Zadanie 1a
State the median and interquartile range for machine B.
- Materiał graficzny
Matematyka AA IB SL — maj 2024, 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 27 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Compare the two sample distributions using (i) their medians; (ii) their interquartile ranges. Justify both comparisons.
- Materiał graficzny
Zadanie 2a
Find its value at the end of the first year.
Zadanie 2b
Find its value 9 years after purchase, to the nearest dollar.
Zadanie 2c
Find the least number n of complete years after which its value is below 15% of its original price.
Zadanie 3a
Find the radius r of the hopper.
Zadanie 3b
Find the hopper volume.
Zadanie 4a
Find the probability that X is more than 1.2 standard deviations above its mean.
Zadanie 4b
The probability that X exceeds its mean by more than k standard deviations is.08. Find k.
Zadanie 5a
Find the first time at which the stage changes direction.
Zadanie 5b
Find the interval on which its displacement is increasing.
Zadanie 5c
Find its displacement at t=12.
Zadanie 6a
Find Pearson’s correlation coefficient.
Zadanie 6b
The technician substitutes x=10 into the given regression line to predict y. Give one reason this is inappropriate.
Zadanie 6c
For a missing A reading with y=130, the technician rearranges 130=1.069x+2.184 and rounds to 120. (i) Explain the problem with this method. (ii) Use an appropriate method to show that the estimate is 119 to the nearest integer.
Zadanie 7a
Show that f−1(x) = 2 + ln(4x/5).
Zadanie 7b
Find the distance PQ.
Zadanie 7c
State (i) g(x); (ii) the domain of g.
Zadanie 7d
Solve f(x)=g(x), giving x in the form a+ln b with rational a,b.
Zadanie 8a
For chamber A, the time from a minimum to the next maximum is 5 hours and m minutes. Find m to the nearest integer.
Zadanie 8b
During one complete cycle of chamber A, for how many hours is the temperature below 5.5°C?
Zadanie 8c
Find the rate of change of H at t=10.
Zadanie 8d
Find one valid set of values a,b,c,d for chamber B.
Zadanie 8e
Find the first time T≥0 when the two chambers have equal temperatures.
Zadanie 9a
Find (i) the two possible values of angle OAB; (ii) the corresponding areas of triangle OAB.
Zadanie 9b
A second crossbar CD has length 12 m, with C on OA and D on OB. Triangle OCD has area 50 m². Writing x=OC and y=OD, show that .
Zadanie 9c
A crossbar CD of length 12 m joins C on OA to D on OB and triangle OCD has area 50 m². Find the two possible lengths OC.