A colour map can make one part of a classroom look hotter than another. But colours on a thermal image do not automatically give temperatures, proportions, averages or a reliable verdict. Mathematics turns the display into quantities that can be checked: what area is represented, which temperature scale is used, how are readings weighted, and what precisely does a threshold mean?
This guide is about G3 Mathematics, not an extra thermal-camera syllabus. The original case is a fictional exhibition about a school reading room. We use the numbers to practise ratios, weighted means as applied averages, data representation, bounds, logical conditions and clear working. The scientific limits are explained alongside the arithmetic so that correct calculations do not become incorrect conclusions.
Quick route: identify each measured quantity and unit; verify the grid or zone areas; read the numerical scale rather than the colour; choose an appropriate denominator or weighting; test strict and inclusive thresholds separately; then qualify the decision. An area-weighted average of indicated surface readings is not the temperature of the room air.
Contents
- What the exam does and does not assess
- The exhibition map and its data
- Why the reference area matters
- Building a weighted average
- Reading a threshold precisely
- Rounding intervals and guaranteed claims
- Changing image scales
- Equal rectangles and unequal physical zones
- Graph choices and real-world judgement
- Twenty-four solved decision files
- An examination answer structure
- Four-week route from fundamentals to mastery
- Frequently asked questions
- Official sources and linked learning routes
What the exam does and does not assess
The official 2027 SEAB G3 Mathematics syllabus code is K310. Paper 1 and Paper 2 each carry 50% of the grade, each lasts 2 hours 15 minutes and each has 90 marks. The syllabus assesses mathematical thinking through functions and graphs, geometry and measurement, statistics and probability, and problem solving in real-world contexts. The final problem in Paper 2 is designed around an authentic context. You should be able to identify which data a question supplies, form a model and decide whether the resulting conclusion is reasonable.
This article’s thermal map is a practice context, not an announced SEC item or a separate EMS paper. A task may supply a diagram, table or unfamiliar scientific scenario, but students should use the mathematical principles required by the question rather than assume they must memorise a commercial camera’s technical details. Always follow the specific instructions for rounding; otherwise non-exact numerical answers are generally given to three significant figures and angles to one decimal place when relevant.
The exhibition map and its data
Imagine that a reading room is divided into three non-overlapping floor-plan regions. Zone A has an area of 12 square metres and an indicated surface temperature of 28.0 °C. Zone B covers 18 square metres at 30.0 °C. Zone C covers 10 square metres at 32.0 °C. These are classroom practice values rather than measurements of a real site. For the exercise, assume each given reading represents its entire stated zone. In a real survey that assumption would require evidence.
The zones cover 12 + 18 + 10 = 40 square metres. Their respective fractions of mapped area are 12/40 = 0.30, 18/40 = 0.45 and 10/40 = 0.25. Thus A is 30%, B is 45% and C is 25%. The three percentages add to 100%, an immediate reasonableness check. An answer that calls C 10% because it covers ten square metres has confused the numerator with a percentage.
Why the reference area matters
A map is not automatically a census of surfaces. A floor-plan region represents horizontal area; a wall’s surface, a desk’s surface and the floor are different things. A camera image may show an oblique perspective, with more pixels for a near wall than a distant one. Before counting ‘hot pixels’, ask whether pixels correspond to equal physical areas. If not, a pixel fraction is a fraction of display locations, not a verified fraction of the room’s surface area.
The exercise explicitly supplies zone areas, so these are the valid weights. If all square cells in a rectified plan have the same physical area, counting cells can also work. But if the image has been cropped or distorted, restore the relevant geometry or state the limitation. An accurate calculation always carries its reference population or area along with it.
Building a weighted average
The arithmetic mean of the three displayed readings is (28.0 + 30.0 + 32.0)/3 = 30.0 °C. That treats each zone as one equally weighted observation, even though the zones cover different areas. If the question asks for an area-weighted mean reading across the represented surface, multiply each zone’s reading by its area and divide by total area.
The numerator is 12 × 28.0 + 18 × 30.0 + 10 × 32.0 = 336 + 540 + 320 = 1196 square-metre-degrees Celsius. Dividing by 40 square metres gives 29.9 °C. The unit reduces to degrees Celsius because area appears in both numerator and denominator. This is an area-weighted mean of the stated indicated surface readings. It is not a measurement of the reading-room air temperature and cannot establish heat-loss rate.
Because B covers 45% of the mapped area, it has greater influence on the weighted answer than A or C. You can check the result is reasonable: it lies between the minimum 28.0 and maximum 32.0 and is close to the dominant zone’s 30.0. A weighted mean outside the range of the inputs is an arithmetic warning when all weights are positive.
