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Register now## Mathematical Reasoning

As a regular element of their routine all pilots encounter situations or tasks that have a mathematical background. Basic arithmetics, cross multiplication strategies, simple geometry and rudimental trigonometry are the most frequent mathematical operations applied. Although most calculations are performed by a computer there are three main reasons why a professional pilot should have at least a basic command of maths: Firstly, pilots input data into computers which involves a risk for human error. In this case, an error may only be detected if the pilot has a rough idea of what the correct answer should be. Secondly, if the computer malfunctions it is good to have a pilot on board who understands how to calculate at least very basic tasks.

Thirdly, solving mathematical tasks involves psychological concepts that are - additional to ‘pure mathematical skills' - positive predictors of job success:

**Reading Comprehension:** Although the level of English language used in the tasks is not especially high familiarity with the English language is a prerequisite to understand the problems. **Attention Control:** Attention is the cognitive process of selectively concentrating on one aspect of the environment (for example the mathematical problem) while ignoring other things such as noise or irrelevant visual features of the room.

**Number Facility:** The ability to efficiently apply basic mathematical operations: addition, subtraction, multiplication and division.

**Working Memory:** Sometimes labelled short-term memory is the ability to remember information over a brief period of time and actively deal with it. During a mathematical task the working memory span determines how well we remember the information we have just read or intermediate results. Furthermore the integration of information from the Long Term Memory is carried out by this mental instance.

**Long Term Memory:** While working on a mathematical problem this kind of memory function refers to the reliable and accessible storage of information from school days or previous training.

**Reasoning:** Sometimes labelled fluid intelligence means applying logic and analytical thinking. Reasoning also includes separating relevant from irrelevant information and drawing correct conclusions; identifying similarities between new problems and familiar concepts; and transferring adequately established solution strategies to new problems.**Stress Resistance:** The ability to solve problems under disadvantageous or even threatening conditions. During the maths assessment these conditions are mainly time pressure and the awareness that mistakes may have severe negative consequences.**Short Term Motivation:** The ambition to find the correct approach even when the task is difficult. The tenacity to not give up when being faced with a problem that is difficult to solve right away.**Long Term Motivation:** We may also call this Achievement Motivation: The drive to analyze the outcomes of the trial runs for mistakes. The energy to invest time and effort during several days or even weeks to research how to solve the tasks that you have answered incorrectly before. The willingness to sacrifice leisure time for studying and training. The ambition to improve not only poor results of a trial run but even good ones and aim at 100%. The strength/seriousness of your interest in joining the organisation asking you to do this test.

**Further important information and recommendations: **

- In the supervised test run test takers will be allowed to use scratch paper but no calculator. Scratch paper will be provided by the test administrator and collected afterwards.
- We recommend performing the unsupervised training runs under test-like conditions, i.e. set aside the required testing time and ask the persons around you not to interrupt you during your training. Clear your table of everything except paper and pencil.
- Some items have a multiple-choice design with exactly one correct answer that has to be selected using the mouse. Most items however are in free-answer design i.e. they require short typed responses. This method is preferred because it represents a more realistic simulation of problem solving situations in the cockpit.
- As a decimal marker we use the dot on the line (.) not a comma (,). For example, your solution is one and a half kilometer, you enter 1.5
- For numbers less than one, a zero is written before the decimal marker. For example, 0.25 is the correct form, not .25
- No separator symbols are used to separate thousands from hundreds or millions from thousands. For example: Enter the number 'one million twenty thousand six hundred and thirty-nine' as '1020639'. Examples for incorrect entries are '1,020,639' or '1 020 639'
- Enter your solution as a number only without any units or other extra text. If your solution is 1500 meters type '1500'. Examples for incorrect entries are '1500 meters' or '1500m'.
- Read each problem carefully and identify the relevant information. Similar to real life, irrelevant information may also be presented!
- As easy and difficult items are randomly ordered, a higher total score may be achieved if you skip items that seem difficult and time consuming. Go back to these items after you have completed the easier items. An overview function allows you to identify and directly go to unanswered items.
- To control the advantage of guessing answers in a multiple-choice design, a special scoring system is used. Selecting the correct answer results in the score of '1 point'. Whereas, selecting the wrong answer out of six given options leads to a deduction of one fifth of a point (-0.20). Selecting the wrong answer out of five given options leads to a deduction one quarter of a point (-0.25). Selecting the wrong answer out of four given options leads to a deduction of one third of a point (-0.33), and so on. In a formula the value of the deduction equals one divided by the number of false options. This application of negative scores for a wrong answer is limited to multiple-choice items. Therefore even if you are unsure of the answer, it is recommended that you make an attempt for free-answer items as incorrect answers do not lead to a deduction. In multiple-choice items however, think carefully before guessing.
- Many items with a free-answer design include a tolerance range. If your answer is within that range, you earn half a score. The width of the tolerance range is indicated either as an absolute number or as a percentage at the end of the item by the code 'TRHS' (Tolerance Range for Half Score). Examples are 'TRHS 200' or 'TRHS ten percent'. This means if your answer is not exactly correct but within a range of plus or minus 200 around the correct solution (or plus minus ten percent as in the second example) you still earn half a point. Answers that are outside the TRHS will not lead to a negative score but simply count as zero, similar to omitting an answer. Therefore, as mentioned previously, venturing a good guess in a free-answer item instead of not answering at all may result in a high total score.
- You do NOT get extra credit for finishing before the time allowance has run out.