Choosing a model and naming what it ignores · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Model predictions depend on assumptions

Mathematics · Mathematical Thinking · ages 14-15
Name ______________________   Date ____________

  1. A taxi model gives C = 5 + 2d pounds for d kilometres. For a 7 km trip, the actual bill is £23. How many pounds higher is the actual bill than the prediction?

    Answer: ______________

  2. T = 10 + 4d models travel time T in minutes for distance d in kilometres. What does d represent?

    • Time in minutes
    • Distance in kilometres
    • Speed in kilometres per minute
    • Starting delay in minutes

  3. A gym charges a 20 pound joining fee plus 15 pounds per month. Which formula gives total cost C for m months?

    • C equals 20 plus 15m
    • C equals 15 plus 20m
    • C equals 35m

  4. Jay says a model that fitted last year perfectly is automatically safe next year. Is Jay right?

    Circle one:   True   False

  5. In a hypothetical case, a weather-only model predicts 200 visitors. A football final reduces attendance to 120. What does this show?

    • The final affects attendance more than sunshine.
    • The final affects attendance but is missing from the model.
    • The next match weekend will also have an observed count of 120 visitors.

  6. A hall uses an attendance forecast to plan seats. For this check, it accepts an error of at most 15 people. The forecast is 240 and the observed count is 228. Which conclusion is supported?

    • It fails: the gap is 12 people.
    • It passes, so the next event's forecast is reliable.
    • It fails: the forecast is 12 people below the count.
    • It passes: the 12-person gap is within 15.

  7. Two population forecasts differ only in their starting counts, by 100 people. Both use 10% annual growth. How far apart are their predictions after two years?

    • 100 people
    • 110 people
    • 121 people
    • 120 people

  8. D = 3 + 2h predicts snow depth in cm after h hours. Snow stops after one hour, with no melting or settling. Which assumption fails when predicting the depth after four hours?

    • The depth is 3 cm at the start.
    • The depth rises by 2 cm every hour.
    • The clock measures elapsed time in hours.

  9. A forecast changes a lot when its starting value and growth rate are both changed. You want to identify which uncertainty matters more for a five-year prediction. Which follow-up is a fair sensitivity test?

    • Test each plausible change separately at five years.
    • Change both again and compare a ten-year prediction.
    • Compare equal numerical changes in people and percent.

  10. A membership model is C = 24 + 12m, with C in pounds and m paid months. It excludes extra charges. Which report is supported for six months?

    • £96, including any extra charges.
    • £96, even if the monthly price changes before the six months finish.
    • £96, if fees stay fixed and no extra charges apply.
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Model predictions depend on assumptions W1-mt_UtK9aauJ6e-s1

  1. 4 · The prediction is 5 + 2 × 7 = £19. The actual bill is £23, which is £4 higher.
  2. Distance in kilometres · The variable definitions say that d is distance in kilometres. The coefficient 4 represents minutes per kilometre.
  3. C equals 20 plus 15m · The 20 pound fee is paid once and each month adds 15.
  4. False · Past fit is useful evidence, but it does not guarantee future predictions. Conditions may change.
  5. The final affects attendance but is missing from the model. · The stated event effect identifies a relevant factor the model leaves out. The information does not compare the sizes of the sunshine and football effects.
  6. It passes: the 12-person gap is within 15. · The gap is 240 - 228 = 12 people, within the allowed 15. This check meets the tolerance, without guaranteeing future performance.
  7. 121 people · The starting gap grows by the same annual multiplier: 100 × 1.10 × 1.10 = 121 people.
  8. The depth rises by 2 cm every hour. · The formula keeps adding 2 cm each hour. Once snowfall stops, the continuing depth increase no longer matches the stated situation.
  9. Test each plausible change separately at five years. · Test plausible uncertainty changes separately, holding other inputs fixed and using the same five-year output. A combined change cannot reveal the separate effects.
  10. £96, if fees stay fixed and no extra charges apply. · 24 + 12 × 6 = £96. That prediction assumes the stated fees stay fixed and no excluded extra charges apply.
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