G2 Mathematics K210 modelling becomes more reliable when learners ask how the answer should respond to a small change in one input. This is a practical form of sensitivity checking: hold the rest of the model fixed, perturb one quantity, and predict what the output should do.
This ninety-fourth Learner’s Guide extends Vol 0082 Direction-of-Change Checks. Direction asks whether an answer moved the right way; sensitivity asks how strongly, smoothly or discontinuously it should respond when one input changes.
The sensitivity protocol
Choose one input, hold other relevant quantities fixed, predict the output direction, then compare two nearby cases. Ask whether the response is linear, reciprocal, squared, cubed, thresholded or dependent on a changing denominator.
1. unit price
Perturbation: increase unit price while quantity fixed.
Expected response: total cost should increase proportionally. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
2. quantity
Perturbation: increase quantity while unit price fixed.
Expected response: total cost should increase. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
3. fixed fee
Perturbation: increase fixed fee while usage fixed.
Expected response: total cost should rise by same fee change. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
4. discount rate
Perturbation: increase discount with marked price fixed.
Expected response: sale price should decrease. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
5. markup rate
Perturbation: increase markup with cost fixed.
Expected response: selling price should increase. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
6. interest rate
Perturbation: increase positive rate with principal/time fixed.
Expected response: interest and accumulated amount should increase. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
7. time under simple interest
Perturbation: increase time with other inputs fixed.
Expected response: interest should increase linearly. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
8. growth rate
Perturbation: increase positive growth rate.
Expected response: future value should increase. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
9. depreciation rate
Perturbation: increase depreciation rate.
Expected response: future value should decrease. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
10. original value in percentage change
Perturbation: increase original while percentage fixed.
Expected response: absolute change increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
11. numerator
Perturbation: increase positive numerator with denominator fixed.
Expected response: fraction increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
12. denominator
Perturbation: increase positive denominator with numerator fixed.
Expected response: fraction decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
13. both ratio parts common scale
Perturbation: multiply both by same positive factor.
Expected response: ratio stays unchanged. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
14. one ratio part
Perturbation: increase first part with second fixed.
Expected response: first-to-second ratio increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
15. distance
Perturbation: increase distance with time fixed.
Expected response: speed required increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
16. time
Perturbation: increase time with distance fixed.
Expected response: required average speed decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
17. speed
Perturbation: increase speed with distance fixed.
Expected response: travel time decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
18. radius circumference
Perturbation: increase radius.
Expected response: circumference increases linearly. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
19. radius area
Perturbation: increase radius.
Expected response: area increases faster because radius is squared. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
20. side square area
Perturbation: increase side.
Expected response: area increases quadratically. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
21. length rectangle area
Perturbation: increase one side with other fixed.
Expected response: area increases linearly. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
22. length rectangle perimeter
Perturbation: increase one side with other fixed.
Expected response: perimeter increases linearly. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
23. scale factor
Perturbation: increase enlargement factor.
Expected response: image lengths increase. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
24. scale factor area
Perturbation: increase length factor.
Expected response: area factor rises as square. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
25. scale factor volume
Perturbation: increase length factor.
Expected response: volume factor rises as cube. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
26. mean one value
Perturbation: increase one observation with count fixed.
Expected response: mean increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
27. mean count with added equal-to-mean value
Perturbation: add value equal to current mean.
Expected response: mean stays unchanged. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
28. mean add high value
Perturbation: add value above current mean.
Expected response: mean increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
29. mean add low value
Perturbation: add value below current mean.
Expected response: mean decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
30. frequency one category
Perturbation: increase category count with total allowed to change.
Expected response: raw frequency increases but relative frequency direction depends on total. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
31. favourable outcomes fixed total
Perturbation: increase favourable count.
Expected response: probability increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
32. total outcomes fixed favourable
Perturbation: increase total outcomes.
Expected response: probability decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
33. remove unfavourable outcome
Perturbation: favourable count fixed, total decreases.
Expected response: probability increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
34. remove favourable outcome
Perturbation: both favourable and total decrease.
