Zadanie 1a
Find the chord length AB.
Matematyka AA IB HL — maj 2022, 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 32 zadania z tego arkusza, razem 110 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find the area of the major sector between OA and OB.
Zadanie 2
A function g satisfies g′(x) = 4x3 − 6e−2x and g(0)=8. Find g(x).
Zadanie 3
Independent events A,B satisfy P(A)=2P(B) and P(A∪B)=0.72. Find P(B).
Zadanie 4a
State the median warm-cache latency.
- Materiał graficzny
Zadanie 4b
Verify that the warm-cache reading 0.60 s is not an outlier.
- Materiał graficzny
Zadanie 4c
Explain why the warm-cache mean appears likely to exceed its median.
- Materiał graficzny
Zadanie 4d
Comment on whether the plots provide evidence of greater latency with a cold cache.
- Materiał graficzny
Zadanie 5a
Find when it changes direction.
Zadanie 5b
Find all times when acceleration is −3 m/s².
Zadanie 5c
Find its acceleration when its speed is greatest.
Zadanie 6
A bowl’s outer interior wall is obtained by revolving x2 + (y − 5)2 = 25, x≥0 and h≤y≤5, about the y-axis. Coordinates are centimetres. A solid coaxial cylinder of radius 1 cm occupies the centre; water fills only the annular space outside it. A horizontal base…
Zadanie 7a
Show that a finite limit is possible only when k=ln3.
Zadanie 7b
For k=ln3, use l’Hôpital’s rule to prove that L=−2/3.
Zadanie 8
A sensor of type A gives normally distributed signal readings with mean 48 and standard deviation 4. A type-B sensor has mean 50 and standard deviation 3. Every reading is independent, including across the two sensors. Each sensor is tested four times and…
Zadanie 9a
How many codes have all digits distinct?
Zadanie 9b
How many have distinct digits in increasing order?
Zadanie 10a
Find the initial contents of (i) B; (ii) A to three significant figures.
Zadanie 10b
Find every time when the two contents are equal.
Zadanie 10c
Prove that A contains more than B whenever 7<t≤8.
Zadanie 10d
Find the total time in[0,8] when B’s content increases faster than A’s.
Zadanie 11a
Find B’s three-figure bearing.
Zadanie 11b
Show that A moves faster than B.
Zadanie 11c
Find the acute angle between their paths, in degrees.
Zadanie 11d
(i) Find P. (ii) Find the elapsed time between the two vehicles reaching P.
Zadanie 11e
Find their minimum simultaneous separation during the stated interval.
Zadanie 12a
Interpret dP/dt in this model.
Zadanie 12b
Show that d2P/dt2 = k2(P − H)(1 − P/N)[1 + (H − 2P)/N].
Zadanie 12c
Using P′′ = k2(P − H)(1 − P/N)[1 + (H − 2P)/N], show that the rate of adoption is greatest at P = (N + H)/2, and justify the maximum.
Zadanie 12d
Given that the maximum occurs at P=(N+H)/2, find the maximum dP/dt in terms of k,H,N.
Zadanie 12e
Solve the differential equation with P(0)=P₀ and show that .
Zadanie 12f
For a particular network H=P₀/2,N=4P₀ and P(8)=3P₀. Using , find k.