Zadanie 1a
Find (i) the mean power and mean rise; (ii) the equation of Model A.
Matematyka AA IB SL — listopad 2025, 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 25 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find a and b for Model B.
Zadanie 1c
Use Model B to estimate the temperature rise at 140 W.
Zadanie 2a
Find angle LPB.
Zadanie 2b
Find LB.
Zadanie 3a
Show that .
Zadanie 3b
Hence or otherwise solve for 0° ≤ x ≤ 180°.
Zadanie 4a
Explain why the median of all 26 masses remains 18 g.
Zadanie 4b
Find L and H.
Zadanie 5a
Show that r = 24π/(2 + θ).
Zadanie 5b
Find θ.
Zadanie 6a
Given μ+Aσ=45, find A.
Zadanie 6b
Find μ and σ.
Zadanie 7a
For Fund A: (i) find the monthly credit to two decimal places; (ii) find the yearly credit; (iii) write its balance after n years as 6000+pn; (iv) show that its balance after 5 years is USD 6990.
Zadanie 7b
For Fund B, find to the nearest dollar (i) its balance after 5 years; (ii) the interest earned during those 5 years.
Zadanie 7c
(i) Write Fund B’s balance after n years in the form 6000qⁿ. (ii) Find the smallest number of complete years after which Fund B exceeds Fund A.
Zadanie 8a
For r=2.5 cm,h=7 cm: (i) show that V=78.5 cm³ to 3 significant figures; (ii) find S.
- Materiał graficzny
Zadanie 8b
For a redesigned housing V=96 cm³. Show that h = (288 − 2πr3)/(πr2).
Zadanie 8c
For V=96 cm³, show that .
Zadanie 8d
For V=96 cm³ and positive r,h, find the minimum S and its corresponding r.
Zadanie 9a
Find (i) the maximum displacement; (ii) the maximum velocity, over t≥0.
Zadanie 9b
Find (i) the minimum value of s(t) for t≥0; (ii) s(4.6).
Zadanie 9c
Hence find the total distance travelled during the first 4.6 seconds.
Zadanie 9d
State the first positive time T at which the stage crosses the reference mark.
Zadanie 9e
The stage crosses the reference mark at T,2T,3T,… . Let uₙ be its greatest distance from the mark during (n−1)T<t<nT. These distances form a geometric sequence. Find (i) its common ratio; (ii) the total distance travelled if the model continues indefinitely.