Reading a threshold precisely
The statement ‘above 30 °C’ means strictly greater than 30 °C. Under the three-zone assumptions, only Zone C qualifies, so the relevant fraction is 10/40 or 25%. In contrast, ‘at least 30 °C’ includes 30 °C, so Zones B and C qualify: (18 + 10)/40 = 28/40 = 70%. The difference is not pedantry. It changes which regions are counted and whether a rule is triggered.
For a policy exercise, write the mathematical condition before selecting rows. For example, T > 30 includes 32 but excludes 30; T ≥ 30 includes both. Never assume that a bright yellow colour implies the condition when the legend and numerical readings are available. Equally, a 70% area share cannot be presented as a 70% share of students, minutes or energy consumption.
Rounding intervals and guaranteed claims
A displayed whole-degree reading of 30 °C, rounded to the nearest whole degree, represents a value from 29.5 °C up to but not including 30.5 °C under the usual rounding convention. Therefore a rounded 30 does not guarantee that the original reading exceeded 30. A reading rounded to 31 represents the interval from 30.5 to less than 31.5 and does guarantee an original reading greater than 30, assuming the device’s rounding is correctly specified.
A lower or upper bound is not merely another guess. Bounds identify all possible values consistent with the reporting precision. When a total or threshold depends on rounded values, calculate the most favourable and least favourable cases. If they lead to different decisions, the evidence is not sufficient to make a guaranteed classification. Exact data, if obtainable, may resolve that uncertainty.
Changing image scales
Suppose two maps represent exactly the same numerical reading of 29.9 °C. One uses a display range of 20–32 °C; another uses 0–60 °C. The first may show the value near its warm-colour end, while the second may place it near the middle. The mathematics of the reading is unchanged. A colour comparison is a comparison of mapped positions on two different scales, so it does not establish an absolute difference in temperature.
In a simple illustrative linear colour legend, the relative position of 29.9 within 20–32 would be (29.9 − 20)/(32 − 20) = 9.9/12 = 82.5% of the legend span. Within 0–60, it would be 29.9/60, about 49.8%. The model assumes equal steps across the legend and is only appropriate if the question explicitly says the scale is linear. Real false-colour palettes are not necessarily linear to the eye, so never calculate a temperature solely from a colour gradient unless mapping information is provided.
Equal rectangles and unequal physical zones
A rectangular plan 8 metres by 5 metres covers 40 square metres. If a printed version measures 16 cm by 10 cm, the scale is 2 cm to 1 m. A region measuring 4 cm by 6 cm on the plan corresponds to 2 m by 3 m, with an actual area of 6 square metres, assuming the plan is uniformly scaled. To calculate an area, square the linear scale factor instead of multiplying the printed area by the linear factor once.
However, our three zones are not necessarily tidy rectangles. When exact zone areas are given, use those rather than estimating from an irregular display. For an examination question, the clean solution often begins by asking which number is a measurement and which is an impression. If you cannot identify a physically meaningful area for each pixel, explain that a pixel count cannot establish a real-world area percentage.
Graph choices and real-world judgement
A bar chart can compare the temperature assigned to each zone. A second bar chart can compare their areas, but those are different quantities. A pie chart may show the fractions of total area, while a line graph might represent readings over time at one fixed sensor. Each has a purpose. Connecting the three zone readings A, B and C with a line could suggest a continuous spatial trend that the data do not justify if their labels have no numerical ordering along a physical axis.
A useful report keeps the visual representation tied to a clear claim. State whether the chart measures zone area, the average indicated reading or the number of observations. If you combine area and temperature on one diagram, provide explicit axes and units. Avoid three-dimensional decoration that makes small differences appear large. It is possible for an eye-catching chart to be less useful than a four-column table.
Thirty worked decisions
The records below range from basic fractions to integrated interpretation. Use them as a bank of short, original practice tasks rather than a prediction of what will be asked in the examination. Each model response states its mathematical basis and its interpretive limit. Try replacing one number in each case and solving again before reading the explanation.
1. Simple area share
Question. Zone A measures 12 m² and the total measured plan is 40 m².
Worked answer. 12/40 × 100% = 30% of the mapped area. Reason. The numerator and denominator both measure area. The percentage is not a proportion of pupils.
Transfer practice. If the mapped region grows to 50 m² while A stays at 12 m², the share becomes 24%. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
2. Three regions sum
Question. The given areas are 12 m², 18 m² and 10 m².
