Kenneth ChengMathematical modeling
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Find f(15).

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TOPIC 01

2024 JM01

The recurrence decreases, rather than increases, the value.

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Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Find f(15).

f(x)=f(x+1)+1,f(0)=16f(x)=f(x+1)+1,\quad f(0)=16

Official paper · jm01-2024 · I.2 · PDF 2

Official original and suggested answers ↗ · Suggested answer PDF page 5

Skills and prerequisite lessons
  1. Option A00
  2. Option B11
  3. Option C1515
  4. Option D1616
  5. Option E1717

Working and explanation

BUILD THE REASONING

Hint 1
Rearrange to express the next value.
Hint 2
Apply fifteen decreases of one.
Worked solution

  1. Each unit increase of the argument lowers the value by one.

    f(x+1)=f(x)−1f(x+1)=f(x)-1

  2. Iterate from zero.

    f(15)=16−15=1f(15)=16-15=1

B: 1.

Checks and common pitfalls: The recurrence decreases, rather than increases, the value.

Reasoning checklist · self / teacher assessment
  • Teaching assessment checklist, independently authored. Use the original paper for official marks.
  • Each unit increase of the argument lowers the value by one.
    f(x+1)=f(x)−1f(x+1)=f(x)-1
  • Iterate from zero.
    f(15)=16−15=1f(15)=16-15=1

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