Zadanie 1a
Find a and b.
Matematyka AA IB SL — maj 2025, 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 28 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Use this model to estimate the energy use of a 12-hour cycle.
Zadanie 2a
Calculate VX.
- Materiał graficzny
Zadanie 2b
Calculate AC.
Zadanie 2c
Find the angle between edge VC and the base, in degrees.
Zadanie 3a
Find the intervals on which f is decreasing.
Zadanie 3b
Find the interval on which its graph is concave up.
Zadanie 4
In the expansion of (3x + k)8, where k is an integer, the coefficient of x4 equals 9.072 × 104. Find all possible values of k.
Zadanie 5a
Find its maximum speed over this interval.
Zadanie 5b
Find the total distance travelled during these 5.5 seconds.
Zadanie 5c
Find the acceleration when the shuttle reverses direction for the second time after it starts.
Zadanie 6
A circular window is divided by chord AB. Its minor segment P has area 18 cm2. The triangle OAB, labelled Q, and segment P have areas in the ratio P : Q = 2 : 3. The circle has centre O, radius r cm, and with 0 < θ < π.…
- Materiał graficzny
Zadanie 7a
Find JL.
- Materiał graficzny
Zadanie 7b
Find the ground distance BL.
- Materiał graficzny
Zadanie 7c
Find the bearing of B from L.
Zadanie 7d
Find how many minutes the service vehicle from L takes to reach B.
Zadanie 7e
Determine which service vehicle arrives first. Justify your conclusion.
Zadanie 8a
Find P(R < 990).
Zadanie 8b
The highest 15% of resistances exceed r ohms. Find r to four significant figures.
Zadanie 8c
What percentage of resistors pass inspection?
Zadanie 8d
Find the probability that a tray contains at least 20 resistors that pass.
Zadanie 8e
Find the probability that exactly three trays in a batch each contain at least 20 passing resistors.
Zadanie 8f
At a second factory resistance is normal with unknown mean μ and standard deviation σ. Exactly 84% pass the same inspection thresholds. The fraction below 990 Ω is three times the fraction above 1030 Ω. Find μ.
Zadanie 9a
Find the maximum height in cycle 6 of run 1.
Zadanie 9b
Find the distance travelled in run 1 immediately before contact 6.
Zadanie 9c
Show that a run starting at height x has total travel distance d = 7x.
Zadanie 9d
Write down d1.
Zadanie 9e
Run 2 starts at 11.6 m. The 20 values d1, d2, …, d20 form an arithmetic sequence. Which run is the first to have total travel below 40 m?