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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 289

A modular structural analysis of a skyscraper uses a load-bearing index L(m)L(m)L(m) for the mmm-th floor. This index is calculated by the difference between two cumulative load sums:

L(m)=∑k=0m5k4−∑k=0m−15k4 L(m) = \sum_{k=0}^{m} 5k^4 - \sum_{k=0}^{m-1} 5k^4 L(m)=k=0∑m​5k4−k=0∑m−1​5k4

where mmm is a positive integer representing the floor number.

a.

Find the load-bearing index for the 4th floor, L(4)L(4)L(4), and the 10th floor, L(10)L(10)L(10).

[2]
b.

An engineer determines that the maximum theoretical limit for a floor's load-bearing index is 3.125×10113.125 \times 10^{11}3.125×1011. Calculate the floor number mmm that reaches this limit.

[3]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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