Zadanie 1a
Estimate the median response time.
- Materiał graficzny
Matematyka AA IB HL — maj 2026, 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 31 zadań z tego arkusza, razem 110 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
The class frequencies are 5 for 20 ≤ h < 25, 11 for 25 ≤ h < 30, 16 for 30 ≤ h < 35, p for 35 ≤ h < 40 and q for 40 ≤ h < 45. (i) Find p and q. (ii) Estimate the mean from this table, to four significant figures.
- Materiał graficzny
Zadanie 2
A differentiable function has derivative f′(x) = 2x2 + x − 4 for all real x. Find where f is decreasing.
Zadanie 3a
Find a, b and c.
- Materiał graficzny
Zadanie 3b
The same height is written as . Find the least positive integer d.
Zadanie 4a
Find A and B.
- Materiał graficzny
Zadanie 4b
Find the area of R.
Zadanie 5
A process duration H is normally distributed with mean μ seconds and standard deviation σ seconds. It is known that P(H > 48) = 0.35 and P(H > 54 ∣ H > 48) = 0.40. Find μ and σ.
Zadanie 6
A rectangular light spot maintains area 240 cm2 as its length L and width W change, so LW = 240. At one instant L=12 cm and L is decreasing at 3 cm/s. Find the rate of increase of W.
- Materiał graficzny
Zadanie 7a
Show that b = 1/3.
- Materiał graficzny
Zadanie 7b
Given E(X) = 4.8, find a.
Zadanie 8a
Find c.
Zadanie 8b
State the other two roots in Cartesian form.
Zadanie 8c
Find all solutions of (−iz)3 = c in Cartesian form.
Zadanie 8d
The three solutions in (c) are the roots of (−iz)3 = c. The three solutions in (c) form a triangle in the complex plane. Find its area.
Zadanie 9a
Show that .
- Materiał graficzny
Zadanie 9b
If V = 135π2 cm3, find d exactly.
Zadanie 10a
Find the balance on 1 January 2030, to the nearest dollar.
Zadanie 10b
Show that the balance first exceeds the original USD 31,000 price during 2035.
Zadanie 10c
The machine price depreciates at a constant annual percentage rate r. After one year its price is USD 29,140. Find r.
Zadanie 10d
The machine price depreciates at a constant annual percentage rate r. After one year its price is USD 29,140. For any real number t of years after 1 January 2026, model the price by 31000(1 − r/100)t. The club buys as soon as its credited account balance can…
Zadanie 11a
Find a vector equation for the axis through V and the centre of C.
- Materiał graficzny
Zadanie 11b
Find the centre of C.
Zadanie 11c
(i) Show that the radius is cm. (ii) Find the total external surface area of the housing.
Zadanie 11d
The housing rotates about the fixed point V so that P moves to P′ = (1, −9, 13). Find in degrees.
Zadanie 11e
The housing rotates about the fixed point V so that P moves to P′ = (1, −9, 13). Find an equation of the plane through P, V and P′, with integer coefficients.
Zadanie 12a
First suppose is finite. (i) Show that b=2a−4. (ii) Find the limit in terms of a.
Zadanie 12b
Now instead suppose f has a vertical asymptote, oblique asymptote y=x−5, and at least one point of zero gradient. State its vertical asymptote.
Zadanie 12c
Now instead suppose f has a vertical asymptote, oblique asymptote y=x−5, and at least one point of zero gradient. Show that a=−3.
Zadanie 12d
Now instead suppose f has a vertical asymptote, oblique asymptote y=x−5, and at least one point of zero gradient. Show that b ≥ −9.
Zadanie 12e
For a=−3 and b=1: (i) sketch y = f(∣x∣), marking all asymptote equations, its vertical-axis intercept, and all local extrema; (ii) solve f(∣x∣) < f(x).