Zadanie 1a
Find a and b for the least-squares line of T on L, T=aL+b.
Matematyka AA IB HL — 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 37 zadań z tego arkusza, razem 110 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 1d
Find p and q for the regression of L on T, L=pT+q.
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
Find θ.
- Materiał graficzny
Zadanie 4b
Hence find r.
Zadanie 5a
Find its maximum displacement on this interval.
Zadanie 5b
Find the time intervals on which acceleration is negative.
Zadanie 6a
State a.
- Materiał graficzny
Zadanie 6b
Rotate R through a full turn about the y-axis. Find its volume.
Zadanie 7a
Find P(0.5≤X<1.5).
Zadanie 7b
Find (i) b; (ii) a,c.
Zadanie 7c
Find E(Y).
Zadanie 8a
Show that .
- Materiał graficzny
Zadanie 8b
Find dr/dt when h=3 cm.
Zadanie 9a
How many arrangements have no two silver objects adjacent?
Zadanie 9b
Require that no two silver objects are adjacent. How many arrangements additionally have silver objects at both ends?
Zadanie 10a
(i) Find μ,σ. (ii) Find P(15<T<22).
Zadanie 10b
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 10c
The workshop can accommodate 32 attendees. Find the greatest number of registrations for which the probability that everyone who arrives can be accommodated is at least 0.99.
Zadanie 11a
State d.
Zadanie 11b
Show that b=7.
Zadanie 11c
Find c.
Zadanie 11d
Sketch y=f(x) for −25≤x≤25, labelling asymptotes, axis intercepts and local extrema.
Zadanie 11e
Find all k for which |f(x)|=k has four real solutions.
Zadanie 11f
Find the vertical asymptotes of y=1/g(x).
Zadanie 12a
Use Euler’s method with step length 0.02 to estimate y(1.10).
Zadanie 12b
Use 1/y2 = −4z to show that dz/dx − 2z/x = 1.
Zadanie 12c
Hence solve the differential equation explicitly. You may use z = −1/(4y2).
Zadanie 12d
Find the maximal domain and range of f.
Zadanie 12e
Use the curve’s shape to explain whether the Euler estimate at x=1.10 is above or below the exact value.