Choose algebraic, graphical or numerical methods to solve equations and interpret solutions within a model's domain.
Tę umiejętność sprawdza 18 zadań wzorowanych na arkuszach IB z lat 2022–2026.
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…
Find the intervals on which f is decreasing.
The tangent at x = 1 has inclination 35° to the positive horizontal axis. Determine all possible values of a.
A circular window is divided by chord AB. Its minor segment P has area 18 cm2. The triangle OAB, labelled Q, and segment P have areas in the ratio P : Q = 2 : 3. The circle has centre O, radius r cm, and with 0 < θ < π.…
A record of completed assembly units has the following frequency distribution, where p, q are positive integers. Its population mean is 27 and its population variance is 153. Determine p and q.
At an instant when θ = 0.2 radians, the angle is increasing at 6 radians per hour. Find the aircraft’s speed.
A complete assembly uses a whole number of boxes with no rods left over. Find its smallest possible positive number of tiers.
(i) State u(1). (ii) Find the time when the first cart’s velocity is 4 m/s.
Find the median total measurement time.
Using tables or another suitable method, find the smallest count greater than 1 that occurs in both the r=1 and r=17 schemes.
A rational point has two rational coordinates. On C : y2 = x3 − 3x + 4, let P=(0,2). The tangent at P meets C again at Q; let S=(0,−2). Use the tangent construction to determine Q, then find the third intersection of the full straight line through Q and S with C.
The remaining plate has area 25π − 9 cm². Find θ.
Consider Fc(x) = x3 + cx2 − 6x + 1, where c is real. You may use the sufficient condition: a real cubic x³+px²+qx+r, r≠0, has a nonreal root if q²<3pr. A student claims that q²≥3pr guarantees all roots are real. (i) By varying the positive integer c, find the…
Solve f(x)≥g(x).
Find the time needed to fill the vessel.
Find every time when the two contents are equal.
Find the x-coordinate of B.
Find the point where the tangent to the graph of f is parallel to y=2x.
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