Zadanie 1a
Find the final balance of reserve A.
Matematyka AA IB SL — maj 2022, 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 26 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find r so that both reserves have equal final balances.
Zadanie 1c
Find the interest earned in reserve B at the matching rate.
Zadanie 2a
Find x.
Zadanie 2b
Find the population standard deviation.
Zadanie 3a
Express the area of one hole in terms of θ.
Zadanie 3b
The remaining plate has area 25π − 9 cm². Find θ.
Zadanie 4a
Show that 2k²−k+0.105=0.
Zadanie 4b
Find k and justify your choice.
Zadanie 4c
Hence find E(X).
Zadanie 5a
Find the time when the particle is at rest.
Zadanie 5b
Find its acceleration when it changes direction.
Zadanie 5c
Find its total distance travelled over the given interval.
Zadanie 6a
Find x.
Zadanie 6b
Find P(A′|B′).
Zadanie 7a
Find AV.
Zadanie 7b
Find the base edge AB.
Zadanie 7c
Find the height VX.
Zadanie 7d
An open-top rectangular container has internal dimensions 3x by x by y centimetres, with x,y>0. Its volume is 71.6 cm³. Ignore wall thickness. Find the minimum material area needed for its base and four sides.
Zadanie 8a
For the graph of f, (i) state the vertical asymptote; (ii) find the horizontal asymptote.
Zadanie 8b
(i) Find the inverse function. (ii) Prove algebraically that reflecting the graph of f in the y-axis and then in the x-axis produces the graph of its inverse.
Zadanie 8c
The graphs of f and its inverse intersect at x=p and x=q, where p<q. (i) Find p,q. (ii) Hence find the area enclosed by the two curves.
Zadanie 9a
Find the probability that a line-A piece has thickness below 117 μm.
Zadanie 9b
Among 15 independently selected line-A pieces, find the probability that exactly 6 have thickness below 117 μm.
Zadanie 9c
A piece is selected from the combined output. (i) Find the probability its thickness is below 117 μm. (ii) Given that its thickness is below 117 μm, find the probability it came from line A.
Zadanie 9d
Line A is adjusted: its mean stays 120 μm but its standard deviation becomes σ>0. Line B and the output proportions are unchanged. The combined probability of thickness below 117 μm is now 0.18. Find σ.