Police Initial Recruitment Test (PIRT/SEARCH) Numerical Reasoning and Work-Based Numeracy Flashcards

24 sample cards from the Numerical Reasoning and Work-Based Numeracy deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

1. A clearance rate rises from $20\%$ to $25\%$. State both the percentage-point increase and the percentage increase.

   Percentage-point increase $= 25 - 20 = 5$ percentage points. Percentage increase $= \frac{5}{20} \times 100 = 25\%$.

2. How do you convert from the 12-hour clock to the 24-hour clock, e.g. 3:45 pm?

   For pm times (except 12 pm) add 12 to the hour: 3:45 pm becomes 15:45. Times after midnight (12 am) become 00:xx, and morning times stay the same (e.g. 9:00 am = 09:00).

3. How do you calculate the duration of a shift from 22:00 to 06:00?

   Count to midnight then onward: 22:00 to 24:00 is 2 hours, plus 00:00 to 06:00 is 6 hours, giving a total of 8 hours.

4. When adding times, why can't you treat minutes like ordinary decimals?

   Because there are 60 minutes in an hour, not 100. When minutes exceed 60 you carry 1 hour and subtract 60. E.g. 1 h 45 min + 1 h 30 min = 2 h 75 min = 3 h 15 min.

5. State the speed-distance-time formula and its two rearrangements.

   $$\text{speed} = \frac{\text{distance}}{\text{time}}, \quad \text{distance} = \text{speed} \times \text{time}, \quad \text{time} = \frac{\text{distance}}{\text{speed}}$$

6. A patrol car travels 90 miles in 2 hours. What is its average speed?

   $\text{speed} = \frac{90}{2} = 45$ mph.

7. How long does it take to travel 150 miles at 50 mph?

   $\text{time} = \frac{\text{distance}}{\text{speed}} = \frac{150}{50} = 3$ hours.

8. How do you convert a time of 1 hour 30 minutes into hours for use in a speed calculation?

   Convert minutes to a fraction of an hour: 30 minutes $= \frac{30}{60} = 0.5$ h, so 1 hour 30 minutes $= 1.5$ hours.

9. List the key metric length conversions a candidate should memorize.

   $1$ cm $= 10$ mm; $1$ m $= 100$ cm $= 1000$ mm; $1$ km $= 1000$ m.

10. State the key metric mass and volume conversions to memorize.

    Mass: $1$ kg $= 1000$ g; $1$ tonne $= 1000$ kg. Volume: $1$ litre $= 1000$ ml; $1$ litre $= 100$ cl.

11. When converting from a larger unit to a smaller unit (e.g. km to m), do you multiply or divide?

    Multiply, because there are more of the smaller units. E.g. $3$ km $= 3 \times 1000 = 3000$ m. Converting smaller to larger means dividing.

12. A map has a scale of $1:50{,}000$. What real distance does $4$ cm on the map represent?

    $4$ cm $\times 50{,}000 = 200{,}000$ cm $= 2000$ m $= 2$ km.

13. On a $1:25{,}000$ map, how do you find the map distance for a real distance of $5$ km?

    Convert $5$ km to cm: $5 \times 100{,}000 = 500{,}000$ cm. Divide by the scale factor: $\frac{500{,}000}{25{,}000} = 20$ cm on the map.

14. What does a map scale of $1:50{,}000$ literally mean?

    One unit of length on the map represents $50{,}000$ of the same units in reality (e.g. 1 cm on the map = 50,000 cm = 500 m on the ground).

15. When reading a data table, what are the first things you should check before extracting a number?

    Check the row and column headings, the units stated (and any '000s' or 'millions' multipliers), and any footnotes, so you read the correct cell with the correct scale.

16. How do you read a value from a line or bar chart accurately?

    Trace from the data point straight to the relevant axis, read off against the axis scale (noting the size of each gridline interval and the units), and never assume the scale starts at zero.

17. Define the mean, median and mode.

    Mean: the sum of all values divided by how many values there are. Median: the middle value when the data are placed in order. Mode: the value that occurs most frequently.

18. Find the mean of $4, 8, 6, 10, 2$.

    $\text{mean} = \frac{4+8+6+10+2}{5} = \frac{30}{5} = 6$.

19. How do you find the median of an even-numbered data set, e.g. $3, 5, 8, 12$?

    Order the data, then take the mean of the two middle values: $\frac{5+8}{2} = 6.5$.

20. Define the range of a data set and calculate it for $12, 7, 20, 5$.

    The range is the largest value minus the smallest value: $20 - 5 = 15$.

21. In multi-source data synthesis questions, what is the key skill being tested?

    Combining information from two or more tables/charts (e.g. a rate from one and a total from another) in the correct sequence to answer a single question, while keeping units consistent.

22. Name three common ways figures can be presented misleadingly in charts.

    A truncated vertical axis that doesn't start at zero (exaggerating differences); inconsistent or non-linear axis scales; and using percentages without the underlying totals (a large % of a tiny base can be a tiny number).

23. What is a sensible time-allocation strategy when a numerical test has, say, 25 questions in 12 minutes?

    Divide total time by questions to get an average per question ($\frac{12 \times 60}{25} \approx 29$ seconds each), keep moving, and never let one hard question consume time owed to several easier ones.

24. Describe the estimation-and-elimination technique for multiple-choice numerical questions.

    Round numbers to estimate the approximate answer, then eliminate options that are clearly too large or too small, often leaving only one plausible choice without full calculation. Useful for saving time under the no-calculator constraint.

What this deck covers

Numerical Reasoning and Work-Based Numeracy flashcards FAQ