Zadanie 1a
Find its initial temperature.
Matematyka AA IB SL — maj 2026, TZ1, 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 its temperature after 12 minutes.
Zadanie 1c
State the ambient temperature predicted by the model.
Zadanie 2a
Estimate the median response time.
- Materiał graficzny
Zadanie 2b
The class frequencies are 5 for 20 ≤ h < 25, 11 for 25 ≤ h < 30, 16 for 30 ≤ h < 35, p for 35 ≤ h < 40 and q for 40 ≤ h < 45. (i) Find p and q. (ii) Estimate the mean from this table, to four significant figures.
- Materiał graficzny
Zadanie 3
A differentiable function has derivative f′(x) = 2x2 + x − 4 for all real x. Find where f is decreasing.
Zadanie 4a
Find a, b and c.
- Materiał graficzny
Zadanie 4b
The same height is written as . Find the least positive integer d.
Zadanie 5a
Find A and B.
- Materiał graficzny
Zadanie 5b
Find the area of R.
Zadanie 6
A process duration H is normally distributed with mean μ seconds and standard deviation σ seconds. It is known that P(H > 48) = 0.35 and P(H > 54 ∣ H > 48) = 0.40. Find μ and σ.
Zadanie 7a
Find C.
Zadanie 7b
Show that the sphere’s radius is cm.
Zadanie 7c
Find the volume of the sphere.
Zadanie 7d
A point P satisfies AP=3 cm and BP=2 cm. Find (i) angle BAP; (ii) the area of triangle BAP.
- Materiał graficzny
Zadanie 7e
A point P satisfies AP=3 cm and BP=2 cm. (i) Find CP. (ii) Hence show that P is inside the sphere.
Zadanie 8a
Find the balance on 1 January 2030, to the nearest dollar.
Zadanie 8b
Show that the balance first exceeds the original USD 31,000 price during 2035.
Zadanie 8c
The machine price depreciates at a constant annual percentage rate r. After one year its price is USD 29,140. Find r.
Zadanie 8d
The machine price depreciates at a constant annual percentage rate r. After one year its price is USD 29,140. For any real number t of years after 1 January 2026, model the price by 31000(1 − r/100)t. The club buys as soon as its credited account balance can…
Zadanie 9a
Show that the bag contains 11 red markers.
Zadanie 9b
Find the probability of at least seven gold markers in one play, to five significant figures.
Zadanie 9c
One play costs 6 credits. At least seven red markers win 50 credits, at least seven blue markers win B credits (a positive integer), and at least seven gold markers win 15 credits. Otherwise the prize is zero. These prize events are mutually exclusive. Let X…
Zadanie 9d
One play costs 6 credits. At least seven red markers win 50 credits, at least seven blue markers win B credits (a positive integer), and at least seven gold markers win 15 credits. Otherwise the prize is zero. These prize events are mutually exclusive. Let X…
Zadanie 9e
One play costs 6 credits. At least seven red markers win 50 credits, at least seven blue markers win B credits (a positive integer), and at least seven gold markers win 15 credits. Otherwise the prize is zero. These prize events are mutually exclusive. Let X…