Zadanie 1a
Find its radius.
- Materiał graficzny
Matematyka AA IB SL — maj 2025, TZ3, 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 28 zadań z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Hence find the total surface area, including the flat face.
Zadanie 2a
Find QR.
- Materiał graficzny
Zadanie 2b
Find .
Zadanie 3a
How many nonzero terms does the fully expanded expression contain?
Zadanie 3b
The coefficient of x5 is 36288. Find k.
Zadanie 4a
(i) Find a. (ii) State the mode of X.
Zadanie 4b
Find E(X).
Zadanie 4c
To gather feedback, the coordinator interviews the first 40 members who enter the workshop on Monday. Identify the sampling method.
Zadanie 5
A circle has centre O. Points A and B subtend a minor central angle of 2.2 radians. Triangle AOB has area 18 cm2. Point C is on the major arc from A to B. Find the length of arc ACB.
- Materiał graficzny
Zadanie 6a
Find f′(x).
Zadanie 6b
The tangent at x = 1 has inclination 35° to the positive horizontal axis. Determine all possible values of a.
Zadanie 7a
(i) State the amplitude. (ii) Find the period.
- Materiał graficzny
Zadanie 7b
Point P has coordinates (1.42, 4.50). Is P above, below or on the graph? Justify your answer.
Zadanie 7c
Line L1 has equation 2x − 12y + 47 = 0. State its gradient.
Zadanie 7d
L1 is normal to the graph at A = (1/2, 4). Line L2 is the tangent at A. (i) Find its gradient. (ii) Hence or otherwise find its equation.
Zadanie 7e
The normal L1 at A = (1/2, 4) has equation 2x − 12y + 47 = 0. L1 also meets the curve at B with xB > 1.3. Find B.
- Materiał graficzny
Zadanie 7f
Let A = (1/2, 4). The normal to the curve at A meets it again at B with xB > 1.3. The region comprises all areas between this normal and the curve from xA to xB. Find the total shaded area between the curve and the normal line from A to B.
- Materiał graficzny
Zadanie 8a
State two conditions needed to model a count by a binomial distribution.
Zadanie 8b
Find the expected number who join soldering.
Zadanie 8c
Find (i) P(D = 512); (ii) P(490 ≤ D ≤ 520).
Zadanie 8d
Given 490 ≤ D ≤ 520, find the probability that at most 501 visitors join soldering.
Zadanie 8e
A visitor joins 3D printing with probability 0.68, independently of that visitor’s soldering decision. Find the probability of joining both.
Zadanie 8f
On Sunday there are n visitors, and each joins 3D printing with probability 0.68. The probability that at most 450 join is approximately 0.762. Find n.
Zadanie 9a
(i) State u(1). (ii) Find the time when the first cart’s velocity is 4 m/s.
Zadanie 9b
Find the time when the first cart’s acceleration is 3 m/s2.
Zadanie 9c
(i) Find . (ii) Explain why this limit is not an attained trial velocity.
Zadanie 9d
The cart modelled by u finishes first. How far is the other cart from its endpoint at that instant?