Worked answer. The total is 40 m² and the checks are 30% + 45% + 25% = 100%. Reason. If the parts overlap, this simple sum would not be valid; this case assumes no overlap.
Transfer practice. Describe what you would do if the diagram shows an overlapping corner. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
3. Ordinary mean
Question. The three representative readings are 28, 30 and 32 °C.
Worked answer. Their unweighted mean is 90/3 = 30 °C. Reason. This gives equal weight to each named zone, not to its physical area.
Transfer practice. Explain why this differs from the mean reading over the mapped area. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
4. Area-weighted mean
Question. The areas 12,18,10 correspond respectively to 28,30,32 °C.
Worked answer. The sum of products is 1196, and 1196/40 = 29.9 °C. Reason. Larger areas contribute more because the question defines an area-weighted average.
Transfer practice. Identify what physical assertion would still be unjustified from this mean. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
5. Above a value
Question. A threshold requires temperatures strictly greater than 30 °C.
Worked answer. Only the 10 m² region at 32 qualifies, so the share is 25%. Reason. The 18 m² region at exactly 30 must be excluded.
Transfer practice. Explain why the symbol ‘>’ is not interchangeable with ‘≥’. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
6. At least a value
Question. A rule applies at 30 °C or higher.
Worked answer. B and C have 18 + 10 = 28 m², giving 28/40 = 70%. Reason. The word ‘at least’ changes the mathematical selection.
Transfer practice. Write the inequality before counting the regions. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
7. Below 30
Question. A sign asks for the fraction with readings lower than 30 °C.
Worked answer. Only A at 28 qualifies: 12/40 = 30%. Reason. Reading exactly 30 is not ‘below’ 30.
Transfer practice. Identify the difference if the sign instead says ‘no higher than 30’. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
8. No higher than 30
Question. The condition is that temperature must be at most 30 °C.
Worked answer. A and B total 30 m², so the area fraction is 75%. Reason. An inclusive upper boundary includes readings equal to 30.
Transfer practice. Compare this with the 70% ‘at least 30’ result. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
9. Unequal zone counts
Question. There are four small zones with areas 1,1,1 and 17 m².
Worked answer. Three of four zones is 75% by zone count but only 3/20 = 15% by area. Reason. Choosing the wrong denominator radically changes the message.
Transfer practice. State which quantity each percentage describes in a public sign. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
10. Rounding a threshold
Question. A display rounds a measurement to 30 °C.
Worked answer. The true pre-rounded number might range from 29.5 to below 30.5 °C. Reason. It may fall either side of the strict 30 °C condition.
Transfer practice. Identify a rounded value that guarantees a number exceeds 30. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
11. Rounded 31
Question. A device rounds to the nearest degree and displays 31 °C.
Worked answer. The original indicated value lies from 30.5 up to but not including 31.5 °C. Reason. Every value in that interval exceeds 30.
Transfer practice. Does that guarantee the physical surface temperature exceeded 30 if calibration error is unspecified? No. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
12. Range and midpoint
Question. A calibration summary gives an interval 28.8 to 29.4 °C.
Worked answer. Its midpoint is (28.8+29.4)/2 = 29.1 °C, and the interval width is 0.6 °C. Reason. The midpoint is a central descriptor, not a new exact measurement.
Transfer practice. Say whether the entire interval lies below the 30 °C threshold. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
13. Comparison of ranges
Question. Camera A reports 29.8 ± 0.4 °C and B reports 30.0 ± 0.4 °C.
Worked answer. Their stated intervals are 29.4–30.2 and 29.6–30.4, which overlap. Reason. The displayed central difference of 0.2 does not on its own establish a definite ordering.
Transfer practice. State why overlapping ranges are not a formal significance test without a specified uncertainty model. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
14. Different palette ranges
Question. The same 29.9 °C value appears on a 20–32 legend and a 0–60 legend.
Worked answer. Under an explicitly linear mapping it sits at 82.5% and approximately 49.8% of the respective scales. Reason. Different colours can arise from changed display settings without changed readings.
Transfer practice. Why must an exam question provide the mapping before a colour-to-number calculation? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
15. Change in degrees
Question. A marked point reads 27.5 °C in one controlled observation and 29.0 °C later.
Worked answer. The numerical change is an increase of 1.5 °C. Reason. A temperature difference may be reported in degrees Celsius without converting to kelvins.
Transfer practice. Name one environmental condition that could explain the increase. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
16. Relative percentage change
Question. A stylised exercise compares 28.0 with 29.4 as positive numerical readings.