Expected response: direction depends on proportions. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
35. gradient rise
Perturbation: increase vertical change with horizontal change fixed positive.
Expected response: gradient increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
36. gradient run
Perturbation: increase positive horizontal change with rise fixed.
Expected response: gradient magnitude decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
37. linear coefficient
Perturbation: increase positive slope coefficient.
Expected response: line becomes steeper upward. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
38. intercept
Perturbation: increase y-intercept with slope fixed.
Expected response: line shifts upward without changing slope. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
39. translation x
Perturbation: increase horizontal translation amount.
Expected response: image moves farther horizontally. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
40. translation y
Perturbation: increase vertical translation amount.
Expected response: image moves farther vertically. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
41. rotation angle
Perturbation: change angle while centre fixed.
Expected response: distance from centre remains unchanged. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
42. reflection line shift
Perturbation: move mirror line.
Expected response: image position changes but size remains. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
43. sample size
Perturbation: increase observations while pattern stable.
Expected response: mean may stabilise but does not have predetermined direction. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
44. outlier magnitude
Perturbation: move one high outlier higher.
Expected response: mean rises; median may remain unchanged. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
45. outlier low
Perturbation: move one low outlier lower.
Expected response: mean falls; median may remain unchanged. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
46. range maximum
Perturbation: increase maximum with minimum fixed.
Expected response: range increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
47. range minimum
Perturbation: increase minimum with maximum fixed.
Expected response: range decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
48. all values shift
Perturbation: add same constant to all observations.
Expected response: mean/median shift; range unchanged. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
49. all values scale positive
Perturbation: multiply all values by factor.
Expected response: mean/median/range scale by factor. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
50. class width
Perturbation: increase width with same frequency.
Expected response: frequency density decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
51. population size
Perturbation: increase population with cases fixed.
Expected response: case rate decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
52. case count
Perturbation: increase cases with population fixed.
Expected response: case rate increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
53. area population density
Perturbation: increase area with people fixed.
Expected response: density decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
54. people population density
Perturbation: increase people with area fixed.
Expected response: density increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
55. capacity
Perturbation: increase capacity with usage fixed.
Expected response: utilisation decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
56. usage
Perturbation: increase usage with capacity fixed.
Expected response: utilisation increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
57. budget
Perturbation: increase budget with spending fixed.
Expected response: percentage used decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
58. spending
Perturbation: increase spending with budget fixed.
Expected response: percentage used increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
59. revenue
Perturbation: increase revenue with cost fixed.
Expected response: profit increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
60. cost
Perturbation: increase cost with revenue fixed.
Expected response: profit decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
61. profit with revenue fixed
Perturbation: increase profit.
Expected response: margin increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
62. profit with cost fixed
Perturbation: increase profit.
Expected response: markup increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
63. exchange rate quoted SGD/USD
Perturbation: increase SGD per USD for fixed USD.
Expected response: SGD amount increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
64. reciprocal exchange quote
Perturbation: increase one quoted direction.
Expected response: reciprocal direction decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
65. conversion metres to centimetres
Perturbation: increase metres.
Expected response: centimetres increase with fixed factor. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
66. measurement resolution
Perturbation: coarser rounding unit.
Expected response: possible true-value interval widens. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
67. lower bound input
Perturbation: raise lower bound with other positive factor fixed.
Expected response: lower bound on product rises. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
68. upper bound input
Perturbation: raise upper bound.
Expected response: upper bound on product rises. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
69. denominator lower bound
Perturbation: raise denominator lower bound.
Expected response: maximum possible quotient can fall. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
70. constraint minimum
Perturbation: raise minimum required value.
Expected response: feasible set shrinks or stays same. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
71. constraint maximum
Perturbation: lower maximum allowed value.
Expected response: feasible set shrinks or stays same. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
72. container capacity
Perturbation: increase capacity per container.
Expected response: containers needed cannot increase. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
73. items total
Perturbation: increase items with capacity fixed.
