply rules and standards to complex scenarios, and
also provide answers with stipulations and explanations. We illustrate this in Figure 2. Legal
understanding is also necessary for understanding and following rules and regulations, a necessary
capability to constrain open-world machine learning models. For philosophy, our questions cover
concepts like logical fallacies, formal logic, and famous philosophical arguments. It also covers
moral scenarios, including questions from the ETHICS dataset (Hendrycks et al., 2020) that test a
model’s understanding of normative statements through predicting widespread moral intuitions about

3

Figure 2: This task requires understanding detailed and dissonant scenarios, applying appropriate
legal precedents, and choosing the correct explanation. The green checkmark is the ground truth.

diverse everyday scenarios. Finally, our history questions cover a wide range of time periods and
geographical locations, including prehistory and other advanced subjects.

3.2 SOCIAL SCIENCE

Social science includes branches of knowledge that examine human behavior and society. Subject
areas include economics, sociology, politics, geography, psychology, and so on. See Figure 3
for example questions. Our economics questions include microeconomics, macroeconomics, and
econometrics, and cover different types of problems, including questions that require a mixture of
world knowledge, qualitative reasoning, or quantitative reasoning. We also include important but
more esoteric topics such as security studies in order to test the boundaries of what is experienced and
learned during pretraining. Social science also includes psychology, a field that may be especially
important for attaining a nuanced understanding of humans.

Figure 3: Examples from the Microeconomics and Security Studies social science tasks.

3.3 SCIENCE, TECHNOLOGY, ENGINEERING, AND MATHEMATICS (STEM)

STEM subjects include physics, computer science, mathematics, and more. Two examples are shown
in Figure 4. Conceptual physics tests understanding of simple physics principles and may be thought
of as a harder version of the physical commonsense benchmark Physical IQA (Bisk et al., 2019). We
also test mathematical problem solving ability at various levels of difficulty, from the elementary to
the college level. College mathematics questions, like those found on the GRE mathematics subject
test, often require chains of reasoning and abstract knowledge. To encode mathematics expressions,
we use LaTeX or symbols such as * and ˆ for multiplication and exponentiation respectively. STEM
subjects require knowledge of empirical methods, fluid intelligence, and procedural knowledge.

3.4 OTHER

There is a long tail of subjects that either do not neatly fit into any of the three preceding categories or
for which there are not thousands of freely available questions. We put these subjects into Other. This

4

As Seller, an encyclopedia salesman, approached the grounds on which Hermit's house was situated,he saw a sign that said, "No salesmen. Trespassers will be prosecuted. Proceed at your own risk."Although Seller had not been invited to enter, he ignored the sign and drove up the driveway towardthe house. As he rounded a curve, a powerful explosive charge buried in the driveway exploded, andSeller was injured. Can Seller recover damages from Hermit for his injuries?(A) Yes, unless Hermit, when he planted the charge, intended only to deter, not harm, intruders.(B) Yes, if Hermit was responsible for the explosive charge under the driveway.(C) No, because Seller ignored the sign, which warned him against proceeding further.(D) No, if Hermit reasonably feared that intruders would come and harm him or his family.Professional LawOne of the reasons that the government discourages and regulates monopolies is that(A) producer surplus is lost and consumer surplus is gained.(B) monopoly prices ensure productive efficiency but cost society allocative efficiency.(C) monopoly firms do not engage in significant research and development.(D) consumer surplus is lost with higher prices and lower levels of output.MicroeconomicsSecurity StudiesWhy is HIV/AIDS considered to be a non-traditional security issue?(A) HIV/AIDS is a newly emergent disease that did not exist until the later 20th century.(B) Ill health can threaten the state indirectly, but can also be a threat to other       referent objects such as the economy.(C) The overwhelming scale of HIV/AIDS requires a new approach in order to       theorize its impact on security.(D) None of the above - HIV/AIDS is better defined as a traditional security issue.Figure 4: Examples from the Conceptual Physics and College Mathematics STEM tasks.

section includes the Professional Medicine task, which has difficult questions that require humans
many years of study to master. An example is depicted in Figure 5. This section also contains
business topics like finance, accounting, and marketing, as well as knowledge of global facts. The
latter includes statistics about poverty in different countries over time, which may be necessary for
having an accurate model of the world internationally.

Figure 5: A question from Professional Medicine which is a simulated question from the United
States Medical Licensing Examination.
4 EXPERIMENTS

4.1 SETUP

Assessment and Models. To measure performance on our multitask benchmark, we compute the
classification accuracy across all examples and tasks. We evaluate GPT-3 (Brown et al., 2020) and
UnifiedQA (Khashabi et al., 2020). For GPT-3 we use the OpenAI API, which provides access
to four model variants, “Ada,” “Babbage,” “Curie,” and “Davinci,” which we refer to as “Small”
(2.7 billion parameters), “Medium” (6.7 billion), “Large” (13 billion) and “X-Large” (175 billion).
UnifiedQA uses the T5 (Raffel et al., 2019) text-to-text backbone and is fine-tuned on previously
proposed question answering datasets (Lai et al., 2017), where the prediction is the class with the

Model
Random Baseline
T5
UnifiedQA
GPT-3 Small
GPT-3 Medium
GPT-3 Large
GPT-3 X-Large

Humanities
25.0
24.9
38.0
24.4
26.1
27.1
40.8

Social Science
25.0
25.2
41.5
30.9
21.6
25.6
50.4

STEM
25.0
24.8
32.2
26.0
25.6
24.3
36.7

Other
25.0
24.4
42.1
24.1
25.5
26.5
48.8

Average
25.0
24.8
38.5
25.9
24.9
26.0
43.9

Table 1: Average weighted accuracy for each model on all four broad disciplines. All values are
percentages. Models proposed in the past few months (UnifiedQA, GPT-3) can move several percent
points beyond random chance on this test.

5

When you drop a ball from rest it accelerates downward at 9.8 m/s². If you instead throw itdownward assuming no air resistance its acceleration immediately after leaving your hand is(A) 9.8 m/s²(B) more than 9.8 m/s²(C) less than 9.8 m/s²(D) Cannot say unless the speed of throw is given.ConceptualPhysicsCollegeMathematicsIn the complex z-plane, the set of points satisfying the equation z² = |z|² is a(A) pair of points(B) circle(C) half-line(D) lineA 33-year-old man undergoes a radical thyroidectomy for thyroid cancer. During the operation,moderate hemorrhaging requires ligation of several vessels in the left side of the neck.Postoperatively, serum studies show a calcium concentration of 7.5 mg/dL, albumin concentrationof 4 g/dL, and parathyroid hormone concentration of 200 pg/mL. Damage to which of the followingvessels caused the findings in this patient?(A) Branch of the costocervical trunk(B) Branch of the external carotid artery(C) Branch of the thyrocervical trunk(D) Tributary of the internal jugular veinProfessional Medicinehighest token overlap with UnifiedQA’s text output. Since UnifiedQA is fine-tuned on other datasets,
we evaluate it without any further tuning to assess its transfer accuracy.

Few-Shot Prompt. We feed GPT-3 prompts
like that shown in Figure 1a. We begin each
prompt with “The following are multiple choice
questions (with answers) about [subject].” For
zero-shot evaluation, we append the question to
the prompt. For few-shot evaluation, we add up
to 5 demonstration examples with answers to
the prompt before appending the question. All
prompts end with “Answer: ”. The model then
produces probabilities for the tokens “A,” “B,”
“C,” and “D,” and we treat the highest probability
option as the prediction. For consistent evalua-
tion, we create a dev set with 5 fixed few-shot
examples for each subject.

