A habitat harvest report says that 240 kg of leafy crops and 180 kg of herbs arrived at the packing station. After inspection, 10% of the first crop and 15% of the second crop were rejected. The distribution team wants whole cartons, not fractional cartons. A dashboard shows two more days of harvest in a matrix, and a poster promises that ‘all orders can be met’. Before accepting that conclusion, a G3 Mathematics learner must separate gross yield, saleable yield, package sizes and the demand for each product. Good working is a model of the real quantities, not a series of attractive percentages.
This is the next step after Vol 1272 on water and food movement in plants. The biological chapter asks how materials move within a plant. This one asks what can be claimed from numerical harvest records after collection. Earlier Vol 1265 owns crop-trial sampling and rates, while Vol 1269 owns supply-mixing constraints. Here our new focus is how inventory, matrix operations, reverse percentages and discrete carton decisions interact.
- Translate gross and saleable quantities into a clear ledger.
- Apply percentages to the correct original base and recover a base by reverse percentage.
- Use rows, columns and compatible dimensions correctly in matrix data.
- Respect integer carton counts and demand constraints.
- Explain what a feasible calculation does and does not establish.
The official 2027 SEC G3 Mathematics arrangements
SEAB lists G3 Mathematics as syllabus K310 in 2027, with the former code 4052 shown for reference. Paper 1 and Paper 2 each last 2 hours 15 minutes, carry 90 marks and contribute 50%. Paper 1 consists of about 26 short-answer questions; Paper 2 has nine or ten questions of varying lengths, with a final extended question applying Mathematics to a real-world scenario. The syllabus covers percentage and reverse percentage, linear inequalities, matrices, data interpretation and probability, alongside broader areas of number, algebra, geometry and statistics. Approved calculators may be used in both papers. Show essential working, use appropriate units and follow the specified rounding instructions.
These examination details come from SEAB’s official 2027 G3 list and syllabus K310. The harvest quantities below are invented teaching data, and none of the worked questions is an official SEC question. This is Mathematics preparation, not a commercial production plan.
Define the units before doing anything else
There are four different sorts of quantity in this story. Kilograms measure a crop mass; a percentage measures a proportion of a defined base; a carton count must be a whole non-negative integer; and a matrix cell represents a value at the intersection of a named row and column. Students lose marks when they treat these as interchangeable numbers. For instance, 216 kg of saleable crop packed into 6-kg cartons gives 36 full cartons, but 216 itself is not the number of cartons. A method may be algebraically correct and still answer the wrong question because its units were never identified.
Create the stock ledger: gross, rejection, saleable and packed
Let crop A begin at 240 kg. Ten per cent rejected means 24 kg rejected and 216 kg saleable. Crop B begins at 180 kg. Fifteen per cent rejected means 27 kg rejected and 153 kg saleable. The two saleable quantities total 369 kg, but it does not follow that 369 kg can be packed into any combination of cartons: the size and product type of each carton matter. A carton holding 6 kg of A allows 36 complete cartons; a carton holding 9 kg of B allows 17. In this deliberately exact example no crop is left over. Changing either carton size would change the floor division and potentially leave unpacked stock.
Reverse percentages require the changed base
Suppose 176 kg remains after a 12% rejection. The remaining amount is 88% of the original, so original mass = 176 ÷ 0.88 = 200 kg. Dividing by 0.12 would use the rejected share rather than the remaining share and would be wrong. Reversing a change is not usually achieved by adding the original percentage back to the reduced figure. For example, decreasing 200 by 12% gives 176, but adding 12% of 176 gives 197.12, not 200. The percentage base has changed.
Understand a harvest matrix as information with positions
Suppose an example shows two days in rows and two crop varieties in columns. M = [[120, 90], [80, 60]], where the first column is crop A and the second is crop B, all in kilograms. The first row represents day 1, the second day 2. Row totals are 210 kg and 140 kg; column totals are 200 kg and 150 kg. Multiplying by a price column [5, 8] gives 1320 and 880 as two day-level amounts in fictional monetary units. The operation is meaningful only when the column ordering and prices correspond. The first result means 120×5 + 90×8, not merely 120+90+5+8.