Worked answer. The arithmetic percentage increase relative to 28.0 is 1.4/28 × 100% = 5%. Reason. For temperatures on the Celsius scale, a percentage of the number itself is not a meaningful universal measure of thermodynamic temperature; prefer the absolute difference unless a question defines a suitable ratio.
Transfer practice. Explain why subtracting is more appropriate for two readings in °C. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
17. Plan scale
Question. A plan scale of 2 cm per metre shows a region 4 cm by 6 cm.
Worked answer. The dimensions represent 2 m by 3 m, and the true rectangular area is 6 m². Reason. Linear scale factors and area scale factors must not be confused.
Transfer practice. Would the same rule hold if the image were stretched differently in x and y? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
18. A crop of the plan
Question. A rectangular 8 × 5 m plan is cropped to display half its width but its full height.
Worked answer. The displayed portion covers 4 × 5 = 20 m² if the crop is a true half-width section. Reason. Half the map’s horizontal extent is not necessarily half the measured heat readings.
Transfer practice. Check whether the cropped area excludes one of the high-reading zones. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
19. Pixel count
Question. A colour map contains 100 equally sized screen pixels, of which 30 are orange.
Worked answer. Orange makes up 30% of displayed pixels, but not necessarily 30% of actual room surface. Reason. Physical area percentages need geometric calibration or an equal-area representation.
Transfer practice. What changes if perspective causes far surfaces to occupy fewer pixels? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
20. Weighted median caution
Question. Area shares of 30%, 45%, and 25% correspond to 28, 30 and 32 °C.
Worked answer. Half of area is reached within the 30 °C category, so an area-weighted median reading is 30 °C. Reason. The weighted median and the weighted mean (29.9 °C) answer different questions.
Transfer practice. Which result is more sensitive to extreme zone readings? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
21. An extra region
Question. A 10 m² zone at 34 °C is added to the original three zones.
Worked answer. The total area becomes 50 m²; the sum of weighted readings is 1196 + 340 = 1536, giving 30.72 °C. Reason. Do not average the old 29.9 and the new 34 as though they represent equal areas.
Transfer practice. How would the answer change if the new region were only 1 m²? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
22. A missing region
Question. A 40 m² map includes 5 m² with no usable reading.
Worked answer. A temperature-based average can cover only the 35 m² measured subset unless a justified missing-data treatment is supplied. Reason. Do not silently represent the missing region as zero degrees or as the observed mean.
Transfer practice. Explain how selective missingness could bias a comparison. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
23. Threshold within measurement bounds
Question. A marked point has an indicated interval 29.7–30.3 °C.
Worked answer. The interval crosses 30 °C, so a strict-above classification is not guaranteed. Reason. A midpoint of 30 may appear tidy but does not decide the inequality.
Transfer practice. What tighter measurement could allow a confident decision? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
24. Whole-room headline
Question. A poster claims ‘our room is 29.9 °C’ because the three-zone weighted surface reading equals 29.9 °C.
Worked answer. The arithmetic is a weighted mean over the assigned surface readings; it is not an air-temperature reading. Reason. A technically correct number becomes misleading when its physical meaning is replaced.
Transfer practice. Rewrite the caption as ‘The area-weighted mean of these three indicated surface readings is 29.9 °C under the exercise assumptions’. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
25. Time series against zones
Question. A graph connects the zone labels A, B, C with a line.
Worked answer. Without a spatial or temporal axis, joining category values can suggest continuity not established by the data. Reason. A bar chart labelled by zone is often clearer for discrete locations.
Transfer practice. What would be necessary before an interpolated line along a wall became meaningful? Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
26. A threshold policy
Question. An illustrative policy flags surfaces with an indicated reading of at least 31 °C for follow-up inspection.
Worked answer. Only 32 °C zone C is flagged, covering 25% of the mapped area. Reason. A trigger for follow-up is not proof of a safety violation or defect.
Transfer practice. Explain the separate roles of numerical classification and qualified inspection. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
27. Area and people
Question. A notice says ‘70% of our class feels warm’ because 70% of mapped area is at least 30 °C.
Worked answer. The evidence concerns area of a map, not the experiences of people. Reason. The category of the denominator must survive into the conclusion.
Transfer practice. Suggest what independent evidence would be needed to make a people-based claim. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
28. Different sampling times
Question. The Monday area-weighted mean is 29.9 °C and Tuesday is 29.5 °C, but measurements were taken at different times of day.
Worked answer. The calculated difference is 0.4 °C; the cause cannot be isolated from time and environmental conditions. Reason. The numbers are comparable as reported values, but the causal story is not established.
