Problem Bank - Approximations & Error

Access custom-built, exam-style problems for approximations & error. Each problem has a full solution and mark-scheme, as well as AI grading and support.

9 Problems Available

Select a Difficulty

IB: 4

IB: 5

IB: 6

IB: 4

0 / 6

The total market value of all the gold in the world is 2.7×1013 US dollars.

Given that a kilogram of gold costs $110000, calculate the mass of all the gold in the world.
[2]

Olympic swimming pools have dimensions 50m by 25m by 2m. It is given that 1cm3 of gold weighs 19g.

Find the number of olympic swimming pools needed to store all the world's gold.
[4]

0 / 6

The largest number a computer memory chip can store is 2n, where n is the number of bits the computer chip has.

Find the number of bits needed to store the number 8213110.
[3]

Perplex makes two chips, version 1 with 32 bits, and version 2 with 64 bits. The largest number that can be stored on version 2 is k times the largest number that can be stored on version 1.

Find the value of k.
[3]

0 / 10

A baby marmot lies next to its mama on a sunlit log in the mountains. A researcher is studying how much solar energy the baby marmot absorbs over time. Due to the remote location, all quantities are approximated or measured with some instrument error.

The baby marmot's exposed surfaced error is estimated to be A=0.031 m2. At the altitude, the solar irradiance is measured at P=1.2×103 J/sec/m2. The baby marmot lies still for t=25 minutes.

The energy absorbed by the baby marmot, in Joules, is given by E=P⋅A⋅t.

Find the total energy absorbed by the baby marmot.
[2]
Write your answer to part (a) in the form a×10k, where 1≤a<10 and k∈Z.
[1]
The researcher's estimate of the baby marmot's exposed surface area is accurate to ±0.005 m2.
1. Find the upper and lower bounds for the amount of energy the baby marmot absorbs.
  [4]
2. Hence calculate the maximum percent error in energy absorption E, assuming all other qualities are exact.
  [3]

0 / 6

A spherical raindrop has a diameter of 2mm.

Find the volume of the raindrop in cm3.
[2]

In the following parts of the problem, give all your answers in the form a×10k where 1≤a<10 and k∈Z.

During a large thunderstorm, 7000m3 of water falls.

Estimate the number of raindrops that fell.
[2]

The number of HX2O molecules in 1mL is 3.34×1022.

Calculate the number of HX2O molecules that fell during the storm.
[2]