How the app chooses each question, and the research behind it. Where something is our own choice rather than an established finding, we say so.
Trying to recall a fact strengthens your memory of it more than reading it again. Psychologists call this retrieval practice, or the testing effect. In one well-known study, students who read a passage once and then took three recall tests remembered more of it a week later than students who read it four times.
In the app: everything is a question. You still need to read the handbook, but most of your study time goes on recall.
The psychologist Lev Vygotsky described a "zone of proximal development": the gap between what a learner can already do and what they cannot do yet. Learning is quickest inside that gap. A related idea, "desirable difficulty", holds that practice which feels a little hard produces stronger memories than practice which feels easy.
A 2019 study in Nature Communications found that, for a class of simple learning algorithms, training is fastest when about 85% of answers are right. That work was mostly theoretical, not a study of people revising for a citizenship test.
In the app: each question is one you have about a 70% predicted chance of getting right. The exact figure is our choice. It is lower than 85% partly because a multiple-choice question can be answered correctly by guessing, and the prediction includes that chance.
Memories fade quickly at first and then more slowly, a pattern first measured by Hermann Ebbinghaus in the 1880s. Reviewing a fact just as it starts to fade, with longer gaps each time, keeps it for far less effort than cramming. A review of more than 300 experiments found the benefit of spacing to be large and reliable.
In the app: a question you get wrong returns four questions later; if you miss it again, the gap doubles to 8, then 16. One you get right returns after about 2, then 5, then 12 days. Each question has its own memory estimate, which fades between reviews.
Practising different kinds of problem in a shuffled order, rather than in blocks, tends to improve learning, although it feels harder at the time. This is called interleaving.
In the app: questions come from all 12 topics, mixed together, and topics you have seen least come up more often. The real test is mixed too.
To predict your chance on each question, the app keeps three kinds of estimate: an overall level, a level for each topic and a memory for each question. Every answer updates them, in the way that chess ratings move after each game. Adaptive learning systems commonly use this approach, known as the Elo rating system. The fading memory for each question is similar in spirit to the model Duolingo published in 2016.
Your chance of passing comes from thousands of simulated 24-question tests, drawn from the whole question bank and marked using the app's predictions.
We set the starting difficulty of each question by hand, and the model's settings have not yet been tuned on real learners. Treat the pass estimate as a guide, not a guarantee. It becomes more reliable as you answer more questions in every topic.