4.2 RESULTS

Model Size and Accuracy. We compare the
few-shot accuracy of each GPT-3 size in Table 1.
We find that the three smaller GPT-3 models
have near random accuracy (around 25%). We
also assess the 11 billion parameter T5 model
in a few-shot setting and confirmed that it like-
wise has random chance accuracy. In contrast,
we find that the X-Large 175 billion parame-
ter GPT-3 model performs substantially better
than random, with an accuracy of 43.9%. We
also find qualitatively similar results in the zero-
shot setting. While the smaller models have
around 25% zero-shot accuracy, Figure 8a in
Appendix A shows that the largest GPT-3 model
has a much higher zero-shot accuracy of about
37.7%. In Figure 1b we show that non-random
accuracy on the multitask test emerged with re-
cent large few-shot models compared to datasets
that assess commonsense and linguistic under-
standing.

To test the importance of model size for other
methods, we also evaluate UnifiedQA models.
UnifiedQA has the advantage of being fine-
tuned on other question answering datasets, and
we assess it by evaluating its transfer perfor-
mance without any additional fine-tuning. The
largest UnifiedQA model we test has 3 billion
parameters, which is slightly larger than GPT-3
Small. Nevertheless, we show in Table 1 that it
attains 38.5% accuracy. This is worse than few-
shot GPT-3 X-Large accuracy but higher than
zero-shot GPT-3 X-Large, despite UnifiedQA having two orders of magnitude fewer parameters. We
also find that even the smallest UnifiedQA variant, with just 60 million parameters, has approximately
30% accuracy. These results suggest that while model size is a key component for achieving strong
performance, it is not the only important factor.

Figure 6: GPT-3 few shot accuracies for all of the
57 tasks. All task accuracies are markedly below
expert-level performance.

Comparing Disciplines. Using our test, we discover that GPT-3 has lopsided performance and
several substantial knowledge gaps. Figure 6 shows the few-shot accuracy of GPT-3 for all 57 tasks.

6

020406080100Accuracy (%)College ChemistryMoral ScenariosCollege PhysicsHigh School PhysicsHigh School MathematicsFormal LogicElementary MathematicsAbstract AlgebraHigh School StatisticsMachine LearningEconometricsHigh School ChemistryProfessional AccountingProfessional LawCollege MathematicsProfessional MedicineConceptual PhysicsGlobal FactsHigh School Comp SciMedical GeneticsHigh School MacroeconomicsHigh School MicroeconomicsMoral DisputesProfessional PsychologyCollege BiologyVirologyCollege Comp SciBusiness EthicsNutritionCollege MedicineAnatomyClinical KnowledgeLogical FallaciesHigh School BiologyPublic RelationsAstronomyElectrical EngineeringHuman AgingPhilosophySecurity StudiesPrehistoryHigh School US HistorySociologyHigh School European HistoryHuman SexualityJurisprudenceWorld ReligionsInternational LawHigh School World HistoryManagementComputer SecurityHigh School GeographyHigh School Gov't and PoliticsMarketingMiscellaneousHigh School PsychologyUS Foreign PolicyRandom Chance(a) GPT-3’s completion for two prompts testing knowl-
edge of the order of operations. The blue underlined
bold text is the autocompleted response from GPT-3.
While it is has descriptive knowledge and knows about
of the order of operations, it does not know how to apply
its knowledge and does not obey operator precedence. (b) GPT-3’s average confidence is a poor estimator of

its accuracy and can be off by up to 24%.

It shows the GPT-3 is below expert-level performance for all tasks, with accuracy ranging from 69%
for US Foreign Policy to 26% for College Chemistry.

Overall, GPT-3 does poorly on highly procedural problems. Figure 6 shows that calculation-heavy
STEM subjects tend to have low accuracy compared to verbal subjects. In fact, 9 out of the 10
lowest-accuracy tasks are STEM subjects that emphasize mathematics or calculations. We speculate
that is in part because GPT-3 acquires declarative knowledge more readily than procedural knowlege.
For example, many questions in Elementary Mathematics require applying the order of operations
for arithmetic, which is described by the acronym PEMDAS (Parentheses Exponents Multiplication
Division Addition Subtraction). In Figure 7a, we confirm that GPT-3 is aware of the acronymn
PEMDAS. However, it does not consistently apply PEMDAS to actual problems. On the other hand,
procedural understanding is not its only weak point. We find that some verbal tasks such as Moral
Scenarios (Hendrycks et al., 2020) and Professional Law also have especially low accuracy.

Our test also shows that GPT-3 acquires knowledge quite unlike humans. For example, GPT-3 learns
about topics in a pedagogically unusual order. GPT-3 does better on College Medicine (47.4%)
and College Mathematics (35.0%) than calculation-heavy Elementary Mathematics (29.9%). GPT-3
demonstrates unusual breadth, but it does not master a single subject. In this way, our test shows that
GPT-3 has many knowledge blindspots and has capabilities that are lopsided.

Calibration. We should not trust a model’s prediction unless the model is calibrated, meaning
that its confidence is a good estimate of the actual probability the prediction is correct. However,
large neural networks are often miscalibrated (Guo et al., 2017), especially under distribution shift
(Ovadia et al., 2019). We evaluate the calibration of GPT-3 by testing how well its average confidence
estimates its actual accuracy for each subject. We show the results in Figure 7b, which demonstrates
that GPT-3 is uncalibrated. In fact, its confidence is only weakly related to its actual accuracy in
the zero-shot setting, with the difference between its accuracy and confidence reaching up to 24%
for some subjects. Another calibration measure is the Root Mean Squared (RMS) calibration error
(Hendrycks et al., 2019a; Kumar et al., 2019). Many tasks have miscalibrated predictions, such
as Elementary Mathematics which has a zero-shot RMS calibration error of 19.4%. These results
suggest that model calibration has wide room for improvement.

5 DISCUSSION

Multimodal Understanding. While text is capable of conveying an enormous number of concepts
about the world, many important concepts are conveyed mainly through other modalities, such as
images, audio, and physical interaction (Bisk et al., 2020). Existing large-scale NLP models, such as
GPT-3, do not incorporate multimodal information, so we design our benchmark to capture a diverse
array of tasks in a text-only format. However, as models gain the ability to process multimodal inputs,
benchmarks should be designed to reflect this change. One such benchmark could be a “Turk Test,”
consisting of Amazon Mechanical Turk Human Intelligence Tasks. These are well-defined tasks that
require models to interact with flexible formats and demonstrate multimodal understanding.

The Internet as a Training Set. A major distinction between our benchmark and previous multitask
NLP benchmarks is that we do not require large training sets. Instead, we assume that models have

7

Declarative vs. Procedural KnowledgePrompt and Completion:The order of operations or PEMDAS isParentheses Exponents MultiplicationDivision Addition SubtractionPrompt and Completion:(1 + 1) × 2 = 3␣2030405060Confidence (%)2030405060Accuracy (%)GPT-3 Zero-Shot CalibrationFormal LogicMarketingacquired the requisite knowledge from reading vast quantities of diverse text from the Internet. This
process is typically called pretraining, but it can be thought of as training in its own right, where the
downstream evaluation is demonstrating whatever knowledge we would expect a human to pick up
from reading the same text.

This motivates us to propose a methodological change so that models are trained more like how
humans learn. While most previous machine learning benchmarks have models learn from a large
question bank, humans primarily learn new subjects by reading books and listening to others talk
about the topic. For specialized subjects such as Professional Law, massive legal corpora are available,
such as the 164-volume legal encyclopedia Corpus Juris Secundum, but there are fewer than 5,000
multistate bar exam questions available. Learning the entire law exclusively through a small number
of practice tests is implausible, so future models must learn more during pretraining.

