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Numeracy Higher November 2016 Unit 2 Q5

WJECHigherCurrent spec12 marksGrouped DataRatio & Basic ProportionVolume & Surface Area

5. Rhodri has carried out an experiment to measure the diameters of 20 spherical dust particles, in microns.

Here are his results.

Diameter, \(d\) (microns)Frequency
\(1 \leqslant d \lt 2\)2
\(2 \leqslant d \lt 4\)6
\(4 \leqslant d \lt 5\)8
\(5 \leqslant d \lt 9\)4
(a)
(i) Calculate an estimate of the mean diameter of a dust particle. [4]
(ii) Rhodri measures the diameters of another 25 dust particles.

Rhodri is told,

‘The ratio of dust particles with diameters less than 4 microns to those with diameters greater than or equal to 4 microns is 7 : 8.’

He finds this fact is true when he considers all 45 dust particles.

How many of the extra 25 dust particles have a diameter of less than 4 microns?
You must show your working. [3]

(b) Rhodri studies a cylindrical cell under his microscope.
The height of the cell is 2 microns.
The circumference of the cell is 5 microns.

Calculate the volume of the cell he sees under the microscope.
Give your answer in microns3, correct to 1 significant figure. [5]

Volume is ……………… microns3

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