Zadanie 1a
Show that f(x) = 2x − 1 − 6/x.
Matematyka AA IB SL — maj 2025, 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 28 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Hence find .
Zadanie 2a
Find the area of fabric in the sector.
Zadanie 2b
Find the radius of the open base.
Zadanie 3a
Write down the period of f.
Zadanie 3b
Find a and b.
Zadanie 4
At the beginning of 2021, a sealed reservoir holds 420000 litres. Its modelled rate of water loss is described by litres per year, where t is years after the beginning of 2021. Find the volume predicted for the beginning of…
Zadanie 5a
Use the appropriate regression equation to estimate height for a tree whose crown is 6 m wide.
Zadanie 5b
Find the mean height and the mean crown width.
Zadanie 5c
Find s.
Zadanie 6a
Find the gradient of Lk in terms of k.
Zadanie 6b
The smaller angle between Lk and the horizontal is π/10. Find all possible k.
Zadanie 7a
Show that the probability of scoring 4 points is 6/25.
Zadanie 7b
Find the probability of scoring zero.
Zadanie 7c
Find E(X).
Zadanie 7d
Hence estimate the total score over 75 rounds.
Zadanie 7e
A player wins a bonus if the total score in exactly five rounds is greater than 48. Find the probability of winning the bonus.
Zadanie 8a
The first three assemblies are shown. Write down t3.
- Materiał graficzny
Zadanie 8b
Find t4.
Zadanie 8c
Show that .
Zadanie 8d
Rods are supplied in boxes of 50. Find the maximum number of tiers that can be built using 12 boxes.
Zadanie 8e
A complete assembly uses a whole number of boxes with no rods left over. Find its smallest possible positive number of tiers.
Zadanie 8f
Each rod is 12 cm long. Find the minimum number of rods needed for an assembly whose height exceeds 2.5 m. Ignore rod thickness.
Zadanie 9a
Show that f−1(x) = f(x).
Zadanie 9b
(i) Find k. (ii) Hence give the coordinates of P.
Zadanie 9c
In terms of c, d, write the equations of (i) the vertical asymptote and (ii) the horizontal asymptote of g.
Zadanie 9d
Given g−1 = g, find d.
Zadanie 9e
Impose g−1 = g to determine d. Take c = 2 and the value of d from (d). Sketch y = 1/g(x), showing intercepts, any excluded points, and all asymptotes with their equations.