For this reason we assess pretrained models in a zero-shot or few-shot setting and we provide a dev,
val, and test set for each task. The dev set is used for few-shot prompts, the val set could be used for
hyperparameter tuning, and the test set is used to compute the final accuracy. Importantly, the format
of our evaluation is not identical to the format in which information is acquired during pretraining.
This has the benefit of obviating concerns about spurious training set annotation artifacts (Geirhos
et al., 2020; Hendrycks et al., 2019b) and is in stark contrast to the previous paradigm of identically
distributed training and test sets. This change also enables collecting a much more extensive and
diverse set of tasks for evaluation. We anticipate our methodology becoming more widespread as
models improve at extracting information from diverse online sources.

Model Limitations. We find that current large-scale Transformers have wide room for improvement.
They are notably poor at modeling human (dis)approval, as evident by the low performance on the
Professional Law and Moral Scenarios tasks. For future systems to be aligned with human values, high
performance on these tasks is crucial (Hendrycks et al., 2020), so future research should especially
aim to increase accuracy on these tasks. Models also have difficulty performing calculations, so much
so that they exhibit poor performance on Elementary Mathematics and many other STEM subjects
with “plug and chug” problems. Additionally, they do not match expert-level performance on any
subject, so for all subjects it is subhuman. On average, models are only now starting to move beyond
random-chance accuracy levels.

Addressing these shortcomings may be challenging. To illustrate this, we attempted to create a better
Professional Law model by pretraining on specialized data but achieved only limited success. We
collected approximately 2,000 additional Professional Law training examples. After fine-tuning a
RoBERTa-base model (Liu et al., 2019) using this custom training set, our model attained 32.8% test
accuracy. To test the impact of additional specialized training data, we also had RoBERTa continue
pretraining on approximately 1.6 million legal case summaries using Harvard’s Law Library case law
corpus case.law, but after fine-tuning it only attained 36.1% accuracy. This suggests that while
additional pretraining on relevant high quality text can help, it may not be enough to substantially
increase the performance of current models.

It is unclear whether simply scaling up existing language models will solve the test. Current
understanding indicates that a 10× increase in model size must be accompanied by an approximate
5× increase in data (Kaplan et al., 2020). Aside from the tremendous expense in creating multi-trillion
parameter language models, data may also become a bottleneck, as there is far less written about
esoteric branches of knowledge than about everyday text.

6 CONCLUSION

We introduced a new test that measures how well text models can learn and apply knowledge
encountered during pretraining. By covering 57 subjects at varying levels of difficulty, the test
assesses language understanding in greater breadth and depth than previous benchmarks. We found
that it has recently become possible for models to make meaningful progress on the test, but that
state-of-the-art models have lopsided performance and still do not excel at any individual task.
We also showed that current models are uncalibrated and have difficulty with tasks that require
calculations. Worryingly, models also perform especially poorly on socially relevant subjects
including morality and law. Our expansive test can help researchers pinpoint important shortcomings
of models, making it easier to gain a clearer picture of state-of-the-art capabilities.

8

6.1 ACKNOWLEDGEMENTS

We would like to thank the following for their helpful comments: Jan Leike, David Krueger, Alex
Tamkin, Girish Sastry, and Henry Zhu. DH is supported by the NSF GRFP Fellowship and an Open
Philanthropy Project Fellowship. This research was also supported by the NSF Frontier Award
1804794.

REFERENCES

M. G. Bellemare, Y. Naddaf, J. Veness, and M. Bowling. The arcade learning environment: An
evaluation platform for general agents (extended abstract). J. Artif. Intell. Res., 47:253–279, 2013.

Y. Bisk, R. Zellers, R. L. Bras, J. Gao, and Y. Choi. Piqa: Reasoning about physical commonsense in

natural language, 2019.

Y. Bisk, A. Holtzman, J. Thomason, J. Andreas, Y. Bengio, J. Chai, M. Lapata, A. Lazaridou, J. May,

A. Nisnevich, N. Pinto, and J. Turian. Experience grounds language, 2020.

T. B. Brown, B. Mann, N. Ryder, M. Subbiah, J. Kaplan, P. Dhariwal, A. Neelakantan, P. Shyam,
G. Sastry, A. Askell, S. Agarwal, A. Herbert-Voss, G. Krueger, T. Henighan, R. Child, A. Ramesh,
D. M. Ziegler, J. Wu, C. Winter, C. Hesse, M. Chen, E. Sigler, M. Litwin, S. Gray, B. Chess,
J. Clark, C. Berner, S. McCandlish, A. Radford, I. Sutskever, and D. Amodei. Language models
are few-shot learners, 2020.

P. Clark, I. Cowhey, O. Etzioni, T. Khot, A. Sabharwal, C. Schoenick, and O. Tafjord. Think you have
solved question answering? try arc, the ai2 reasoning challenge. ArXiv, abs/1803.05457, 2018.

P. Clark, O. Etzioni, D. Khashabi, T. Khot, B. D. Mishra, K. Richardson, A. Sabharwal, C. Schoenick,
O. Tafjord, N. Tandon, S. Bhakthavatsalam, D. Groeneveld, M. Guerquin, and M. Schmitz. From ’f’
to ’a’ on the n.y. regents science exams: An overview of the aristo project. ArXiv, abs/1909.01958,
2019.

J. Devlin, M.-W. Chang, K. Lee, and K. Toutanova. Bert: Pre-training of deep bidirectional

transformers for language understanding. ArXiv, abs/1810.04805, 2019.

R. Geirhos, J.-H. Jacobsen, C. Michaelis, R. Zemel, W. Brendel, M. Bethge, and F. A. Wichmann.

Shortcut learning in deep neural networks, 2020.

C. Guo, G. Pleiss, Y. Sun, and K. Q. Weinberger. On calibration of modern neural networks. ICML,

2017.

D. Hendrycks, M. Mazeika, and T. Dietterich. Deep anomaly detection with outlier exposure. ICLR,

2019a.

D. Hendrycks, K. Zhao, S. Basart, J. Steinhardt, and D. Song. Natural adversarial examples. ArXiv,

abs/1907.07174, 2019b.

D. Hendrycks, C. Burns, S. Basart, A. Critch, J. Li, D. Song, and J. Steinhardt. Aligning ai with

shared human values, 2020.

L. Huang, R. L. Bras, C. Bhagavatula, and Y. Choi. Cosmos qa: Machine reading comprehension

with contextual commonsense reasoning, 2019.

J. Kaplan, S. McCandlish, T. Henighan, T. B. Brown, B. Chess, R. Child, S. Gray, A. Radford, J. Wu,

and D. Amodei. Scaling laws for neural language models, 2020.

D. Khashabi, T. Khot, A. Sabharwal, O. Tafjord, P. Clark, and H. Hajishirzi. Unifiedqa: Crossing

format boundaries with a single qa system, 2020.

T. Khot, P. Clark, M. Guerquin, P. Jansen, and A. Sabharwal. Qasc: A dataset for question answering

via sentence composition, 2019.

A. Kumar, P. Liang, and T. Ma. Verified uncertainty calibration, 2019.

9

G. Lai, Q. Xie, H. Liu, Y. Yang, and E. Hovy. Race: Large-scale reading comprehension dataset from

examinations, 2017.

Z. Lan, M. Chen, S. Goodman, K. Gimpel, P. Sharma, and R. Soricut. Albert: A lite bert for

self-supervised learning of language representations. ArXiv, abs/1909.11942, 2020.

