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AMO 2027 Grades 10-12 SET 1 - Self-study Question 10

AMO · AMO 2027 Grades 10-12 SET 1 - Self-study

Question 10

**Authorized replacement.** The original Grades 10–12 source has no Question 9 stem. This question is supplied from Grades 9–11 SET 1 Q13 of the 2027 self-study edition (original booklet SET 1 Q15, statement PDF page 10, worked solution page 35). It is a replacement, not a reconstruction. The orphan source Q9 key A does not apply to it.

Given $f:\mathbb{R}\to\mathbb{R}$ is a quadratic polynomial with $$f(1)=1,\qquad f(2)=\frac12,\qquad f(3)=\frac13,$$ find $f(4)$.

Question illustration

Choose one option.
  1. $\frac14$
  2. 4
  3. $\frac7{24}$
  4. $\frac12$
  5. Insufficient information