STPM Management Mathematics 950 common mistakes
STPM Management Mathematics 950 · Understand the traps and how to avoid them.
When converting a linear programming model from word problem to algebra, candidates omit or mis-sign a constraint - most often writing the labour-hours limit as ≥ instead of ≤, or forgetting a non-negativity condition entirely - and then optimise the wrong feasible region without noticing.
Candidates translate prose to inequalities in one pass and never re-read the original wording against the algebra. The phrase 'at least' and 'no more than' are easily swapped under exam time pressure, and non-negativity is treated as an implicit assumption rather than a written constraint.
What to do instead
After writing the model, re-read each sentence of the question and tick off the corresponding constraint, checking the direction word by word. Always write x ≥ 0, y ≥ 0 explicitly. Test one arbitrary feasible point in each constraint to confirm it satisfies the intended real-world limit.
In the simplex method, candidates choose the leaving row by dividing the pivot column entries by the wrong column (the RHS column instead of the entering column), or ignore negative and zero entries in the ratio test, producing an infeasible or cycling tableau.
The ratio test is mechanical and candidates memorise the procedure without understanding that only strictly positive entries in the entering column are eligible. Zero entries produce a zero ratio that is mistakenly treated as the minimum, and negative entries invert the inequality.
What to do instead
Before dividing, cross out every entry in the pivot column that is ≤ 0. Compute ratios only for the remaining rows using RHS ÷ pivot-column entry. If all entries are ≤ 0 the problem is unbounded - state that rather than forcing a pivot. Verify the new tableau by checking the objective row and that all RHS values remain non-negative.
In critical path analysis, candidates compute earliest and latest event times but then read the float of activities off the wrong node pair, or identify the critical path as the one with the largest total duration rather than zero total float, so the reported project duration and critical activities disagree.
Forward and backward passes are learned as separate procedures, and the link between them - total float = latest finish minus earliest start minus duration - is not practised. Candidates also confuse free float with total float, which changes which activities are called critical.
What to do instead
Always draw the network with activity-on-arrow or activity-on-node conventions and label ES, EF, LS, LF on every activity. Compute total float for each activity explicitly and list activities with zero float as the critical path. Cross-check that the sum of durations along that path equals the project completion time from the forward pass.
In decision analysis under uncertainty, candidates apply the wrong criterion - using maximin when the question asks for minimax regret, or reporting an expected monetary value without the probabilities summing to one - and give a recommendation that does not match the stated decision rule.
The four criteria (maximin, maximax, Hurwicz, minimax regret) share similar arithmetic and candidates skim the instruction. Regret tables require subtracting each payoff from the row maximum, and candidates often subtract from the column maximum instead, reversing the logic.
What to do instead
Underline the named criterion before starting. For minimax regret, build the regret table by subtracting each entry from the best payoff in its state-of-nature column, then take the maximum regret per alternative and choose the minimum. Check that probabilities sum to 1 before computing EMV, and state the chosen alternative explicitly with its value.
In EOQ problems, candidates plug annual demand into the formula where the holding cost per unit per year is required, or use the per-order cost in the wrong position, and report an order quantity in the wrong units or of absurd magnitude without sanity-checking it.
The formula Q = sqrt(2DS/H) mixes symbols from different sources and candidates memorise the letters without tracking units. Holding cost given as a percentage of unit cost is often used directly rather than multiplied by the unit price.
What to do instead
Write the units beside every symbol before substituting: D in units per year, S in currency per order, H in currency per unit per year. If holding cost is a percentage, convert H = i × unit cost first. After computing Q, check that total annual ordering cost and total annual holding cost are equal at the EOQ - they must be - and confirm the magnitude is plausible against annual demand.
In queueing theory, candidates use the M/M/1 formulas for an M/M/s system, or report the average number in the system when the question asks for the average number in the queue, and fail to check the stability condition that utilisation must be less than one.
The single-server and multi-server formulas look similar and candidates default to the simpler one. The distinction between L, Lq, W and Wq is glossed over, and utilisation ρ = λ/(sμ) is rarely computed, so an unstable system is analysed as if it had a steady state.
What to do instead
First compute ρ = λ/(sμ) and state that ρ < 1 is required for a steady state; if ρ ≥ 1, say the queue grows without bound. Then select the correct formula set for the number of servers. Use Little's Law (L = λW, Lq = λWq) to derive the quantity asked for and to cross-check your answer.
In two-person zero-sum games, candidates find a saddle point by comparing row minima and column maxima but mislabel which is the maximin and which the minimax, or declare a saddle point when the two values differ, then give a mixed-strategy answer when a pure strategy exists.
The maximin and minimax values are computed by similar-looking scans and candidates rush the comparison. When no saddle point exists, candidates also forget to reduce the payoff matrix by dominance before solving, producing unnecessary algebra and errors.
What to do instead
Write the row minima in a column and the column maxima in a row, then compare the largest row minimum with the smallest column maximum. A saddle point exists only if these are equal; state the value and the optimal pure strategies. If they differ, apply dominance to reduce the matrix, then solve the 2×2 game with the standard probability formulas and verify the value lies between the maximin and minimax.
In time series forecasting, candidates compute a moving average and then use it as the forecast for the same period rather than the next period, or centre a moving average incorrectly when the period is even, so the forecast is shifted by half a cycle and the seasonal pattern is misread.
The distinction between the smoothed value and the one-step-ahead forecast is subtle and rarely stated explicitly in teaching. Even-order moving averages require a two-stage centring step that candidates skip, leaving the series misaligned with the original data.
What to do instead
Label each smoothed value with the period it forecasts, not the period it summarises. For an even order, compute the centred moving average by averaging two consecutive moving averages and align it to the middle period. Always plot or tabulate the original and smoothed series side by side to confirm alignment before interpreting trend or seasonality.
In index number construction, candidates compute a Laspeyres or Paasche index using the wrong year's quantities as weights, or fail to apply the base-year = 100 convention when chaining or splicing two series with different bases.
Laspeyres and Paasche differ only in whether base-period or current-period quantities are used, and the formulas are memorised as symbols without the economic meaning. Splicing requires rescaling one series onto the other's base, which candidates attempt by simple averaging.
What to do instead
State explicitly which year's quantities you are using before substituting: base-year quantities for Laspeyres, current-year quantities for Paasche. To splice, multiply the old series by the ratio of the new base value to the old base value at the overlap period, then continue. Check that a price index with unchanged prices equals 100.
In financial mathematics, candidates apply the nominal annual rate directly to a period shorter than a year without dividing by the compounding frequency, or discount a cash flow by the wrong number of periods, producing present values that ignore compounding entirely.
The nominal rate i per annum is confused with the periodic rate i/m, and the number of periods n is confused with the number of years. Candidates also mix simple and compound discounting within one problem.
What to do instead
Write down m (compounding periods per year), the periodic rate i/m, and the total number of periods n×m before any calculation. Convert every time given in the question to periods, not years. Where payments occur at different dates, draw a time line and discount each cash flow to time zero separately, then sum.
In management modelling questions, candidates set up a model, solve it, and then present the mathematical answer without interpreting it in the context of the original scenario - for example reporting an optimal order quantity of 412.7 units or a decision to produce a fractional number of machines without rounding and stating the practical implication.
Candidates treat the final number as the answer and stop. Interpretation requires re-reading the question's decision context and recognising that continuous models give fractional solutions that must be translated into actionable integers or policies.
What to do instead
Finish every answer with a sentence that states the recommendation in the units and terms of the original problem, including any rounding and its cost consequence. Where the model is continuous but the decision is discrete, evaluate the integer values either side of the optimum and compare objective values before recommending.