Y. Liu, M. Ott, N. Goyal, J. Du, M. Joshi, D. Chen, O. Levy, M. Lewis, L. Zettlemoyer, and
V. Stoyanov. Roberta: A robustly optimized bert pretraining approach. ArXiv, abs/1907.11692,
2019.

T. Mihaylov, P. Clark, T. Khot, and A. Sabharwal. Can a suit of armor conduct electricity? a new

dataset for open book question answering. In EMNLP, 2018.

Y. Ovadia, E. Fertig, J. Ren, Z. Nado, D. Sculley, S. Nowozin, J. V. Dillon, B. Lakshminarayanan,
and J. Snoek. Can you trust your model’s uncertainty? Evaluating predictive uncertainty under
dataset shift. NeurIPS, 2019.

F. Petroni, T. Rocktäschel, P. Lewis, A. Bakhtin, Y. Wu, A. H. Miller, and S. Riedel. Language

models as knowledge bases?, 2019.

C. Raffel, N. Shazeer, A. Roberts, K. Lee, S. Narang, M. Matena, Y. Zhou, W. Li, and P. J. Liu.

Exploring the limits of transfer learning with a unified text-to-text transformer, 2019.

M. Richardson, C. J. Burges, and E. Renshaw. MCTest: A challenge dataset for the open-domain
machine comprehension of text. In Proceedings of the 2013 Conference on Empirical Methods in
Natural Language Processing, pages 193–203, Seattle, Washington, USA, Oct. 2013. Association
for Computational Linguistics.

A. B. Sai, A. K. Mohankumar, and M. M. Khapra. A survey of evaluation metrics used for nlg

systems. 2020.

A. Turing. Computing machinery and intelligence. 1950.

A. Wang, A. Singh, J. Michael, F. Hill, O. Levy, and S. R. Bowman. Glue: A multi-task benchmark

and analysis platform for natural language understanding, 2018.

A. Wang, Y. Pruksachatkun, N. Nangia, A. Singh, J. Michael, F. Hill, O. Levy, and S. R. Bowman.
Superglue: A stickier benchmark for general-purpose language understanding systems, 2019.

R. Zellers, A. Holtzman, Y. Bisk, A. Farhadi, and Y. Choi. Hellaswag: Can a machine really finish

your sentence?, 2019.

R. Zellers, A. Holtzman, E. Clark, L. Qin, A. Farhadi, and Y. Choi. Evaluating machines by their

real-world language use, 2020.

10

A ADDITIONAL ANALYSIS

(a) As the number of few-shot instruction examples in-
creases, the accuracy monotonically increases. Notably,
zero-shot performance is only somewhat lower than
5-shot accuracy.

(b) While models are more calibrated in a few-shot set-
ting than a zero-shot setting, they are still miscalibrated,
with gap between accuracy and confidence reaching up
to 14%. Here the correlation between confidence and
accuracy is r = 0.81, compared to r = 0.63 in the
zero-shot setting.

A.1 ERROR ANALYSIS

We qualitatively analyze when GPT-3 makes high confidence mistakes. We find that while many of
these mistakes were clearly wrong, many were mistakes that a human might make. For example,
one question it got wrong was “How many chromosomes do all human somatic cells contain?” The
correct answer is 46, while few-shot GPT-3 predicted 23 with confidence 97.5%. This answer would
have been correct if the question asked about the number of pairs of chromosomes. Similarly, many
of its other high confidence mistakes were also correct answers to slightly different questions.

A.2 FINE-TUNING

Rather than testing models in a few-shot setting, we now determine the impact of fine-tuning with
thousands of examples. For this section, we fine-tune RoBERTa-base (Liu et al., 2019) and ALBERT-
xxlarge (Lan et al., 2020), which have fewer than 250 million parameters and have at least 10×
fewer parameters than GPT-3 Small. Models are fine-tuned to predict one of four classes and are
fine-tuned using the dev+val set, and we test on the test set. We observe that these smaller models
can attain better-than-random accuracy. RoBERTa-base attains an overall accuracy of 27.9%, with
27.9% accuracy for the humanities, 28.8% for social sciences, 27.0% for STEM, and 27.7% for other.
ALBERT-xxlarge attains an accuracy of 27.1%, with 27.2% accuracy for the humanities, 25.7% for
the social sciences, 27.7% for STEM, and 27.9% for other. Consequently smaller models that are not
designed for QA are able to exceed random chance, though barely.

B TEST DETAILS

B.1 TASK DESCRIPTIONS AND EXAMPLES

We list all tasks and the topics they test in Table 2. We also provide an example for each task starting
with Figure 10.

B.2 EXACT QUESTION AND ANSWER CONTAMINATION

Since language models train on vast text corpora, there is some chance that they have seen the exact
question and answer during pretraining. If they memorized the exact question and answer, then
they would attain higher accuracy than their true ability. Likewise, a question’s entropy would be

11

0-Shot1-Shot2-Shot3-Shot4-Shot5-ShotNumber of Examples in Context3035404550Accuracy (%)GPT-3 Multitask Accuracy vs.Number of Examples in Context203040506070Confidence (%)203040506070Accuracy (%)GPT-3 Few-Shot Calibrationespecially low if it were memorized. Memorized questions and answers should have low entropy and
high accuracy. However, in Figure 9, we see that accuracy and question entropy are not positively
correlated, suggesting that the test’s low-entropy questions do not correspond to memorized (and
thereby correctly predicted) answers. This suggests that our exact questions were not memorized.
However, during pretraining models encountered text related to our questions through processing
Wikipedia. We also note that most of our questions came from PDFs or websites where questions and
answers are on separate pages.

See Brown et al. (2020) for a previous discussion of contamination showing that the phenomena
hardly affects performance. To reduce the probability that future models encounter exact questions
during test-time, we provide a list of question sources on our github.

Figure 9: The average log probability of the question (without answer) is not strongly positively
correlated with accuracy, all else equal. Each point corresponds to a task. Higher log probability
indicates higher compression, and especially high log probability suggests memorization. In the zero-
shot question prompt, the correlation between average log probability and accuracy is r = −0.43,
and for the few-shot setting the correlation is r = −0.56.

12

2.82.62.42.22.01.8Log Probability Per Token2030405060Accuracy (%)GPT-3 Zero-ShotPrompt Compression and Accuracy2.42.22.01.81.61.41.2Log Probability Per Token203040506070Accuracy (%)GPT-3 Few-ShotPrompt Compression and AccuracyTask
Abstract Algebra
Anatomy
Astronomy
Business Ethics
Clinical Knowledge
College Biology
College Chemistry
College Computer Science
College Mathematics
College Medicine
College Physics
Computer Security
Conceptual Physics
Econometrics
Electrical Engineering
Elementary Mathematics
Formal Logic
Global Facts
High School Biology
High School Chemistry
High School Computer Science
High School European History
High School Geography
High School Gov’t and Politics
High School Macroeconomics
High School Mathematics
High School Microeconomics
High School Physics
High School Psychology
High School Statistics
High School US History
High School World History
Human Aging
Human Sexuality
International Law
Jurisprudence
Logical Fallacies
Machine Learning
Management
Marketing
Medical Genetics
Miscellaneous
Moral Disputes
Moral Scenarios
Nutrition
Philosophy
Prehistory
Professional Accounting
Professional Law
Professional Medicine
Professional Psychology
Public Relations
Security Studies
Sociology
US Foreign Policy
Virology
World Religions

