Zadanie 1a
State the mode.
Matematyka AA IB SL — maj 2026, 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 27 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find (i) the mean; (ii) the median; (iii) the population standard deviation.
Zadanie 1c
Draw a box-and-whisker plot on the scale provided.
- Materiał graficzny
Zadanie 2a
Find (i) q; (ii) p and r.
- Materiał graficzny
Zadanie 2b
Find the probability that a randomly chosen worker subscribes to both.
Zadanie 2c
Show that membership of C and membership of D are not independent.
Zadanie 3
Two vertical structures AD and BC stand on level ground DC, with DC=60 m. A is above B. The elevation angle BDC is 14°, and the angle ABD between the two sightlines is 40°. Find the height AD.
- Materiał graficzny
Zadanie 4a
Show that h = 720/(πr2).
Zadanie 4b
Show that A = πr2 + 1440/r.
Zadanie 4c
Use a graph or another method to find (i) the least material area; (ii) the corresponding radius.
Zadanie 5a
Find the initial velocity.
Zadanie 5b
Find the total distance travelled during the first six seconds.
Zadanie 5c
Find the time when acceleration is 17 m/s².
Zadanie 6a
Find p.
Zadanie 6b
Find P(X = 12 ∣ X ≥ 9).
Zadanie 7a
Find (i) the common ratio of the geometric sequence; (ii) its first term.
Zadanie 7b
Express Gₙ in terms of n.
Zadanie 7c
For the arithmetic sequence find (i) the first term; (ii) the common difference; (iii) the nth term.
Zadanie 7d
Find the smallest positive integer n for which Aₙ>Gₙ.
Zadanie 8a
For a randomly selected type-R battery find the probability that its duration is (i) below 224 minutes; (ii) between 224 and 242 minutes; (iii) between 224 and 242 minutes given it exceeds 224 minutes.
Zadanie 8b
For type S, P(S<200)=0.30854 and P(200<S<224)=0.62465. Find μ and σ.
Zadanie 8c
For type S, P(S<200)=0.30854 and P(200<S<224)=0.62465. Independently select one battery of each type. Find the probability that at least one lasts more than 224 minutes.
Zadanie 9a
Sketch y=h(x), labelling the maximum point.
Zadanie 9b
Find h′(x).
Zadanie 9c
(i) Show that . (ii) Find the inflection point P.
Zadanie 9d
P is the inflection point of the pulse curve. Let R be the region enclosed by the curve and the horizontal line through P. Find its area.
Zadanie 9e
P is the inflection point of the pulse curve. R is the region enclosed by this curve and the horizontal line through P. The area under the pulse from x=0 to x=k is twice the area of R, with 0≤k≤π/3. Find k.