College of Policing National Sift / Online Assessment Process Numerical, Verbal and Logical Reasoning Syllabus

Numerical, Verbal and Logical Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Numerical, Verbal and Logical Reasoning in College of Policing National Sift / Online Assessment Process, not a summary of it.

1. 1

   Numerical Reasoning Fundamentals

   4 topics

   • Core arithmetic for policing contexts
     • Percentages, ratios and proportions
     • Averages and rates
   • Interpreting tables, charts and graphs
     • Crime statistics and incident data
   • Working with time, distance and speed
   • Estimation and sense-checking answers
2. 2

   Verbal Reasoning and Comprehension

   4 topics

   • True / False / Cannot Say judgements
     • Distinguishing inference from assumption
   • Critical reading of statements and reports
   • Vocabulary, meaning and precision
   • Identifying logical flaws in arguments
3. 3

   Logical and Abstract Reasoning

   4 topics

   • Pattern and sequence recognition
   • Deductive reasoning from rules
     • Drawing valid conclusions
   • Spatial and diagrammatic logic
   • Speed and accuracy under timed conditions
4. 4

   Test Technique and Preparation

   4 topics

   • Practising under realistic timing
   • Managing test anxiety
   • Avoiding common careless errors
   • Using elimination strategically

Numerical, Verbal and Logical Reasoning flashcards for College of Policing National Sift / Online Assessment Process

21 of 51 cards from the Numerical, Verbal and Logical Reasoning deck — real questions with worked answers.

1. What is the formula for calculating a percentage of a quantity, e.g. finding $p\%$ of $N$?

   $\frac{p}{100} \times N$. For example, $15\%$ of $240 = \frac{15}{100} \times 240 = 36$.

2. How do you calculate the percentage change between an old value and a new value?

   $\text{Percentage change} = \frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$. A positive result is an increase, a negative result is a decrease.

3. In a policing context, how do you convert a ratio such as 3:5 into a fraction of the total?

   Add the parts ($3 + 5 = 8$) to get the total, then each part is a fraction of the whole: $\frac{3}{8}$ and $\frac{5}{8}$. Multiply by the total quantity to find actual numbers.

4. What is the formula linking distance, speed and time?

   $\text{Distance} = \text{Speed} \times \text{Time}$. Rearranged: $\text{Speed} = \frac{\text{Distance}}{\text{Time}}$ and $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$.

5. A patrol car travels $90$ miles in $1.5$ hours. What is its average speed?

   $\text{Speed} = \frac{\text{Distance}}{\text{Time}} = \frac{90}{1.5} = 60$ mph.

6. How do you convert a time given in minutes into a fraction of an hour for speed calculations?

   Divide the minutes by $60$. For example, $45$ minutes $= \frac{45}{60} = 0.75$ hours, and $20$ minutes $= \frac{20}{60} \approx 0.33$ hours.

7. What is the quickest mental method to find $10\%$, $5\%$ and $1\%$ of a number?

   $10\%$ = divide by $10$ (move the decimal one place left); $5\%$ = half of $10\%$; $1\%$ = divide by $100$. Combine these to build other percentages (e.g. $15\% = 10\% + 5\%$).

8. How do you calculate an average (arithmetic mean) of a set of values?

   $\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$. For example, the mean of $4, 6, 8, 10$ is $\frac{28}{4} = 7$.

9. What is the difference between the mean, median and mode?

   Mean = sum divided by count (the average). Median = the middle value when data is ordered. Mode = the most frequently occurring value.

10. When reading a data table to answer a question, what should you check first before doing any calculation?

    Check the row and column headings, the units (e.g. thousands, %, £), and any footnotes or totals, so you extract the correct figure and operate on the right basis.

11. On a pie chart, how do you convert a sector's angle into a quantity?

    A sector's fraction of the whole is $\frac{\text{angle}}{360^{\circ}}$. Multiply that fraction by the total quantity. For example, a $90^{\circ}$ sector of $400$ incidents = $\frac{90}{360} \times 400 = 100$.

12. What is the key difference between a bar chart and a histogram when interpreting data?

    A bar chart compares separate (categorical) groups with gaps between bars; a histogram shows the distribution of continuous data across intervals with no gaps, where bar area (not just height) represents frequency.

13. In estimation, what is 'rounding to sense-check' and why is it useful?

    Rounding each number to a convenient value (e.g. nearest $10$ or $100$) to get an approximate answer quickly, then confirming your exact calculation lands near that estimate. It catches gross errors and misplaced decimal points.

14. How can you sense-check whether a calculated percentage answer is reasonable?

    Compare it to known anchors: an answer over $100\%$ of an original whole is suspect unless growth is expected; $50\%$ should be about half; if the part is clearly small but the percentage is large, recheck which number is the base.

15. In a True / False / Cannot Say question, what does 'True' specifically mean?

    The statement logically follows from, or is directly supported by, the information given in the passage. You must rely only on the passage, not outside knowledge.

16. In a True / False / Cannot Say question, what does 'False' mean?

    The statement directly contradicts the information in the passage, or the passage provides enough information to show the statement cannot be true.

17. In a True / False / Cannot Say question, what does 'Cannot Say' mean?

    The passage does not provide enough information to determine whether the statement is true or false. You cannot use assumptions, general knowledge or inference beyond what is stated.

18. What is the single most important rule when answering True / False / Cannot Say items?

    Base your answer ONLY on the information in the passage, never on prior or outside knowledge, even if you personally know the real-world answer differs.

19. Why is 'Cannot Say' often the trap answer people get wrong?

    Candidates over-infer: they treat a likely or commonsense conclusion as 'True', when the passage gives no explicit support. If the passage does not state or directly imply it, the correct answer is 'Cannot Say'.

20. In critical reading, what is the difference between a fact and an inference?

    A fact is explicitly stated in the text; an inference is a conclusion you draw from combining stated facts. Valid inferences must be necessarily supported, not merely plausible.

21. What is the difference between a necessary condition and a sufficient condition in deductive reasoning?

    A sufficient condition guarantees the outcome (if A then B). A necessary condition is required for the outcome but does not alone guarantee it. 'A is necessary for B' means B cannot occur without A.

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