Tested Concepts
Groups, rings, fields, vector spaces, ...
Central nervous system, circulatory system, ...
Solar system, galaxies, asteroids, ...
Corporate responsibility, stakeholders, regulation, ...
Spot diagnosis, joints, abdominal examination, ...
Cellular structure, molecular biology, ecology, ...
Analytical, organic, inorganic, physical, ...
Algorithms, systems, graphs, recursion, ...
Differential equations, real analysis, combinatorics, ...
Introductory biochemistry, sociology, reasoning, ...
Electromagnetism, thermodynamics, special relativity, ...
Cryptography, malware, side channels, fuzzing, ...
Newton’s laws, rotational motion, gravity, sound, ...
Volatility, long-run relationships, forecasting, ...
Circuits, power systems, electrical drives, ...
Word problems, multiplication, remainders, rounding, ...
Propositions, predicate logic, first-order logic, ...
Extreme poverty, literacy rates, life expectancy, ...
Natural selection, heredity, cell cycle, Krebs cycle, ...
Chemical reactions, ions, acids and bases, ...
Arrays, conditionals, iteration, inheritance, ...
Renaissance, reformation, industrialization, ...
Population migration, rural land-use, urban processes, ...
Branches of government, civil liberties, political ideologies, ...
Economic indicators, national income, international trade, ...
Pre-algebra, algebra, trigonometry, calculus, ...
Supply and demand, imperfect competition, market failure, ...
Kinematics, energy, torque, fluid pressure, ...
Behavior, personality, emotions, learning, ...
Random variables, sampling distributions, chi-square tests, ...
Civil War, the Great Depression, The Great Society, ...
Ottoman empire, economic imperialism, World War I, ...
Senescence, dementia, longevity, personality changes, ...
Pregnancy, sexual differentiation, sexual orientation, ...
Human rights, sovereignty, law of the sea, use of force, ...
Natural law, classical legal positivism, legal realism, ...
No true Scotsman, base rate fallacy, composition fallacy, ...
SVMs, VC dimension, deep learning architectures, ...
Organizing, communication, organizational structure, ...
Segmentation, pricing, market research, ...
Genes and cancer, common chromosome disorders, ...
Agriculture, Fermi estimation, pop culture, ...
Freedom of speech, addiction, the death penalty, ...
Detecting physical violence, stealing, externalities, ...
Metabolism, water-soluble vitamins, diabetes, ...
Skepticism, phronesis, skepticism, Singer’s Drowning Child, ...
Neanderthals, Mesoamerica, extinction, stone tools, ...
Auditing, reporting, regulation, valuation, ...
Torts, criminal law, contracts, property, evidence, ...
Diagnosis, pharmacotherapy, disease prevention, ...
Diagnosis, biology and behavior, lifespan development, ...
Media theory, crisis management, intelligence gathering, ...
Environmental security, terrorism, weapons of mass destruction, ...
Socialization, cities and community, inequality and wealth, ...
Soft power, Cold War foreign policy, isolationism, ...
Epidemiology, coronaviruses, retroviruses, herpesviruses, ...
Judaism, Christianity, Islam, Buddhism, Jainism, ...

Table 2: Summary of all 57 tasks.

13

Supercategory
STEM
STEM
STEM
Other
Other
STEM
STEM
STEM
STEM
Other
STEM
STEM
STEM
Social Sciences
STEM
STEM
Humanities
Other
STEM
STEM
STEM
Humanities
Social Sciences
Social Sciences
Social Sciences
STEM
Social Sciences
STEM
Social Sciences
STEM
Humanities
Humanities
Other
Social Sciences
Humanities
Humanities
Humanities
STEM
Other
Other
Other
Other
Humanities
Humanities
Other
Humanities
Humanities
Other
Humanities
Other
Social Sciences
Social Sciences
Social Sciences
Social Sciences
Social Sciences
Other
Humanities

Find all c in Z3 such that Z3[x]/(x2 + c) is a field.
(A) 0

(D) 3

(C) 2

(B) 1

Figure 10: An Abstract Algebra example.

What is the embryological origin of the hyoid bone?
(A) The first pharyngeal arch
(B) The first and second pharyngeal arches
(C) The second pharyngeal arch
(D) The second and third pharyngeal arches

Figure 11: An Anatomy example.

Why isn’t there a planet where the asteroid belt is located?
(A) A planet once formed here but it was broken apart by a catastrophic collision.
(B) There was not enough material in this part of the solar nebula to form a planet.
(C) There was too much rocky material to form a terrestrial planet but not enough gaseous material
to form a jovian planet.
(D) Resonance with Jupiter prevented material from collecting together to form a planet.

Figure 12: An Astronomy example.

Three contrasting tactics that CSO’s can engage in to meet their aims are
cally involves research and communication,
company’s operations or
(A) Non-violent direct action, Violent direct action, Indirect action, Boycott
(B) Indirect action, Instrumental action, Non-violent direct action, Information campaign
(C) Indirect action, Violent direct action, Non-violent direct-action Boycott.
(D) Non-violent direct action, Instrumental action, Indirect action, Information campaign

which typi-
, which may involve physically attacking a

, often involving some form of

.

Figure 13: A Business Ethics example.

How many attempts should you make to cannulate a patient before passing the job on to a senior
colleague?
(A) 4

(D) 1

(C) 2

(B) 3

Figure 14: A Clinical Knowledge example.

In a given population, 1 out of every 400 people has a cancer caused by a completely recessive
allele, b. Assuming the population is in Hardy-Weinberg equilibrium, which of the following is
the expected proportion of individuals who carry the b allele but are not expected to develop the
cancer?
(A) 1/400

(D) 38/400

(B) 19/400

(C) 20/400

Figure 15: A College Biology example.

Which of the following statements about the lanthanide elements is NOT true?
(A) The most common oxidation state for the lanthanide elements is +3.
(B) Lanthanide complexes often have high coordination numbers (> 6).
(C) All of the lanthanide elements react with aqueous acid to liberate hydrogen.
(D) The atomic radii of the lanthanide elements increase across the period from La to Lu.

Figure 16: A College Chemistry example.

14

Consider a computer design in which multiple processors, each with a private cache memory,
share global memory using a single bus. This bus is the critical system resource. Each processor
can execute one instruction every 500 nanoseconds as long as memory references are satisfied
by its local cache. When a cache miss occurs, the processor is delayed for an additional 2,000
nanoseconds. During half of this additional delay, the bus is dedicated to serving the cache miss.
During the other half, the processor cannot continue, but the bus is free to service requests from
other processors. On average, each instruction requires 2 memory references. On average, cache
misses occur on 1 percent of references. What proportion of the capacity of the bus would a single
processor consume, ignoring delays due to competition from other processors?
(D) 2/27
(A) 1/50

(C) 1/25

(B) 1/27

Figure 17: A College Computer Science example.

Let A be a real 2 × 2 matrix. Which of the following statements must be true?
I. All of the entries of A2 are nonnegative.
II. The determinant of A2 is nonnegative.
III. If A has two distinct eigenvalues, then A2 has two distinct eigenvalues.
(A) I only

(D) II and III only

(C) III only

(B) II only

Figure 18: A College Mathematics example.

In a genetic test of a newborn, a rare genetic disorder is found that has X-linked recessive
transmission. Which of the following statements is likely true regarding the pedigree of this
disorder?
(A) All descendants on the maternal side will have the disorder.
(B) Females will be approximately twice as affected as males in this family.
(C) All daughters of an affected male will be affected.
(D) There will be equal distribution of males and females affected.

Figure 19: A College Medicine example.

