Zadanie 1a
Find angle JDL.
Matematyka AA IB SL — maj 2023, 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 LD.
Zadanie 2a
State the annual depreciation rate.
Zadanie 2b
Find the modelled value on 1 January 2029.
Zadanie 2c
How much additional money is needed beyond the account balance on that date?
Zadanie 3a
Find (f∘g)(x).
Zadanie 3b
Sketch y=(f∘g)(x) for −0.55≤x≤0.55, labelling local extrema.
Zadanie 4a
Estimate the visitor count for a nine-hour opening period.
Zadanie 4b
Find a regression equation suitable for predicting bookings x from visitor count y.
Zadanie 4c
Hence predict bookings for a nine-hour opening period.
Zadanie 5
A calibrated sensor has normally distributed response delay D with mean 18 milliseconds and unknown standard deviation σ. Its interquartile range is 0.42 milliseconds. Find σ.
Zadanie 6
For a,b>0, the coefficient of x⁴ in (ax2 + b)7 is 6048, and its coefficient in (ax2 + b)9 is 41472. Find a and b.
Zadanie 7a
Find (i) the initial temperature; (ii) the temperature after four minutes.
Zadanie 7b
Find H′(4).
Zadanie 7c
Interpret H′(4) in context.
Zadanie 7d
Find the least positive integer k such that the chamber is ready at t=k minutes.
Zadanie 7e
Find the constant enclosure temperature approached by the chamber.
Zadanie 7f
Find the limit of H′(t) as t tends to infinity.
Zadanie 8a
Find (i) p; (ii) q.
Zadanie 8b
Three distinct audited shipments are chosen uniformly without replacement. Find the probability that all three are regular.
Zadanie 8c
(i) Use P(R|B)=2/5 to find x. (ii) State the probability that a uniformly chosen audited shipment is regular and used a bike.
Zadanie 8d
Are R and B independent? Justify your answer.
Zadanie 8e
Assume these proportions apply to future shipments. For twelve independent future shipments, find the probability that at least seven use vans.
Zadanie 9a
Show that θ=2.20 radians, to three significant figures.
- Materiał graficzny
Zadanie 9b
Find the cross-sectional area.
- Materiał graficzny
Zadanie 9c
Determine whether overflow occurs before the first flush. Justify your answer.
- Materiał graficzny