Zadanie 1a
Find its value at the end of the first year.
Matematyka AA IB HL — 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 33 zadania z tego arkusza, razem 110 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find its value 9 years after purchase, to the nearest dollar.
Zadanie 1c
Find the least number n of complete years after which its value is below 15% of its original price.
Zadanie 2a
Find the radius r of the hopper.
Zadanie 2b
Find the hopper volume.
Zadanie 3a
Find the probability that X is more than 1.2 standard deviations above its mean.
Zadanie 3b
The probability that X exceeds its mean by more than k standard deviations is.08. Find k.
Zadanie 4a
Find the first time at which the stage changes direction.
Zadanie 4b
Find the interval on which its displacement is increasing.
Zadanie 4c
Find its displacement at t=12.
Zadanie 5a
Find Pearson’s correlation coefficient.
Zadanie 5b
The technician substitutes x=10 into the given regression line to predict y. Give one reason this is inappropriate.
Zadanie 5c
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 6a
Find P(X=7).
Zadanie 6b
Find P(X≥7).
Zadanie 6c
Find the probability that the first failure is the seventh transmission.
Zadanie 7
Solve dy/dx = 2x − 3y, with y(0)=4, giving y explicitly as a function of x.
Zadanie 8a
Show that 5k³=6.
Zadanie 8b
Find the median.
Zadanie 9a
How many seating assignments satisfy this condition?
Zadanie 9b
Researchers C and D must also be nonadjacent, while A,B remain adjacent. Find the number of assignments.
Zadanie 10a
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 10b
During one complete cycle of chamber A, for how many hours is the temperature below 5.5°C?
Zadanie 10c
Find the rate of change of H at t=10.
Zadanie 10d
Find one valid set of values a,b,c,d for chamber B.
Zadanie 10e
Find the first time T≥0 when the two chambers have equal temperatures.
Zadanie 11a
Show that dy/dx = (2x − ex+y)/(ex+y − 2y) wherever the denominator is nonzero.
Zadanie 11b
(i) Show that the horizontal-tangent x-coordinates satisfy 2x2 + [ln(2x)]2 − 2xln(2x) − 2x − 1 = 0, with x>0. (ii) Find P and Q.
Zadanie 11c
Using symmetry, state the coordinates of the two points where the tangent is vertical.
Zadanie 11d
Find the point on C whose tangent has gradient −1.
Zadanie 12a
Use the magnitude definitions of dot and cross products to prove .
Zadanie 12b
Find (i) |u×v|; (ii) |u|; (iii) all possible pairs (p,q).
Zadanie 12c
Take p=1. A new point D defines with . The area of triangle ACD is . Find both possible vectors w.