Zadanie 1a
Find (i) f(0); (ii) f(25).
Matematyka AA IB SL — listopad 2024, TZ2, 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 30 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find both roots of f(x)=0.
Zadanie 1c
Sketch y=f(x) on its full domain, labelling the intercepts, endpoints and maximum.
Zadanie 2
Find the coefficient of x5 in (3x − 2)8.
Zadanie 3a
Find .
Zadanie 3b
Find h(x).
Zadanie 4a
Find k.
Zadanie 4b
Find E(X).
Zadanie 5a
Find angle BAE in degrees.
- Materiał graficzny
Zadanie 5b
Find (i) CE; (ii) BA.
- Materiał graficzny
Zadanie 6
The expression h(x) = log3(3x2 − rx + r − 2) must define a real-valued function for every real x. Find all possible real r.
Zadanie 7a
What percentage of R devices are at least 36 months old?
Zadanie 7b
For 500 random selections from R, find the probability that fewer than 160 selected devices are at least 36 months old.
Zadanie 7c
Given that a randomly selected R device is at least 36 months old, find the probability that it is at least 60 months old.
Zadanie 7d
List the five class midpoints in order.
Zadanie 7e
Using the class midpoints, estimate (i) the mean device age; (ii) its variance.
Zadanie 7f
The panels schematically compare centres and spreads; no normal model is assumed. (i) Which panel best represents R and S? (ii) Which network does its solid line represent?
- Materiał graficzny
Zadanie 8a
(i) Find a,b for the least-squares regression of p on t. (ii) Interpret a in context.
Zadanie 8b
The linear model predicts 23.94 MW for 2034, when t=24. Comment on the reliability of this prediction.
Zadanie 8c
Using B: (i) predict capacity in 2080; (ii) interpret 1.025.
Zadanie 8d
Use C to predict capacity in 2080.
Zadanie 8e
Over 20≤t≤70, determine the calendar year in which the two capacity predictions differ most.
Zadanie 8f
Find (i) B′(50); (ii) C′(50).
Zadanie 8g
Compare and interpret the rates B′(50) and C′(50) in context.
Zadanie 9a
State (i) the amplitude of f; (ii) its period.
Zadanie 9b
By considering the graph of f+g, determine (i) a; (ii) b; (iii) the smallest possible positive c.
Zadanie 9c
When does the scanner first reach its maximum velocity?
Zadanie 9d
How many inspection checkpoints does it pass in the first 120 seconds?
Zadanie 9e
(i) Find v′(t). (ii) Hence, or otherwise, give the maximum acceleration.
Zadanie 9f
Find the distance between consecutive inspection checkpoints.