Expected response: containers needed cannot decrease. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
74. work rate
Perturbation: increase work rate with total work fixed.
Expected response: completion time decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
75. cash burn
Perturbation: increase burn rate with cash fixed.
Expected response: runway decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
76. cash balance
Perturbation: increase cash with burn fixed.
Expected response: runway increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
77. flow rate
Perturbation: increase flow with volume fixed.
Expected response: fill/drain time decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
78. data rate
Perturbation: increase transfer rate with file size fixed.
Expected response: transfer time decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
79. productivity
Perturbation: increase output per hour with target fixed.
Expected response: required hours decrease. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
80. fuel efficiency km/L
Perturbation: increase efficiency with distance fixed.
Expected response: fuel needed decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
81. fuel consumption L/100km
Perturbation: increase consumption with distance fixed.
Expected response: fuel needed increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
82. probability independent stage
Perturbation: increase one path probability with others fixed.
Expected response: path product increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
83. weighted value
Perturbation: increase one value with positive weight fixed.
Expected response: weighted mean increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
84. weight of high value
Perturbation: increase weight on above-mean value.
Expected response: weighted mean moves upward. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
85. weight of low value
Perturbation: increase weight on below-mean value.
Expected response: weighted mean moves downward. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
86. direct proportion constant
Perturbation: increase proportionality constant with x fixed positive.
Expected response: y increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
87. inverse proportion constant
Perturbation: increase constant with x fixed positive.
Expected response: y increases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
88. inverse x
Perturbation: increase x with constant fixed positive.
Expected response: y decreases. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
89. quadratic positive x squared coefficient
Perturbation: increase positive coefficient.
Expected response: positive y contribution grows for nonzero x. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
90. sequence common difference
Perturbation: increase difference.
Expected response: later arithmetic terms increase relative to start. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
91. geometric ratio positive above one
Perturbation: increase ratio.
Expected response: later terms grow faster. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
92. geometric ratio between zero and one
Perturbation: increase ratio toward one.
Expected response: decay becomes slower. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
93. rounding threshold
Perturbation: small input change crosses rounding boundary.
Expected response: displayed answer can jump discretely. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
94. integer ceiling
Perturbation: small input increase may increase required whole count only at threshold.
Expected response: sensitivity is piecewise. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
95. integer floor
Perturbation: small input increase may leave maximum whole count unchanged until threshold.
Expected response: do not expect continuous change. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
96. graph scale
Perturbation: change axis scale only.
Expected response: underlying data do not change though visual steepness does. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
97. unit choice
Perturbation: change units only.
Expected response: physical quantity stays invariant while numerical magnitude changes. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
98. representation
Perturbation: switch equation to graph.
Expected response: relationship stays same though visual features change. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
99. sensitivity final rule
Perturbation: change one input at a time.
Expected response: observe direction, size and threshold of output change. For practice, calculate a baseline case and a slightly changed case. Then explain whether the output changed less, equally, more, or discontinuously relative to the input change.
If the result moves opposite to the expected response, inspect sign, reciprocal structure, denominator, exponent, conversion or constraint. If several inputs change together, sensitivity must be analysed one variable at a time before combining effects.
Sensitivity is not always linear
A 10% change in an input does not always produce a 10% change in output. Squared and cubed relations amplify changes; reciprocal relations reverse direction; averages dilute one observation’s effect; integer constraints create thresholds. The learner should identify the relationship before predicting magnitude.
Links
Use the Mathematics Hub, Vol 0086 Bounding Checks, Vol 0074 Invariant Hunting, the Examination Craft hub and the PSLE Learner’s Guide.
Official-source discipline
For current K210 requirements, use the official SEAB 2027 G2 syllabus directory and linked Mathematics syllabus. Sensitivity checking is an eduKateSengkang reasoning framework, not an additional SEAB syllabus topic.
Final rule
Do not ask only whether the answer is plausible. Ask how it should react if one input changes. A model that responds in the wrong direction, at the wrong scale or across the wrong threshold is telling you where to check.