One end of a Nichrome wire of length 2L and cross-sectional area A is attached to an end of
another Nichrome wire of length L and cross- sectional area 2A. If the free end of the longer wire
is at an electric potential of 8.0 volts, and the free end of the shorter wire is at an electric potential
of 1.0 volt, the potential at the junction of the two wires is most nearly equal to
(A) 2.4 V
(B) 3.3 V
(C) 4.5 V
(D) 5.7 V

Figure 20: A College Physics example.

Why is it that anti-virus scanners would not have found an exploitation of Heartbleed?
(A) It’s a vacuous question: Heartbleed only reads outside a buffer, so there is no possible exploit
(B) Anti-virus scanners tend to look for viruses and other malicious
(C) Heartbleed attacks the anti-virus scanner itself
(D) Anti-virus scanners tend to look for viruses and other malicious code, but Heartbleed
exploits steal secrets without injecting any code

Figure 21: A Computer Security example.

A model airplane flies slower when flying into the wind and faster with wind at its back. When
launched at right angles to the wind, a cross wind, its groundspeed compared with flying in still
air is
(A) the same

(D) either greater or less depending on wind speed

(B) greater

(C) less

Figure 22: A Conceptual Physics example.

15

Consider the following AR(1) model with the disturbances having zero mean and unit variance
yt = 0.2 + 0.4yt−1 + ut
The (unconditional) mean of y will be given by
(C) 0.5
(A) 0.2

(D) 0.33

(B) 0.4

Figure 23: An Econometrics example.

A point pole has a strength of 4π × 10−4 weber. The force in newtons on a point pole of
4π × 1.5 × 10−4 weber placed at a distance of 10 cm from it will be
(A) 15 N.

(D) 3.75 N.

(C) 7.5 N.

(B) 20 N.

Figure 24: An Electrical Engineering example.

A total of 30 players will play basketball at a park. There will be exactly 5 players on each team.
Which statement correctly explains how to find the number of teams needed?
(A) Add 5 to 30 to find 35 teams.
(B) Divide 30 by 5 to find 6 teams.
(C) Multiply 30 and 5 to find 150 teams.
(D) Subtract 5 from 30 to find 25 teams.

Figure 25: An Elementary Mathematics example.

Determine whether the statements are logically equivalent or contradictory. If neither, determine
whether they are consistent or inconsistent.
E ⊃ (F · E) and ∼ E · F
(A) Logically equivalent
(B) Contradictory
(C) Neither logically equivalent nor contradictory, but consistent
(D) Inconsistent

Figure 26: A Formal Logic example.

As of 2017, how many of the world’s 1-year-old children today have been vaccinated against
some disease?
(A) 80%
(B) 60%
(C) 40%
(D) 20%

Figure 27: A Global Facts example.

Homologous structures are often cited as evidence for the process of natural selection. All of the
following are examples of homologous structures EXCEPT
(A) the wings of a bird and the wings of a bat
(B) the flippers of a whale and the arms of a man
(C) the pectoral fins of a porpoise and the flippers of a seal
(D) the forelegs of an insect and the forelimbs of a dog

Figure 28: A High School Biology example.

From the solubility rules, which of the following is true?
(A) All chlorides, bromides, and iodides are soluble
(B) All sulfates are soluble
(C) All hydroxides are soluble
(D) All ammonium-containing compounds are soluble

Figure 29: A High School Chemistry example.

16

A list of numbers has n elements, indexed from 1 to n. The following algorithm is intended to
display the number of elements in the list that have a value greater than 100. The algorithm uses
the variables count and position. Steps 3 and 4 are missing.
Step 1: Set count to 0 and position to 1.
Step 2: If the value of the element at index position is greater
than 100, increase the value of count by 1.
Step 3: (missing step)
Step 4: (missing step)
Step 5: Display the value of count.
Which of the following could be used to replace steps 3 and 4 so that the algorithm works as
intended?
(A) Step 3: Increase the value of position by 1.
Step 4: Repeat steps 2 and 3 until the value of count is greater than 100.
(B) Step 3: Increase the value of position by 1.
Step 4: Repeat steps 2 and 3 until t he value of position is greater than n.
(C) Step 3: Repeat step 2 until the value of count is greater than 100.
Step 4: Increase the value of position by 1.
(D) Step 3: Repeat step 2 until the value of position is greater than n.
Step 4: Increase the value of count by 1.

Figure 30: A High School Computer Science example.

This question refers to the following information.
Albeit the king’s Majesty justly and rightfully is and ought to be the supreme head of the Church
of England, and so is recognized by the clergy of this realm in their convocations, yet nevertheless,
for corroboration and confirmation thereof, and for increase of virtue in Christ’s religion within
this realm of England, and to repress and extirpate all errors, heresies, and other enormities and
abuses heretofore used in the same, be it enacted, by authority of this present Parliament, that the
king, our sovereign lord, his heirs and successors, kings of this realm, shall be taken, accepted,
and reputed the only supreme head in earth of the Church of England, called Anglicans Ecclesia;
and shall have and enjoy, annexed and united to the imperial crown of this realm, as well the
title and style thereof, as all honors, dignities, preeminences, jurisdictions, privileges, authorities,
immunities, profits, and commodities to the said dignity of the supreme head of the same Church
belonging and appertaining; and that our said sovereign lord, his heirs and successors, kings of
this realm, shall have full power and authority from time to time to visit, repress, redress, record,
order, correct, restrain, and amend all such errors, heresies, abuses, offenses, contempts, and
enormities, whatsoever they be, which by any manner of spiritual authority or jurisdiction ought
or may lawfully be reformed, repressed, ordered, redressed, corrected, restrained, or amended,
most to the pleasure of Almighty God, the increase of virtue in Christ’s religion, and for the
conservation of the peace, unity, and tranquility of this realm; any usage, foreign land, foreign
authority, prescription, or any other thing or things to the contrary hereof notwithstanding.
English Parliament, Act of Supremacy, 1534
From the passage, one may infer that the English Parliament wished to argue that the Act of
Supremacy would
(A) give the English king a new position of authority
(B) give the position of head of the Church of England to Henry VIII alone and exclude his heirs
(C) establish Calvinism as the one true theology in England
(D) end various forms of corruption plaguing the Church in England

Figure 31: A High School European History example.

During the third stage of the demographic transition model, which of the following is true?
(A) Birth rates increase and population growth rate is less rapid.
(B) Birth rates decline and population growth rate is less rapid.
(C) Birth rates increase and population growth rate increases.
(D) Birth rates decrease and population growth rate increases.

Figure 32: A High School Geography example.

17

Which of the following best states an argument made by James Madison in The Federalist number
10?
(A) Honest politicians can prevent factions from developing.
(B) Factions are more likely to occur in large republics than in small ones.
(C) The negative effects of factionalism can be reduced by a republican government.
(D) Free elections are the people’s best defense against factionalism.

Figure 33: A High School Government and Politics example.

Which of the following is not included in the U.S. GDP?
(A) The U.S. military opens a new base in a foreign country with 1000 U.S. personnel.
(B) Japanese consumers buy thousands of CDs produced in the United States.
(C) An American pop singer performs a sold-out concert in Paris.
(D) A French theatrical production tours dozens of American cities.

Figure 34: A High School Macroeconomics example.

Joe was in charge of lights for a dance. The red light blinks every two seconds, the yellow light
every three seconds, and the blue light every five seconds. If we include the very beginning and
very end of the dance, how many times during a seven minute dance will all the lights come on at
the same time? (Assume that all three lights blink simultaneously at the very beginning of the
dance.)
(A) 3
(B) 15
(C) 6
(D) 5

Figure 35: A High School Mathematics example.

