Zadanie 1a
Find g(1).
Matematyka AA IB SL — maj 2022, TZ2, Paper 1 (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 (f∘g)(1).
Zadanie 1c
Find x such that f(x)=0.
Zadanie 2a
State u₁.
Zadanie 2b
Given uₙ=−38, find n.
Zadanie 2c
Find the common difference.
Zadanie 3a
Prove that their sum is divisible by 3.
Zadanie 3b
Prove that the sum of their squares is never divisible by 3.
Zadanie 4a
State (i) the vertical asymptote and (ii) the horizontal asymptote.
Zadanie 4b
Sketch y=f(x), indicating its asymptotes and axis intercepts.
Zadanie 4c
Hence solve 0<f(x)<3.
Zadanie 5
Find the least positive x satisfying .
Zadanie 6a
Show that b=40.
Zadanie 6b
The third term is the arithmetic mean of the second and fourth terms. Find all possible x.
Zadanie 7a
State the axis of symmetry of f.
Zadanie 7b
(i) State h,k. (ii) Find a.
Zadanie 7c
Find the equation of the tangent to y=f(x) at Q.
Zadanie 7d
Find d for which g has a strictly positive derivative at every real x.
Zadanie 7e
Find where y=g(x) is concave up.
Zadanie 8a
Find the coordinates of B.
Zadanie 8b
A region lies above the x-axis, below g from A to B, and below f from B to the vertical line x=k, where k is an integer greater than 6. A circular hole of radius 1 centred at (5,1) is removed from the region; this disk lies entirely inside it. On integrating,…
Zadanie 9a
Show that p=0.40 and q=0.25.
Zadanie 9b
Find P(X>2).
Zadanie 9c
After three cycles the recorded total is 2 units. Find the probability the batch passes.
Zadanie 9d
Two independent uniform four-sector spinners each have sector labels 0,2,4,6. Their sum has the following distribution. A replacement pair of independent uniform four-sector spinners must produce this same sum distribution. Their labels are respectively…
- Tabela do uzupełnienia
Zadanie 9e
Two independent uniform four-sector spinners each have sector labels 0,2,4,6. Their sum has the following distribution. A replacement pair of independent uniform four-sector spinners must produce this same sum distribution. Their labels are respectively…
- Tabela do uzupełnienia