Zadanie 1a
Find the chord length AB.
Matematyka AA IB SL — maj 2022, TZ2, Paper 2 (zadania wzorowane)
Zadania wzorowane na pytaniach z tego arkusza: te same umiejętności, format i punktacja, inne dane i kontekst. Treści arkusza IB nie publikujemy.
W bazie 25 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find the area of the major sector between OA and OB.
Zadanie 2
A function g satisfies g′(x) = 4x3 − 6e−2x and g(0)=8. Find g(x).
Zadanie 3a
Find A’s annual grant in 2025, to the nearest credit.
Zadanie 3b
Use the least-squares regression S=at+b for B to show that its modelled grant in 2025 exceeds A’s.
Zadanie 4
Independent events A,B satisfy P(A)=2P(B) and P(A∪B)=0.72. Find P(B).
Zadanie 5a
State the median warm-cache latency.
- Materiał graficzny
Zadanie 5b
Verify that the warm-cache reading 0.60 s is not an outlier.
- Materiał graficzny
Zadanie 5c
Explain why the warm-cache mean appears likely to exceed its median.
- Materiał graficzny
Zadanie 5d
Comment on whether the plots provide evidence of greater latency with a cold cache.
- Materiał graficzny
Zadanie 6a
Find when it changes direction.
Zadanie 6b
Find all times when acceleration is −3 m/s².
Zadanie 6c
Find its acceleration when its speed is greatest.
Zadanie 7a
Find AC.
Zadanie 7b
Find the site’s area.
Zadanie 7c
Find angle CAB.
Zadanie 7d
Find BD for the required area division.
Zadanie 8a
Find the initial contents of (i) B; (ii) A to three significant figures.
Zadanie 8b
Find every time when the two contents are equal.
Zadanie 8c
Find the total time in[0,8] when B’s content increases faster than A’s.
Zadanie 9a
Find σ.
Zadanie 9b
Find the probability of a breach on a randomly selected day.
Zadanie 9c
The server is operated for six days next week. Find the probability of at least one breach.
Zadanie 9d
Given at least one breach in those six days, find the probability of fewer than four breaches.
Zadanie 9e
The monthly service target requires at least 22 non-breach days out of 24 operating days. After 17 days,16 have met the target. Find the probability of meeting the monthly requirement.