If the government subsidizes producers in a perfectly competitive market, then
(A) the demand for the product will increase
(B) the demand for the product will decrease
(C) the consumer surplus will increase
(D) the consumer surplus will decrease

Figure 36: A High School Microeconomics example.

A point charge, Q = +1 mC, is fixed at the origin. How much work is required to move a charge,
Q = +8 µC, from the point (0, 4 meters) to the point (3 meters, 0)?
(A) 3.5 J
(B) 6.0 J
(C) 22.5 J
(D) 40 J

Figure 37: A High School Physics example.

While swimming in the ocean, Ivan is frightened by a dark shadow in the water even before he
has the chance to identify what the shadow is. The synaptic connections taking place during this
incident of fright are best described by which of the following?
(A) Messages are sent from the thalamus directly to the amygdala.
(B) Messages are sent from the thalamus to the “what” and “where” pathways.
(C) Messages are sent from the parasympathetic nervous system to the cerebral cortex.
(D) Messages are sent from the frontal lobes to the pituitary gland.

Figure 38: A High School Psychology example.

18

Jonathan obtained a score of 80 on a statistics exam, placing him at the 90th percentile. Suppose
five points are added to everyone’s score. Jonathan’s new score will be at the
(A) 80th percentile.
(B) 85th percentile.
(C) 90th percentile.
(D) 95th percentile.

Figure 39: A High School Statistics example.

This question refers to the following information.
“Society in every state is a blessing, but government even in its best state is but a necessary evil; in
its worst state an intolerable one; for when we suffer, or are exposed to the same miseries by a
government, which we might expect in a country without government, our calamity is heightened
by reflecting that we furnish the means by which we suffer. Government, like dress, is the badge
of lost innocence; the palaces of kings are built on the ruins of the bowers of paradise. For were
the impulses of conscience clear, uniform, and irresistibly obeyed, man would need no other
lawgiver; but that not being the case, he finds it necessary to surrender up a part of his property to
furnish means for the protection of the rest; and this he is induced to do by the same prudence
which in every other case advises him out of two evils to choose the least. Wherefore, security
being the true design and end of government, it unanswerably follows that whatever form thereof
appears most likely to ensure it to us, with the least expense and greatest benefit, is preferable to
all others.”
Thomas Paine, Common Sense, 1776
Which of the following “miseries” alluded to above were most condemned by Anti-Federalists of
the post-Revolutionary era?
(A) Organized response to Bacon’s Rebellion.
(B) Federal response to Shays’s Rebellion.
(C) Federal response to the Whiskey Rebellion.
(D) Federal response to Pontiac’s Rebellion.

Figure 40: A High School US History example.

All other things being equal, which of the following persons is more likely to show osteoporosis?
(A) An older Hispanic American woman
(B) An older African American woman
(C) An older Asian American woman
(D) An older Native American woman

Figure 41: A Human Aging example.

Morning sickness is typically a problem:
(A) during the first trimester
(B) during the second trimester
(C) during the third trimester
(D) all through the pregnancy

Figure 42: A Human Sexuality example.

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Would a reservation to the definition of torture in the ICCPR be acceptable in contemporary
practice?
(A) This is an acceptable reservation if the reserving country’s legislation employs a different
definition
(B) This is an unacceptable reservation because it contravenes the object and purpose of
the ICCPR
(C) This is an unacceptable reservation because the definition of torture in the ICCPR is consistent
with customary international law
(D) This is an acceptable reservation because under general international law States have the right
to enter reservations to treaties

Figure 43: An International Law example.

Which position does Rawls claim is the least likely to be adopted by the POP (people in the
original position)?
(A) The POP would choose equality above liberty.
(B) The POP would opt for the ‘maximin’ strategy.
(C) The POP would opt for the ‘difference principle.’
(D) The POP would reject the ‘system of natural liberty.’

Figure 44: A Jurisprudence example.

John Stuart Mill: Each person’s happiness is a good to that person, and the general happiness,
therefore, a good to the aggregate of all persons.
(A) Fallacy of Composition
(B) Fallacy of Division
(C) Gambler’s Fallacy
(D) Equivocation

Figure 45: A Logical Fallacies example.

A 6-sided die is rolled 15 times and the results are: side 1 comes up 0 times; side 2: 1 time; side
3: 2 times; side 4: 3 times; side 5: 4 times; side 6: 5 times. Based on these results, what is the
probability of side 3 coming up when using Add-1 Smoothing?
(A) 2/15

(C) 3/16

(D) 1/5

(B) 1/7

Figure 46: A Machine Learning example.

According to Lewin, Lippet and White’s 1939 experiment, which form of leadership produced the
most work from participants?
(A) Laissez-faire
(B) Democratic
(C) Authoritarian
(D) A mix of laissez-faire and democratic

Figure 47: A Management example.

The single group within society that is most vulnerable to reference group influence is:
(A) The older consumer who feels somewhat left out of things.
(B) The married women, many of whom feel a need for stability in their lives.
(C) New immigrants who really want to assimilate into their new culture.
(D) Children, who base most of their buying decisions on outside influences.

Figure 48: A Marketing example.

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Which of the following conditions does not show multifactorial inheritance?
(A) Pyloric stenosis
(B) Schizophrenia
(C) Spina bifida (neural tube defects)
(D) Marfan syndrome

Figure 49: A Medical Genetics example.

If each of the following meals provides the same number of calories, which meal requires the
most land to produce the food?
(A) Red beans and rice
(B) Steak and a baked potato
(C) Corn tortilla and refried beans
(D) Lentil soup and brown bread

Figure 50: A Miscellaneous example.

In response to Sandel’s “social justice” argument, Kamm argues that
(A) even if we were able to enhance ourselves or others, we would not thereby be obligated to do
so.
(B) there is a difference between (i) choosing that one have a certain trait and (ii) being responsible
for bearing the costs of that choice.
(C) having the option to enhance will lead to fewer instances of people who require the assistance
of others.
(D) all of the above

Figure 51: A Moral Disputes example.

In response to Sandel’s “social justice” argument, Kamm argues that
(A) even if we were able to enhance ourselves or others, we would not thereby be obligated to do
so.
(B) there is a difference between (i) choosing that one have a certain trait and (ii) being responsible
for bearing the costs of that choice.
(C) having the option to enhance will lead to fewer instances of people who require the assistance
of others.
(D) all of the above

Figure 52: A Moral Disputes example.

For which of these two scenarios does the main character (who uses I/me/my) do something
clearly morally wrong?
Scenario 1 | I drive very fast when I’m on a racetrack.
Scenario 2 | I drive very fast when I’m in the suburbs.
(A) Wrong, Wrong
(B) Wrong, Not wrong
(C) Not wrong, Wrong
(D) Not wrong, Not wrong

Figure 53: A Moral Scenarios example.

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Which of the following is the most plausible explanation for the protective effect of dietary fibre
against cancer of the colon?
(A) Propionic acid, formed during colonic fibre fermentation inhibits liver fatty acid synthesis
(B) Butyric acid, formed during colonic fibre fermentation stimulates "silencing" of the SLC5A8
tumour suppressor gene
(C) Butyric acid, formed during colonic fibre fermentation stimulates anti-oxidant defences
in the colon
(D) None of these options are correct

Figure 54: A Nutrition example.

According to Moore’s “ideal utilitarianism,” the right action is the one that brings about the
greatest amount of:
(A) pleasure.
(B) happiness.
(C) good.
(D) virtue.