Transfer practice. Design a repeated observation schedule that improves fairness. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
29. Choice of estimate
Question. A reporter asks whether to use ‘average of zones’ 30.0 °C or ‘area-weighted average’ 29.9 °C.
Worked answer. If the target quantity is the average value across mapped area with representative zone readings, use 29.9 °C and identify the assumptions. Reason. The chosen model follows the question; an arithmetic method should not be selected just because it is simpler.
Transfer practice. Explain what would change if each zone supplied many raw measurements instead. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
30. Final decision
Question. A board has to choose between an eye-catching thermal poster and a transparent numerical table.
Worked answer. The table should show zone, area, reading, scale and conditions; a map can accompany it if its legend is clear. Reason. A public claim is useful only when its denominator, method and uncertainty are traceable.
Transfer practice. Write a two-sentence correction that keeps the result readable without calling it room air temperature. Whenever you explain this solution in examination prose, first name the quantity, then the operation and result, and finish by identifying the claim the result actually supports. Show enough working for another reader to reconstruct your choices and check the units.
An examination answer structure
A well-built response to a real-world mathematics problem often has five stages. Write the relevant data and units; identify what must be found; select the calculation; test the value for reasonableness; and answer in the words of the question. If the final sentence asks for a recommendation, a number alone may not be sufficient. A recommendation should point back to the computed condition and any limitation explicitly supplied in the question.
Avoid unnecessary decoration. When asked for an average, say whether it is an unweighted mean, weighted mean or another statistic. When asked for area, name the physical region. When asked whether a rule has been met, copy the inequality and classify boundary values correctly. When asked to compare two diagrams, match scale and units before reaching for a calculator. One carefully qualified sentence can be stronger than several vague claims.
Four-week route from fundamentals to mastery
Week 1, foundations: practise ratios and percentages using sets of two, three and four non-overlapping regions. Reconstruct a table where all areas sum to the stated total. Then practise strict and inclusive inequalities. Work with exactly 30, slightly below 30 and slightly above 30 so that the difference between ‘above’, ‘at least’ and ‘at most’ becomes automatic.
Week 2, averages: calculate unweighted and area-weighted means for ten different sets. Use mental checks to ensure every mean lies between minimum and maximum. Change the area of one zone without changing its reading and predict which way the weighted result will move. Where the data permit, compare median and mean and explain what each communicates.
Week 3, scale and precision: practise enlargements of diagrams, area calculations and measurement intervals. Given rounded temperatures, write the possible range before applying an exact threshold. Compare two maps with different colour legends; identify when the numerical readings are the same despite different appearance. Give one sentence explaining why the display alone cannot determine air temperature.
Week 4, examination transfer: complete an integrated case in 25 minutes: read the map, compute weighted mean and threshold areas, test a rounded value, and write a brief recommendation under the stated assumptions. Mark your own response against a checklist: correct denominator, correct units, transparent working, correct inequality and no unsupported scientific inference. Repeat with changed values after a day or two to check genuine transfer.
Frequently asked questions
Can I average three temperatures without weighting? Yes if the question asks for the mean of three observations treated equally. No if it explicitly asks for an area-weighted mean across unequal regions. Why is the weighted mean 29.9 rather than 30.0? Because the 18 m² zone at 30 has more weight than either of the other two zones, so the arithmetic is based on area, not simply three category values.
Does a hotter image mean the actual room got hotter? Not necessarily. The colour display and measurement conditions may have changed. Does the SEC require thermal-camera software? No. This is a mathematical problem-solving context, not a new topic to memorise. Can I call a surface mean the room temperature? No. Label it as a mean of the indicated surface readings unless an independent room-air measurement has been made.
How can I avoid a threshold mistake? Translate words into symbols before counting regions, and check exact boundary values. What if the data are rounded? Write the possible interval and decide whether the entire interval, rather than just its displayed midpoint, satisfies the condition. Should I give all results to three significant figures? Follow the individual question’s instructions first; the syllabus gives default presentation conventions for non-exact answers.
Official sources and linked learning routes
The authority for exam detail is SEAB 2027 K310 G3 Mathematics syllabus and the official 2027 G3 subject index. The previous Vol 0795 Physics guide explains infrared and false-colour mapping; Vol 0794 EMS guide connects scientific observation to numerical and public claims; and Vol 0792 owns crop geometry.
For longer foundations see the PSLE learning guide, the English, Mathematics and Science Voyage Series and the examination-craft route. These practice contexts are original explanations, not copies of SEAB examination questions.
