Zadanie 1a
Read from the graph (i) f(4); (ii) f(f(4)); (iii) f−1(5).
- Materiał graficzny
Matematyka AA IB SL — maj 2024, TZ2, Paper 1 (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 24 zadania z tego arkusza, razem 80 punktów, każde z kluczem i schematem punktowania.
Zadanie 1b
Sketch the graph of y = f−1(x), clearly identifying its intercepts with both axes.
- Materiał graficzny
Zadanie 2
Solve for 0° ≤ x ≤ 120°.
Zadanie 3a
Solve 2m2 + 7m − 4 = 0.
Zadanie 3b
Hence or otherwise, solve 2 ⋅ 16x + 7 ⋅ 4x − 4 = 0 for real x.
Zadanie 4a
(i) Find the midpoint of AC. (ii) Find the Cartesian equation of OB.
Zadanie 4b
Find the exact area enclosed by OABC.
Zadanie 5a
State the probability of no alert from (i) check A; (ii) check B.
Zadanie 5b
(i) Show that 16k2 − 40k + 9 = 0. (ii) The roots of this equation are 1/4 and 9/4. State the valid value of k and justify your choice.
Zadanie 6a
State the equation of the horizontal asymptote of f.
Zadanie 6b
(i) For m > 0, state the number of real solutions of f(x) = g(x). (ii) Find m for which there is exactly one real solution. (iii) Find all m for which there are two distinct solutions and both are nonnegative.
Zadanie 7a
Show that b = π/6.
- Materiał graficzny
Zadanie 7b
State (i) a; (ii) c.
- Materiał graficzny
Zadanie 7c
For chamber B, (i) find the intensity at t=5; (ii) show that the monitoring threshold is never reached.
- Materiał graficzny
Zadanie 7d
It is found that g(t) = (2/3)f(t) + q. Find q.
- Materiał graficzny
Zadanie 8a
(i) Show that 2x2 − 8x + 11 > 0 for every real x. (ii) Hence determine where f is increasing.
Zadanie 8b
(i) State where f′(x) = 0. (ii) Show that f′′(x) = (−8x2 + 32x − 20)/(2x2 − 8x + 11)2. (iii) Hence justify that the stationary point is a local minimum.
Zadanie 8c
Find an expression for f(x).
Zadanie 8d
Find the equation of the normal to the curve at x=0.
Zadanie 9a
Show that 2p − q = a.
Zadanie 9b
Show that s2 = at.
Zadanie 9c
Show that p>2.
Zadanie 9d
Suppose a=16 and s>0. List the first four terms of (i) the arithmetic sequence; (ii) the geometric sequence.
Zadanie 9e
Suppose a=16 and s>0, and define un = An + ln Gn. (i) Show that u_n is arithmetic and find its common difference. (ii) Show that .