Dimensional checks prevent a plausible wrong answer
A two-row by two-column matrix may multiply a compatible two-row by one-column vector to produce a two-row by one-column result. Reversing the order does not automatically produce the same object and may not be defined. Under the K310 syllabus, students should be comfortable displaying data as matrices, interpreting entries, adding compatible matrices and calculating scalar and suitable matrix products. Many matrices exercises are about representing a relationship correctly before doing multiplication. A column label lost during copying can make a perfectly executed arithmetic procedure useless.
The whole-carton test
If 65 kg is available and every sealed carton contains 8 kg, the maximum number of complete cartons is 8, with 1 kg unpacked. Ordinary rounding of 8.125 to eight happens to agree here, but the reason is not conventional decimal rounding: a ninth carton needs a further 7 kg. Conversely, a delivery of 65 kg using carts of capacity 8 kg would require 9 trips, because a partial final load still needs a trip. The mathematical operation depends on the question. Maximum complete packs uses floor division; minimum trips to carry all goods uses a ceiling.
Need, stock and plan are not the same thing
A feasible plan must satisfy every stated constraint. If demand calls for at least 40 cartons of crop A but the harvest yields only 36, surplus crop B does not automatically repair the shortfall. If a scheme permits substitution, the substitution rate and approval conditions must be stated. If no substitution is allowed, a plan cannot claim success by adding the two carton totals. The number of cartons, the type of cartons, timing, rejection percentages and any reserve requirement each have their own place. Make a small table that shows demand, available, difference and status for each product separately.
When a calculation becomes an explanation
Do not stop with the expression 240 × 0.90 = 216 if the question asks whether the whole order can be filled. Connect the derived quantity to the required number of cartons and state the result. Conversely, if the question asks only for the percentage rejected, an extended decision memo may waste time. The correct G3 response has enough calculation to make the conclusion auditable, and enough interpretation to show that the result answers the question. A clear final sentence often prevents a correct but unidentified number from being overlooked.
Forty-two original worked examination decisions
Work through the cases in order. Start with a single operation, then add units, matrices, integer restrictions and evidence limits. The cases are original practice tasks rather than past-year examination questions. Cover each answer and write the calculation with its units before comparing your approach.
Working habits that protect marks
For every case, follow this order: write the quantity and unit; define the base or row–column meaning; select the operation; calculate without premature rounding; check a boundary or reverse operation; finally interpret the result. When the story looks complicated, make the information smaller, not the working shorter. Number the steps in a mixed question. A strong solution lets a reader reconstruct why the decision followed. Do not hide several assumptions inside a single equals sign.
A timed practice set
Set a short period and answer one item from each of four groups: a reverse percentage, a matrix interpretation, a whole-carton limit and a brief feasibility justification. Give yourself one mark for identifying the correct base or matrix entry, one for valid arithmetic and one for a unit-bearing conclusion where relevant; these are practice checks, not the official marking scheme. When you review, identify the first wrong move. Correcting a sign, denominator or column label before repeating the question is more efficient than simply doing another twenty items.
Decision 1: Identify the original base
Task. 240 kg is harvested and 10% is rejected. Which number is the percentage base?
Worked result. 240 kg is the original quantity; the rejected mass is 0.10×240 = 24 kg.
Reasoning. The percentage is stated relative to harvested mass, not the saleable mass.
Revision check. If you used 216 as the base, correct the ledger order before recalculating.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 2: Find the saleable crop
Task. Find saleable mass after 10% rejection from 240 kg.
Worked result. 216 kg remains, since 90% of 240 is 216.
Reasoning. Subtract the rejected amount or multiply directly by 0.90; both give the same result.
Revision check. Write kilogram units on the final answer.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 3: A second crop
Task. From 180 kg, 15% is rejected. Find the remainder.
Worked result. 153 kg, since 0.85×180 = 153.
Reasoning. Do not confuse the 27 kg rejected with what remains.
Revision check. A quick check is that 153+27=180.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 4: Add compatible masses
Task. Find total saleable mass of 216 kg and 153 kg.
Worked result. 369 kg of saleable produce in total.
Reasoning. The addition is valid because both figures use the same unit and same stage of production.
Revision check. The sum does not yet tell us total cartons.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 5: Calculate rejected share
Task. How much mass was rejected across both crops?
Worked result. 24+27=51 kg, from 420 kg originally.
