Zadanie 1a
Find (i) f(0); (ii) f(25).
Matematyka AA IB HL — listopad 2024, 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 35 zadań z tego arkusza, razem 110 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Find both roots of f(x)=0.
Zadanie 1c
Sketch y=f(x) on its full domain, labelling the intercepts, endpoints and maximum.
Zadanie 2
Find the coefficient of x5 in (3x − 2)8.
Zadanie 3a
Find k.
Zadanie 3b
Find E(X).
Zadanie 4a
Find angle BAE in degrees.
- Materiał graficzny
Zadanie 4b
Find (i) CE; (ii) BA.
- Materiał graficzny
Zadanie 5
The expression h(x) = log3(3x2 − rx + r − 2) must define a real-valued function for every real x. Find all possible real r.
Zadanie 6a
Find E(X).
Zadanie 6b
If E(c−3X)=0, find the constant c.
Zadanie 6c
Find the median of X.
Zadanie 7a
How many assignments are possible if the four probes must not form one adjacent block?
Zadanie 7b
Two additional distinct probes E,F are now installed. A,B,C,D must occupy an adjacent block of four. How many assignments of all six probes are possible?
Zadanie 8a
Prove for every complex w that ww∗ = ∣w∣2.
Zadanie 8b
Find z in Cartesian form.
Zadanie 9a
Find the range of c for which S_n converges as n tends to infinity.
Zadanie 9b
For c=2, find the least integer n for which |S∞−S_n|<0.05.
Zadanie 10a
(i) Find a,b for the least-squares regression of p on t. (ii) Interpret a in context.
Zadanie 10b
The linear model predicts 23.94 MW for 2034, when t=24. Comment on the reliability of this prediction.
Zadanie 10c
Using B: (i) predict capacity in 2080; (ii) interpret 1.025.
Zadanie 10d
Use C to predict capacity in 2080.
Zadanie 10e
Over 20≤t≤70, determine the calendar year in which the two capacity predictions differ most.
Zadanie 10f
Find (i) B′(50); (ii) C′(50).
Zadanie 10g
Compare and interpret the rates B′(50) and C′(50) in context.
Zadanie 11a
Write the equation of L as r=a+λb, λ∈R.
Zadanie 11b
Find the minimum distance from O to L.
Zadanie 11c
Verify that Π contains L.
Zadanie 11d
A line M is parallel to Π, passes through (2,1,3), and intersects the z-axis. Find a vector equation of M.
Zadanie 12a
Show that dy/dx = (3x2 + 6kx + 8k − 2)/(x + k)2.
Zadanie 12b
Find all k>0 for which the curve has a local maximum or minimum.
Zadanie 12c
For k=1, state the vertical asymptote.
Zadanie 12d
For k=1, find the oblique asymptote.
Zadanie 12e
For k=1, prove that dy/dx>3 everywhere on the curve’s domain.
Zadanie 12f
For k=1, sketch the curve with both asymptotes and correct approach behaviour. You need not calculate intercepts.