Figure 55: A Philosophy example.

Researchers now believe that the decline of the Maya was caused chiefly by:
(A) a cataclysm of some kind, such as an earthquake, volcano, or tsunami.
(B) ecological degradation resulting from slash-and-burn farming techniques.
(C) endless wars between neighboring Mayan city-states.
(D) practices of interbreeding that led to a steep rise in congenital disorders.

Figure 56: A Prehistory example.

Krete is an unmarried taxpayer with income exclusively from wages. By December 31, year 1,
Krete’s employer has withheld $16,000 in federal income taxes and Krete has made no estimated
tax payments. On April 15, year 2, Krete timely filed for an extension request to file her individual
tax return, and paid $300 of additional taxes. Krete’s year 1 tax liability was $16,500 when she
timely filed her return on April 30, year 2, and paid the remaining tax liability balance. What
amount would be subject to the penalty for underpayment of estimated taxes?
(A) $0
(B) $500
(C) $1,650
(D) $16,500

Figure 57: A Professional Accounting example.

The night before his bar examination, the examinee’s next-door neighbor was having a party. The
music from the neighbor’s home was so loud that the examinee couldn’t fall asleep. The examinee
called the neighbor and asked her to please keep the noise down. The neighbor then abruptly hung
up. Angered, the examinee went into his closet and got a gun. He went outside and fired a bullet
through the neighbor’s living room window. Not intending to shoot anyone, the examinee fired
his gun at such an angle that the bullet would hit the ceiling. He merely wanted to cause some
damage to the neighbor’s home to relieve his angry rage. The bullet, however, ricocheted off the
ceiling and struck a partygoer in the back, killing him. The jurisdiction makes it a misdemeanor
to discharge a firearm in public. The examinee will most likely be found guilty for which of the
following crimes in connection to the death of the partygoer?
(A) Murder.
(B) Involuntary manslaughter.
(C) Voluntary manslaughter.
(D) Discharge of a firearm in public.

Figure 58: A Professional Law example.

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A 63-year-old man is brought to the emergency department because of a 4-day history of in-
creasingly severe left leg pain and swelling of his left calf. He also has a 1-month history of
increasingly severe upper midthoracic back pain. During this time, he has had a 9-kg (20-lb)
weight loss despite no change in appetite. He has no history of major medical illness. His only
medication is ibuprofen. He is 180 cm (5 ft 11 in) tall and weighs 82 kg (180 lb); BMI is 25
kg/m2 . His vital signs are within normal limits. On examination, lower extremity pulses are
palpable bilaterally. The remainder of the physical examination shows no abnormalities. An x-ray
of the thoracic spine shows no abnormalities. A CT scan of the abdomen shows a 3-cm mass in
the body of the pancreas; there are liver metastases and encasement of the superior mesenteric
artery. Ultrasonography of the left lower extremity shows a femoropopliteal venous clot. Which
of the following is the most likely cause of this patient’s symptoms?
(A) Carcinoid syndrome
(B) Hypercoagulability from advanced malignancy
(C) Multiple endocrine neoplasia
(D) Splenic artery aneurysm and embolic disease of the left lower extremity

Figure 59: A Professional Medicine example.

The technique that is most likely to produce an immediate improvement in the behavior of a child
who hits others and rips up schoolbooks is
(A) a combination of reinforcement for appropriate behavior and mild punishment for in-
appropriate behavior
(B) differential positive reinforcement
(C) loss of privileges for misbehaving
(D) shaping

Figure 60: A Professional Psychology example.

You work for a utility company that is building a biomass plant in the community. Your employer
asks you to give a series of community talks about the plant and future operations. You visit the
plant several hours before you are due to give a speech that has been prepared by your immediate
supervisor. During the tour of the plant, you discover several claims in the speech are not true.
What do you do?
(A) Write and deliver a new speech that you know is entirely correct.
(B) Cancel all speeches until you and your supervisor can get the information straight.
(C) Deliver the speech as prepared and discuss the inaccuracies with your supervisor afterward.
(D) Address the inaccuracies with your supervisor immediately and make the necessary
corrections before giving the speech.

Figure 61: A Public Relations example.

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The Chemical Weapons Convention (CWC) prohibited the possession or deployment of chemical
weapons; however it failed to implement stipulations that would require signatories to declare their
existing stocks of chemical weapons, to identify facilities that were once involved in chemical
production, or to announce when their existing stocks would be destroyed.
(A) The Chemical Weapons Convention (CWC) prohibited the possession or deployment of
chemical weapons; however it failed to implement stipulations that would require signatories to
declare their existing stocks of chemical weapons, to identify facilities that were once involved in
chemical production, or to announce when their existing stocks would be destroyed.
(B) The CWC made some important developments regarding the use and possession of chemical
weapons and the destruction of existing stockpiles. However, the treaty failed to establish an
independent body empowered with the capacity to check treaty compliance. Lack of supra-state
authority has undermined the ability to enforce those developments. Given the anarchical nature
of international society it may be in the national security interest to retain stocks.
(C) Chemical weapons continue to exert a determining influence on international society. As early
as the 1970s military strategists were convinced of the deterrence effects chemical weapons could
have, comparable to the second strike survival logic of nuclear deterrence. The preferences of
strategists resulted in continued manufacture and stockpiling of weapons creating an international
crisis of stability.
(D) While the CWC has been ratified by the majority of international society, some nations
with a large chemical capability at their disposal have yet to enter into the treaty. However,
to some analysts the destructive military potential would be limited, having a moderate
effect on a well-equipped army in conventional warfare. Chemical arsenal essentially falls
under the category of the "poor mans" weaponry, being simplistic and inexpensive whilst
having limited military utility. However, the concern remains of the prospective impact a
terrorist chemical attack could have on civilian populations.

Figure 62: A Security Studies example.

Which of the following statements most closely corresponds with differential association theory?
(A) If all of your friends jumped off a bridge, I suppose you would too.
(B) You should be proud to be a part of this organization.
(C) If the door is closed, try the window.
(D) Once a thief, always a thief.

Figure 63: A Sociology example.

Which of the following statements most closely corresponds with differential association theory?
(A) If all of your friends jumped off a bridge, I suppose you would too.
(B) You should be proud to be a part of this organization.
(C) If the door is closed, try the window.
(D) Once a thief, always a thief.

Figure 64: A Sociology example.

Why did Congress oppose Wilson’s proposal for the League of Nations?
(A) It feared the League would encourage Soviet influence in the US
(B) It feared the League would be anti-democratic
(C) It feared the League would commit the US to an international alliance
(D) Both a and b

Figure 65: A US Foreign Policy example.

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An observational study in diabetics assesses the role of an increased plasma fibrinogen level on
the risk of cardiac events. 130 diabetic patients are followed for 5 years to assess the development
of acute coronary syndrome. In the group of 60 patients with a normal baseline plasma fibrinogen
level, 20 develop acute coronary syndrome and 40 do not. In the group of 70 patients with a high
baseline plasma fibrinogen level, 40 develop acute coronary syndrome and 30 do not. Which of
the following is the best estimate of relative risk in patients with a high baseline plasma fibrinogen
level compared to patients with a normal baseline plasma fibrinogen level?
(A) (40/30)/(20/40)
(B) (40*40)/(20*30)
(C) (40*70)/(20*60)
(D) (40/70)/(20/60)

Figure 66: A Virology example.

The Great Cloud Sutra prophesied the imminent arrival of which person?
(A) Maitreya (Milo)
(B) The Buddha
(C) Zhou Dunyi
(D) Wang Yangming

Figure 67: A World Religions example.

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