Zadanie 1a
Find angle JDL.
Matematyka AA IB HL — 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 29 zadań z tego arkusza, razem 110 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find LD.
Zadanie 2a
Find (f∘g)(x).
Zadanie 2b
Sketch y=(f∘g)(x) for −0.55≤x≤0.55, labelling local extrema.
Zadanie 3a
Estimate the visitor count for a nine-hour opening period.
Zadanie 3b
Find a regression equation suitable for predicting bookings x from visitor count y.
Zadanie 3c
Hence predict bookings for a nine-hour opening period.
Zadanie 4
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 5
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 6a
Find the smallest positive integer n such that z^n=−i.
Zadanie 6b
Describe one geometric transformation taking the point z to z^7 in the Argand plane.
Zadanie 7a
Complete the three blank branch probabilities in the tree.
- Materiał graficzny
Zadanie 7b
Estimate p.
Zadanie 8
The acute angle between line (x − 2)/2 = y + 1 = (3 − z)/2 and plane is α, with 0<α<π/2. Find α in radians.
Zadanie 9
Prove by contradiction that p2 − 12q − 5 ≠ 0 for every pair of integers p,q.
Zadanie 10a
Show that θ=2.20 radians, to three significant figures.
- Materiał graficzny
Zadanie 10b
Find the cross-sectional area.
- Materiał graficzny
Zadanie 10c
Determine whether overflow occurs before the first flush. Justify your answer.
- Materiał graficzny
Zadanie 11a
Find E(X) exactly.
Zadanie 11b
Find P(X<0.6).
Zadanie 11c
Find the least number of trials needed for at least 99% probability of one or more successes.
Zadanie 11d
In twelve trials, find the probability of exactly three successes.
Zadanie 11e
Twelve trial outcomes are placed in the twelve numbered circular slots. If exactly three are successes, how many placements have all three success slots consecutive around the circle?
Zadanie 11f
Consider n≥4 trials with exactly three successes, placed in n numbered circular slots in trial order. (i) Give the number of placements in which all three success slots are consecutive around the circle. (ii) Find the greatest n for which the conditional…
Zadanie 12a
Use Euler’s method to estimate y(0.20), giving six significant figures.
Zadanie 12b
(i) State y′(0). (ii) Show that y″(0)=18.
Zadanie 12c
Given y‴(0)=−34, (i) find the first four terms of the Maclaurin expansion; (ii) use them to estimate y(0.20) to six significant figures.
Zadanie 12d
(i) Using (2x2 − 3)/(x2 + 1) = 2 − 5/(x2 + 1), solve the differential equation with the given initial condition, in explicit form. (ii) Hence evaluate y(0.20) to six significant figures.
Zadanie 12e
Explain why Euler’s method with the specified step underestimates the exact solution at grid points in 0<x<1.