Mathematics A, Further H235: Mathematical Preliminaries Topical Past Paper Questions

Jane wants to travel from home to the local town. Jane can do this by train, by bus or by both train and bus. (a) Give an example of a problem that Jane could be answering that would give a construction problem. [1] A website gives Jane all the possible buses and trains that she…

A set consists of five distinct non-integer values, A, B, C, D and E. The set is partitioned into non-empty subsets and there are at least two subsets in each partition. (a) Show that there are 15 different partitions into two subsets. [2] (b) Show that there are 25 different par…

Mo eats exactly 6 doughnuts in 4 days. (i) What does the pigeonhole principle tell you about the number of doughnuts Mo eats in a day? [1] Mo eats exactly 6 doughnuts in 4 days, eating at least 1 doughnut each day. (ii) Show that there must be either two consecutive days or three…