Reasoning. The total rejection rate is 51÷420≈12.14%, not the simple mean of 10% and 15%.
Revision check. Different starting quantities require weighted reasoning.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 6: Whole-carton rule A
Task. How many complete 6-kg cartons can 216 kg fill?
Worked result. 36 full cartons.
Reasoning. Divide 216 by 6; all the stock fits exactly here.
Revision check. Never report a fractional number of complete sealed cartons.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 7: Whole-carton rule B
Task. How many complete 9-kg cartons can 153 kg fill?
Worked result. 17 full cartons.
Reasoning. The product B carton size is different from A, so keep a separate calculation.
Revision check. Do not divide all 369 kg by whichever carton size is convenient.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 8: Uneven cartons
Task. What if 65 kg must be packed into 8-kg cartons?
Worked result. There are eight complete cartons and 1 kg unpacked.
Reasoning. 8×8=64, whereas nine cartons require 72 kg.
Revision check. Use integer feasibility, not ordinary rounding alone.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 9: Delivery reversal
Task. If 65 kg must travel in loads of at most 8 kg, how many trips?
Worked result. At least nine trips.
Reasoning. Eight trips carry at most 64 kg; one extra trip carries the remainder.
Revision check. Packing and delivery use different whole-number decisions.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 10: Reverse 12% loss
Task. 176 kg remains after 12% rejection. Find original mass.
Worked result. 200 kg because 176÷0.88=200.
Reasoning. The remaining proportion is 88% of the original.
Revision check. Do not divide by the loss rate 0.12.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 11: Reverse 20% gain
Task. A forecast of 144 kg is 20% above a baseline. Find baseline.
Worked result. 120 kg, since 144÷1.20=120.
Reasoning. A 20% increase uses 120% of the baseline.
Revision check. Subtracting 20% of the new number gives an incorrect base.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 12: Two sequential losses
Task. 100 kg loses 10% and then 20% of the remainder. Find final mass.
Worked result. 72 kg: 100×0.9×0.8=72.
Reasoning. The second percentage applies to 90 kg, not 100 kg.
Revision check. Adding loss rates to 30% would overlook compounding.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 13: Two-day table
Task. M has rows [120,90] and [80,60]. What is M(2,1)?
Worked result. 80 kg, day 2 crop A.
Reasoning. The first index identifies row, the second column.
Revision check. Label the axes in words before extracting a cell.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 14: First-day total
Task. Find the total of first-row harvest [120,90].
Worked result. 210 kg.
Reasoning. Add crop A and crop B for that day.
Revision check. Do not mistake 120 for the row total.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 15: Second-crop total
Task. Find total of the second column [90,60].
Worked result. 150 kg across the two days.
Reasoning. Column sums retain the crop identity.
Revision check. A column sum is not a total for the second day.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 16: Matrix addition
Task. Day-block matrices M and N have the same dimensions. What permits M+N?
Worked result. Corresponding cells can be added if they describe compatible entries and units.
Reasoning. Matrix addition is entrywise, not row-total multiplication.
Revision check. Do not add a 2×2 matrix to a 2×1 matrix.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 17: Scalar doubling
Task. If a plan duplicates every day, what does 2M represent?
Worked result. Every entry of M is doubled, giving [[240,180],[160,120]].
Reasoning. A scalar multiplication changes all cells, not one chosen row.
Revision check. Whether a real operation can double capacity is a separate question.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 18: Price vector
Task. With prices [5,8], find revenue for row [120,90].
Worked result. 1320 fictional units: 120×5+90×8.
Reasoning. The order of the price vector must match the crop columns.
Revision check. The arithmetic cannot certify actual prices or sales.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 19: Second-day value
Task. Use [80,60] and prices [5,8].
Worked result. 880 fictional units.
Reasoning. 80×5=400 and 60×8=480.
Revision check. Check that a different product price is not accidentally carried over.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 20: Total two-day value
Task. Combine the two day values 1320 and 880.
Worked result. 2200 fictional units.
Reasoning. This equals 200×5 + 150×8 using column totals.
Revision check. Use the alternative calculation to verify your matrix product.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 21: Matrix product size
Task. A 2×2 harvest matrix multiplies a 2×1 price vector. State output dimension.
