Zadanie 8, Paper 2, maj 2025, TZ3, Matematyka AA IB HL
Wzorowane na: Matematyka AA IB HL — maj 2025, TZ3, Paper 2 (zadania wzorowane), pytanie 8. Treść, dane i kontekst są zmienione; sprawdzane umiejętności, format i punktacja jak w oryginale.
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Zadanie
Polecenie
A calibration network contains n sensors. Each unordered pair is scheduled to exchange three test messages. One sensor is removed after participating in exactly eight messages; all pairs among the remaining sensors complete their three messages. In total 701 messages are exchanged. Find n.
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The remaining n−1 sensors exchange messages, none involving the removed sensor. Therefore . Solving yields n=23 or n=−20. Only n = 23 is a possible sensor count. Equivalently subtract the missing 3(n − 1) − 8 messages from .
Schemat punktowania
A2: correct count 3C(n−1,2) for the remaining sensors. A1: add the eight completed messages involving the removed sensor. M1: equate the total to 701; solving is not required for this M1. A1: n=23. Alternatively A1 scheduled total 3C(n,2), A1 missing count 3(n−1)−8, A1 correct subtraction; then the same M1/A1. Alternative with N=n−1 remaining sensors: A1 correct pair-message count 3C(N,2), A1 add 8, M1 equate total to 701, A1 N=22, A1 n=23. Maximum 5 marks.
Komentarz. Paper 2: a graphic display calculator and the AA HL formula booklet may be used. Give exact values or three significant figures unless specified otherwise. Show mathematical or technology inputs and retain unrounded values between steps. Equivalent valid methods are accepted unless a method is specified.