Aptitude skill lesson
Map and route reasoning: skill lesson
Map and route reasoning is spatial thinking with a clock attached: bearings and turns, map scale, grid references, and the journey-time arithmetic that decides whether a route is feasible at all. It appears in police, fire and ambulance selection, driver and dispatch testing, military navigation batteries, and any logistics or field-service role where a wrong turn is a missed window. The items are rarely hard mathematically; they are lost by rotating the map instead of the number, by averaging two speeds, or by adding a walking leg to the wrong end of a connection. Your practice attempts are stored on this device and go nowhere unless you export them.
Published · last reviewed
Applies to Novus Learn 0.1.0
What changed, and when
- , Replaced the body of all 27 non-judgement lessons with construct-specific material: six worked examples each, carrying the actual arithmetic, the actual inference or the actual procedure, plus expanded objectives, practice tips and glossary. Every 'Related Learn topics' link now points at a real page on this site rather than a generic search. The eight workplace-judgement lessons are unchanged.
- , Rebuilt the lesson page around a sticky contents rail, per-section links, previous/next lesson navigation, and two graded checkpoints drawn from the open practice bank.
- , Repaired the aptitude integrations behind the lessons so each one links to skill-specific practice instead of the unscoped fixture engine.
- , Published one lesson for each of the 35 aptitude skill constructs: objectives, worked examples, practice tips, glossary, Learn topic links, and sources.
These 35 skill lessons are authored and revised as one set, so they share one revision history rather than 35 identical dates.
Objectives
Copy link- Convert any facing into degrees clockwise from north, apply a sequence of left and right turns arithmetically, and convert the result back to a compass point.
- Compute a back bearing and use it to check that an out-and-return leg is consistent.
- Convert map distance to ground distance from a ratio scale such as 1:25,000, and say why the ratio has no units.
- Give and read four-figure and six-figure grid references in the correct order, and state which square or point a reference identifies.
- Compute door-to-door journey time from distance, average speed and fixed stops, and work backwards from a fixed deadline to a latest departure.
- Compare candidate routes against stated constraints and identify which constraint actually binds on the vehicle, the load or the time window.
Checkpoint: does the idea land?
Copy linkBefore the worked examples, check that the objectives above actually landed.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Examples
Copy linkBearings: turn the number, not the map
You are facing north. Turn 90 degrees right and you face 090, east. Turn a further 135 degrees right: 90 + 135 = 225, south-west. Now turn 90 degrees left: 225 - 90 = 135, south-east. The method that survives any number of turns is to hold the facing as a number of degrees clockwise from north, add for right turns, subtract for left turns, take the result modulo 360, and convert back at the end using the eight-point table: 0 north, 45 north-east, 90 east, 135 south-east, 180 south, 225 south-west, 270 west, 315 north-west. Candidates who instead picture themselves rotating lose the left-right convention the moment they are facing south, because on the mental image left now appears on the right of the page. The companion idea is the back bearing: the reverse of a leg is the forward bearing plus or minus 180 degrees, so a leg travelled out on 040 comes home on 220, and a leg out on 250 comes home on 070. Checking that every outbound and return pair differs by exactly 180 catches a dropped turn immediately.
Scale: from the sheet to the ground
On a 1:25,000 sheet, one centimetre of paper represents 25,000 centimetres of ground, which is 250 metres. A path measured at 6.4 cm is therefore 6.4 x 250 = 1,600 m, or 1.6 km. Move to a 1:50,000 sheet and the same 6.4 cm becomes 3.2 km, because each centimetre now stands for 500 m. Two mistakes recur. The first is dividing rather than multiplying, which turns a 1.6 km walk into a 26 m one and should be caught instantly by asking whether the answer is plausible for a footpath. The second is forgetting that a ratio scale carries no units: 1:25,000 means one inch to 25,000 inches just as much as one centimetre to 25,000 centimetres, which is exactly why the printed scale bar is safer than a ruler when a sheet mixes conventions. Finally, map distance is horizontal distance. A route that climbs 300 m over that 1.6 km is meaningfully longer and much slower on foot, which is why walking-time estimates add time for ascent separately rather than inflating the distance.
Grid references: along the corridor, then up the stairs
On a numbered map grid, the four-figure reference 3572 means easting 35 and northing 72. It identifies a whole one-kilometre square, and specifically the square whose south-west corner sits at that intersection: not its centre. To locate a point inside it, divide the square into tenths in each direction: a feature five tenths east and five tenths north of that corner is 355725 in six figures, which pins the position to roughly 100 m. The two failures are reliable enough to be worth naming. The first is giving northings before eastings, so 7235 gets quoted for a feature that is actually at 3572, pointing at an entirely different square or at nothing at all. The second is treating the reference as the centre of the square, which shifts every reported position by half a kilometre to the north-east. The mnemonic that fixes both is 'along the corridor, then up the stairs': you walk along before you go up, and eastings always come first.
Journey time with a stop, and the average-speed trap
A van covers 84 km at an average 56 km/h. Driving time is 84/56 = 1.5 hours, or 90 minutes. Add a 20-minute unload part way and the door-to-door time is 110 minutes, so a 08:20 departure arrives at 10:10. If the receiving bay closes at 10:00, the total budget is only 100 minutes; with the 20-minute stop unavoidable, driving must fit into 80 minutes, and the required average becomes 84 / (80/60) = 63 km/h. That is the shape of most feasibility items: find the fixed time, subtract the fixed stops, and solve for what is left. The trap sits in the word average. Suppose the same 84 km is driven as 42 km at 70 km/h and 42 km at 50 km/h. The mean of the two speeds is 60 km/h, and that is the wrong answer. Add the times instead: 42/70 = 0.60 h and 42/50 = 0.84 h, total 1.44 h, so the true average is 84/1.44 = 58.3 km/h. Average speed is always total distance over total time, never the mean of the speeds.
