Zadanie 1a
Find the common difference.
Matematyka AA IB SL — maj 2024, TZ1, 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 29 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find an expression for its nth term uₙ.
Zadanie 2a
Find p and q.
Zadanie 2b
State the mean displayed score.
Zadanie 3a
Find log5(1/a).
Zadanie 3b
Find log125 a.
Zadanie 4a
Show that r2 − 7r + 12 = 0.
Zadanie 4b
Find r and θ.
Zadanie 5a
Find the x-coordinates of A and C.
Zadanie 5b
Find the exact area of R.
Zadanie 6a
Find Sₙ.
Zadanie 6b
Hence prove S1 + S2 + ⋯ + Sn = [4(4n − 1) − 3n]/9.
Zadanie 7a
Find (i) y′; (ii) y″.
Zadanie 7b
Find the coordinates of A and use y″ to justify your choice.
Zadanie 7c
Find the x-coordinate of B.
Zadanie 7d
Find an equation of L.
Zadanie 8a
Sketch y=f(x), labelling every axis intercept and all asymptotes.
Zadanie 8b
State the range of f.
Zadanie 8c
Show that p=8/3.
Zadanie 8d
Find b and c.
Zadanie 8e
Find the y-coordinate of the vertex of g.
Zadanie 8f
Find the number of solutions of f(x)=g(x).
Zadanie 9a
Let p and q be the probabilities that the second token is amber or violet, respectively, conditional on a violet first selection. Find p,q.
Zadanie 9b
Show that the probability of two selections of the same colour is 10/21.
Zadanie 9c
Given that the two selections have the same colour, find the probability that both are amber.
Zadanie 9d
The distribution of X has P(X=0)=2/21,P(X=1)=a,P(X=2)=b. Find a,b.
Zadanie 9e
Find E(X).
Zadanie 9f
Restart with 4 amber and 2 violet tokens and continue the same replacement rule until the first violet selection. Given that the first two selections are amber, state the probability that the third is violet.
Zadanie 9g
Restart with 4 amber and 2 violet tokens and continue the same rule until the first violet selection. The probability that the first violet occurs on selection n is 20/189. Find n.