Worked result. The result is a 2×1 vector.
Reasoning. Inner dimensions agree and outer dimensions determine the result.
Revision check. A vector of day-level values is not a new crop matrix.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 22: Order reversal
Task. Does multiplying the 2×1 price vector by M necessarily work?
Worked result. No; the stated 2×1 times 2×2 product has incompatible inner dimensions.
Reasoning. Matrix multiplication is order-sensitive and may not be defined.
Revision check. Do not treat it as ordinary number multiplication.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 23: A switched label
Task. A price column was accidentally listed B then A. What is the consequence?
Worked result. The resulting products are mismatched and may be numerically wrong.
Reasoning. Correct the row and column labels before multiplying.
Revision check. An apparently reasonable number may still use the wrong structure.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 24: Demand shortfall
Task. Demand is 40 cartons A; only 36 are available. Find shortfall.
Worked result. Four cartons A.
Reasoning. Subtract available cartons from demand of the same product.
Revision check. Do not use surplus B cartons unless substitution is explicitly permitted.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 25: Two-product condition
Task. There are 36 A and 17 B cartons; demand is 35 A and 18 B. Is the plan feasible?
Worked result. No. A exceeds demand by one but B is short by one.
Reasoning. Meeting aggregate demand of 53 cartons is insufficient when each category has its own condition.
Revision check. State the failed constraint by name.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 26: Reserve stock
Task. Thirty-six cartons A exist; four are reserved. How many can be distributed?
Worked result. At most 32 cartons A.
Reasoning. A reserve requirement reduces available distribution stock.
Revision check. A quantity held in reserve cannot be counted twice.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 27: Minimum allocation
Task. If an order requires at least 28 cartons and 32 are available, what is the feasible integer interval?
Worked result. Any whole number from 28 through 32 inclusive.
Reasoning. Both the lower demand bound and upper stock bound must hold.
Revision check. If cartons must be whole, non-integer choices are not allowed.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 28: One-variable inequality
Task. Let x be cartons dispatched. Express ‘at least 28, at most 32’.
Worked result. 28 ≤ x ≤ 32, with x a whole number.
Reasoning. The signs face the allowed interval.
Revision check. The meaning of x and its units should be stated.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 29: Cost limit
Task. Packing costs 4 units per carton and the budget is 140 units. Maximum cartons?
Worked result. 35 cartons, since 4x≤140.
Reasoning. The answer comes from a budget inequality and integer carton count.
Revision check. A greater inventory amount does not remove the budget.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 30: A second constraint
Task. If only 32 cartons are available despite budget for 35, what is maximum dispatch?
Worked result. 32 cartons.
Reasoning. Both the stock and cost limits apply; take the tighter bound.
Revision check. Do not answer 35 simply because the last calculation produced it.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 31: Percentage points
Task. A rejection rate rises from 10% to 15%. What is the change?
Worked result. Five percentage points, or a 50% relative increase on the old rate.
Reasoning. Percentage points and percentage change are different concepts.
Revision check. State which the question asks instead of using ‘5%’ ambiguously.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 32: Compare quality rates
Task. One crop has 12 rejected of 120; another has 8 of 40. Which has higher rejection proportion?
Worked result. The second crop: 20%, compared with 10%.
Reasoning. Raw rejected counts alone are insufficient because denominators differ.
Revision check. Write each count over its own total.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 33: Uncertain sample
Task. A 20-fruit sample has two defects. Can the true harvest-wide defect rate be declared exactly 10%?
Worked result. No. The sample rate is 10%, but sampling uncertainty remains.
Reasoning. State what was measured and avoid claiming exact population truth.
Revision check. If asked, propose representative sampling across batches.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 34: Required rounding
Task. A calculation gives 12.3478 kg and asks for 3 significant figures. Answer?
Worked result. 12.3 kg.
Reasoning. The fourth significant digit is 4, so the third stays the same.
Revision check. Do not round intermediate calculations prematurely when accuracy matters.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 35: Unreasonable forecast
Task. A proposal allocates 40 A cartons from stock for 36. What quick check catches the error?
Worked result. 40×6=240 kg is needed, but only 216 kg saleable exists.
Reasoning. A reverse calculation tests the proposal against actual stock.
