Zadanie 1a
Find a and b for the least-squares line of T on L, T=aL+b.
Matematyka AA IB SL — maj 2026, TZ3, 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
State Pearson’s correlation coefficient.
Zadanie 1c
Predict the cooling time at 1150 revolutions per minute using the regression of T on L.
Zadanie 2a
Express (i) tan47°; (ii) tan18° in terms of h,x.
- Materiał graficzny
Zadanie 2b
Hence find x.
Zadanie 2c
Find h.
Zadanie 3a
State the initial reading.
Zadanie 3b
Find k.
Zadanie 3c
When does the reading reach 16°C?
Zadanie 4a
Express (i) a; (ii) b in terms of k.
Zadanie 4b
Find k.
Zadanie 4c
Hence find E(X).
Zadanie 5a
Find θ.
- Materiał graficzny
Zadanie 5b
Hence find r.
Zadanie 6a
Find its maximum displacement on this interval.
Zadanie 6b
Find the time intervals on which acceleration is negative.
Zadanie 7a
Determine (i) the sphere centre; (ii) its radius.
Zadanie 7b
Find the volume of the sphere.
Zadanie 7c
(i) Write a volume equation for the cuboid using x and y. (ii) Show that A = 4x3 + 1728/x + 864/x2.
Zadanie 7d
(i) Find the minimum surface area A. (ii) Find the second derivative of A at x=k. (iii) Use it to justify that this stationary value is a minimum.
Zadanie 8a
(i) Find μ,σ. (ii) Find P(15<T<22).
Zadanie 8b
There are 24 registrations. Find (i) the probability that at least 16 attend; (ii) given that at least 16 attend, the probability that more than three fail to attend.
Zadanie 9a
Express a₁ in terms of r.
Zadanie 9b
Show that q=r².
Zadanie 9c
(i) Show that 69r2 − 98r + 29 = 0. (ii) Find r. (iii) Hence find a₁.
Zadanie 9d
Prove that cₙ is arithmetic.
Zadanie 9e
Find the largest integer k for which C₂₄<0.