IB Maths AI HL AI 1.1 Number and approximation questions

A laboratory receives microscopic particles in sealed deliveries. Figure 1 shows the mass of one particle and the numbers of particles and cartridges in a cartridge and a delivery, respectively. The diagram is not to scale.

(a) Calculate the mass of particles in one cartridge. Give your answer in standard form, correct to 2 significant figures. [2]

(b) Calculate the total mass of particles in one delivery. Give your answer in standard form, correct to 2 significant figures. [2]

(c) A laboratory requires at least $1.0\,\text{g}$ of particles. Find the minimum whole number of deliveries required. [2]

A comet lander collects dust during a $4.0$-minute sampling pulse. Figure 1 shows the rate $R$ at which particles enter the collection chamber. Assume that $R$ varies linearly between consecutive readings. The mean mass of a particle is $2.4\times10^{-13}\,\text{kg}$

A remote-sensing archive receives data from two instruments. Instrument A records $4.8\times10^{12}$ observations, each requiring $2.7\times10^3$ bytes. Instrument B produces $2.24\times10^{15}$ bytes of data. The archive has $4.1\times10^{15}$ bytes of free space. Each additional storage module can hold at most $3.6\times10^{14}$ bytes.