Revision check. Do not treat the original raw harvest as still fully available.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 36: No invented substitution
Task. A sign promises ’53 total cartons therefore all orders satisfied’. What is missing?
Worked result. The allocation by product, demand by product and any permitted substitution rules.
Reasoning. Total counts conceal category shortages.
Revision check. A responsible conclusion is conditional until these data are known.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 37: Demand matrix
Task. A table has two markets as rows and A/B as columns. What does its (1,2) cell mean?
Worked result. Market 1’s demand for crop B.
Reasoning. Interpret indices using the declared ordering.
Revision check. Never infer an entry’s meaning from its number alone.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 38: Market totals
Task. Two markets need [12,8] and [17,7] cartons of [A,B]. Find combined requirements.
Worked result. 29 cartons A and 15 cartons B.
Reasoning. Add corresponding categories, giving 44 cartons in total.
Revision check. Compare each category with available stock independently.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 39: Check supply against markets
Task. Can 36 A and 17 B cartons meet combined requirements 29 A and 15 B?
Worked result. Yes under the stated stock and product-only constraints; seven A and two B cartons remain.
Reasoning. The arithmetic establishes numerical feasibility, not delivery confirmation.
Revision check. A real plan may also need timing, vehicle and quality approval evidence.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 40: A mixed order restriction
Task. One market requires nine cartons A, and another requires 28. Can 36 A cartons meet both?
Worked result. No; the combined requirement is 37.
Reasoning. If orders are simultaneous with no new stock, the shortage is one.
Revision check. Do not round one order down to make the totals fit.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 41: Capacity trend
Task. A graph shows harvest increasing but carton output unchanged. Is that necessarily an error?
Worked result. No. Whole-carton thresholds can leave output unchanged despite a small mass increase.
Reasoning. The stair-step behaviour follows integer pack sizes.
Revision check. A graph can be flat across a range even while the underlying mass grows.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
Decision 42: Interpret a final answer
Task. Write a defensible conclusion for 36 A and 17 B cartons against 35 A and 18 B demand.
Worked result. The combined count matches demand, but the plan cannot fill all specified orders: one B carton is missing.
Reasoning. The distinction is between an aggregate equality and component-wise feasibility.
Revision check. This is the final interpretation the working was meant to support.
After marking, explain why the operation matches the quantity being asked for. In an unfamiliar question, the surface story changes but the mathematical relationship remains. Try a changed value or an added condition, and say whether your original calculation would still be valid. A justified change is evidence of understanding rather than imitation.
A useful sequence of three revision sessions
First session: calculate gross, rejected, saleable and packed figures for fresh datasets without using a matrix. Make sure every percentage refers to the right base. Second session: use small matrices to record two or three days of harvest, practise row and column totals, and match price vectors to labelled varieties. Third session: combine the work in an extended decision, including demand by product, budget, reserves and integer cartons. At the end of each session, close the answers and reproduce one calculation in your own handwriting.
Frequently asked questions
Why is dividing by 0.88 correct after a 12% loss?
The remaining mass is 88% of the original. Division by 0.88 restores the entire 100% quantity. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
Do matrices replace ordinary arithmetic?
No. Matrices organise relationships and can make repeated compatible operations concise, but the entries and units still matter. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
Can a calculator decide feasibility?
It can compute numbers; the student must interpret category, integer, cost and timing constraints. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
Why are two 50% papers both important?
K310 allocates half the subject weighting to each of its two separate written Mathematics papers. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
What is the fastest way to check a whole-carton answer?
Multiply the count by carton size and check that the next whole carton would exceed stock. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
Can a percentage rise be expressed in percentage points?
Yes, but the two values describe different comparisons; name the measure and base correctly. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
What should I do after PSLE Maths?
Retain reliable arithmetic, proportion and problem-reading habits, then connect them to equations, matrices and formal working. For stronger SEC answers, write the assumption explicitly and give the final quantity with a unit or a clear category label. A familiar calculation is not complete if it makes the wrong claim about the problem.
Next reading and verified references
For the learning bridge, see the PSLE Mathematics word-problem guide and structural transfer in secondary Mathematics. Earlier connected guides are Vol 1269 on constraints and Vol 1272 on plant transport. For accuracy, consult the current SEAB syllabus index. The next volume teaches how to report the findings without overclaiming.
