Video: Pack 5 β€’ Paper 2 β€’ Question 18

Pack 5 β€’ Paper 2 β€’ Question 18

04:50

Video Transcript

𝐴 is equal to 4.23 correct to two decimal places. 𝐡 is equal to 11.051 correct to five significant figures. 𝐢 is equal to five 𝐴 divided by 𝐡 squared. Work out the value of 𝐢 to a suitable degree of accuracy. Make sure to respect the bounds of each parameter and give a reason for your answer.

Our first step is to calculate the lower and upper bound of 𝐴. Any value between 4.225 and 4.235 will round to 4.23 correct to two decimal places. This means that the lower bound of 𝐴 is 4.225 and the upper bound is 4.235. We can write this as an inequality so that 𝐴 is greater than or equal to 4.225 and less than 4.235. We don’t include the upper bound in our inequality as 4.235 would round up to 4.24.

We can repeat this method to find a lower bound and upper bound of 𝐡. This time, any value between 11.0505 and 11.0515 will round to 11.051 correct to five significant figures. We can, therefore, say that 𝐡 must be greater than or equal to 11.0505 and less than 11.0515.

We now need to consider the equation 𝐢 is equal to five 𝐴 divided by 𝐡 squared and decide which values of 𝐴 and 𝐡 we will use. If we are dividing, as we are in this case, to calculate the maximum value, we need to divide the upper bound of the numerator by the lower bound of the denominator. We want the top to be as large as possible and the bottom to be as small as possible.

To find the minimum value, we need to divide the lower bound of the numerator by the upper bound of the denominator. This time, we want the top to be as small as possible and the bottom to be as large as possible.

In our question, in order to find the maximum value of 𝐢, we want the upper bound of 𝐴 and the lower bound of 𝐡. Substituting these values into the equation five 𝐴 divided by 𝐡 squared gives us five multiplied by 4.235 divided by 11.0505 squared. This is equal to 0.173404 and so on.

In order to find the minimum value of 𝐢, we need to use the lower bound of 𝐴 and the upper bound of 𝐡. Substituting in these values gives us five multiplied by 4.225 divided by 11.0515 squared. This is equal to 0.172963 and so on.

We were asked to give our value of 𝐢 to a suitable degree of accuracy. We’ll do this by rounding. Rounding our answers to five decimal places gives us a maximum value of a 0.17340 and a minimum value of 0.17296.

As these answers are different, we’ll try rounding to four decimal places. Rounding the maximum value of 𝐢 to four decimal places gives us 0.1734. And the minimum value is equal to 0.1730 to four decimal places.

Once again, as these two answers are not equal, we need to try rounding to three decimal places. When we round our maximum and minimum value of 𝐢 to three decimal places, both of our answers are 0.173. We can, therefore, say that 𝐢 is equal to 0.173 to three decimal places as both the upper and lower bounds round to this value.

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