Routing under constraints: find the one that binds
Depot to site, three options. Route A is 18 km and crosses a bridge posted at 7.5 tonnes. Route B is 14 km but the final 300 m is one-way against you, forcing a 1.2 km loop, so it is really 15.2 km. Route C is 16 km and includes 800 m of school zone limited to 20 km/h between 08:00 and 09:00, where you would otherwise do 40 km/h. Your loaded van weighs 3.5 tonnes and you leave at 08:30. Price the constraints. The bridge limit does not bind at all: 3.5 tonnes is well under 7.5, so route A's restriction costs nothing and A is simply the longest at 18 km. The school zone does bind, but barely: 0.8 km at 20 km/h takes 2.4 minutes against 1.2 minutes at 40, a penalty of 1.2 minutes, leaving C at 16 km plus about a minute. Route B, at 15.2 km including its loop, is still the shortest. The trap is choosing A because it is the option with no restriction that applies, a constraint that does not bind is not a cost, and noticing that is precisely what the item measures.
Timetables: work backwards from the fixed event
Buses leave the depot at five and thirty-five minutes past each hour. The ride to the station takes 25 minutes, then a 6-minute walk to the platform. Trains depart at 09:12, 09:42 and 10:12. To catch the 09:42, you must be on the platform by 09:42, so the latest boarding time is 09:42 minus 25 minus 6 = 09:11. The 09:05 bus qualifies: it reaches the station at 09:30 and the platform at 09:36, six minutes clear. The 08:35 bus is on the platform at 09:06 and would also make the 09:12 with a little to spare. The 09:35 bus reaches the platform at 10:06 and can only make the 10:12. The two errors that cost marks are subtracting the walking time from the wrong end (adding it to the train departure instead of the bus arrival, which manufactures twelve minutes of slack that does not exist), and reading a timetable's arrival column as though it were the connection's departure. Fix the deadline first, list every fixed time in one column, then choose.
Checkpoint: can you apply it?
Copy linkNow apply it. These come from a later section of the bank, so they are not more of the same.
Two questions from the open practice bank, answered here and scored on this device. Untimed, ungraded, and not added to your practice history, the full bank is where attempts are recorded.
Practice tips
Copy link- Convert every facing to degrees clockwise from north before you do anything else. Arithmetic on a number survives a question that turns you round four times; mental rotation does not.
- Never rotate the paper. Rotating the map reverses your left and right the instant the route heads south, and that single habit accounts for a large share of lost bearing marks.
- Write the scale conversion once at the top of the page, '1 cm = 250 m', and reuse it for the whole set. Recomputing it per item is where factor-of-ten errors are born.
- For timetable items, work backwards from the fixed deadline and write every fixed time in a single column before you look at the options. Forward-adding invites you to forget the walk or the changeover.
- Never average two speeds. Add the times, then divide total distance by total time. The arithmetic mean of the speeds is almost always one of the offered answers, and it is there deliberately.
- When a route question lists a restriction, ask explicitly whether it binds on this vehicle, this load and this departure time. Practise untimed until spotting a non-binding constraint is automatic; attempts stay on this device, so repetition costs nothing.
Glossary
Copy link- Bearing
- A direction given as degrees measured clockwise from north, conventionally written with three digits so that east is 090 and south-west is 225.
- Back bearing
- The bearing of the return leg, equal to the forward bearing plus 180 degrees if it is under 180, or minus 180 if it is over. A leg out on 040 returns on 220.
- Ratio scale
- A unitless map scale such as 1:25,000, meaning one unit measured on the sheet represents 25,000 of the same units on the ground, whatever unit you choose.
- Easting and northing
- The horizontal and vertical grid coordinates of a position. Eastings are always quoted first, which is what the 'along the corridor, then up the stairs' mnemonic encodes.
- Six-figure grid reference
- A four-figure square reference refined by tenths in each direction, locating a point to roughly 100 m rather than to a one-kilometre square.
- Dead reckoning
- Fixing a position from a known starting point plus the recorded headings, speeds and elapsed times, without any external fix to correct the accumulated error.
- Average speed
- Total distance divided by total elapsed time. When a question asks door to door, the elapsed time includes every stop, not only the time in motion.
- Contour interval
- The fixed height difference between adjacent contour lines. Tightly spaced contours mean steep ground, and therefore a journey time longer than the flat map distance suggests.
- Connection time
- The interval between an arrival and the next scheduled departure, including any walk or transfer. It is the constraint that actually decides most timetable items.
Sources
Copy link- Navigation and scheduling examples computed for Novus Learn from first principles: clockwise bearing arithmetic, ratio-scale conversion, grid-reference convention, and distance-speed-time with fixed stops.
- Terminology checked against the public Wikipedia articles 'Bearing (navigation)', 'Scale (map)', 'Ordnance Survey National Grid' and 'Dead reckoning'. Definitions only; every route, timetable and figure above is original.
- Novus Learn aptitude construct registry (catalog seed) for the construct scope and related suite mapping.
- Public educational framing only: not affiliated with any official exam board, publisher or employer, and no copyrighted map extract or timetable is reproduced.
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