Be an Election Night swinger

To interpret the punditry, analysis and results of the General Election, viewers and listeners should have a basic level of maths, says the Royal Society of Chemistry (RSC). 

To make its point the RSC has arranged an election night "swinger" quiz with a £500 first prize and nine runner-up prizes of £50.

The RSC, eager to demonstrate the need for mathematics skills and logical thinking in daily life, has prepared the brief examination competition to underline the relevance of maths to the election results.

Chief executive Richard Pike said today: "The entire drama of the General Election hinges upon statistics and mathematics. 

"Plainly, there is still human interest to be found in some of the results as political personalities' fortunes ebb and flow, but there can be much more enjoyment where there is a real understanding of the losses and gains as they emerge around the map of Britain through swings in voting."

Dr Pike, who has led an RSC campaign to reverse the erosion of maths standards in British schools, added: "All the population should have the ability to do this quiz. In a technically literate society everybody ought to be reasonably comfortable with this level of mathematics. It brings in probabilities, percentages, swings, areas, and interesting brain-teasers to keep you occupied during a lull in the television coverage. 

"The quiz shows how the mathematics of politics has many similarities to the analysis that underpins science, and this should make the whole subject more appealing."

The winning name will be chosen at random from emails, which have to be with the RSC by noon on 7 May 2010. The £50 prize will go the next nine entrants, selected in the same way, who have submitted correct answers to all ten questions.

Email your answers to swingers AT rsc DOT org.

The quiz:

1. A candidate is planning to talk for one hour in front of the town hall at North Anytown on Saturday, but because of scheduling problems this can be at any time between 9am and 5pm. You go down to the town hall at 12noon on that day, to see momentarily what is going on. What is your probability of hearing the candidate, expressed as a percentage? 

2. A scientist knows that anytime in the next hour his team will make a new element whose atoms are predicted to be observable for a split second before they decay into smaller atoms and sub-atomic particles. He goes away for five minutes to make a cup of tea. What is the probability he will miss observing the event, expressed as a fraction? 

3. In a particular geographical area there are 10 Conservative candidates, 10 Labour, 9 Liberal Democrat and 21 from other political parties. What fraction of candidates are Labour?

4. A carbon dioxide molecule consists of one atom of carbon of atomic mass 12 and two atoms of oxygen, each of atomic mass 16. What is the proportion of carbon in carbon dioxide, by mass, expressed as a percentage, to the nearest whole number? 

5. At the last General Election, in one particular constituency, 10,000 people voted for Party A, 8,000 for Party B and 12,000 for various other parties, which each polled less than the Party B candidate. What percentage swing to Party B would be needed (movement as a ratio of all voters in the constituency) for that Party to just win the constituency in the forthcoming General Election, assuming a proportionately identical shift in voting across all non-Party B voters from the last General Election, and the same overall total number of people voting? Answer to one decimal place. 

6. The concentrations of two non-reacting salts, X and Y, in the same beaker of water are 20 grams per litre and 15 grams per litre, respectively. For a particular experiment, the required concentrations are 16 grams per litre and 12 grams per litre, respectively. What percentage additional water must be added to the beaker to achieve this? Another beaker has 9 grams per litre of a salt Z in a solution of water. What percentage of water has to be evaporated away in this beaker to make the concentration the same as X in its final state in the first beaker? A beaker of one litre of the diluted solution containing X and Y is then placed next to another beaker containing one litre of the concentrated solution of Z. Effectively, by weight, 7 grams has been shifted from one beaker to the other, within a total of 44 grams of salt to make the concentrations of X and Z the same. What is this shift as a percentage? All answers to be to one decimal place.  

7. There are 10 constituencies in a rectangular area 20 miles by 30 miles. What is the average area of a constituency within this region? 

8. A microscopic image shows equally 20 atoms equally-spaced within a rectangular area of 1.08 square nanometres, including those within and on the boundary of the rectangle. What is the average spacing between the atoms, centre-to-centre, in nanometres. 

9. In a section of a politician's speech there 5 sentences of fourteen words, 3 of eight words and 2 of just three words. What is the average number of words in these particular sentences? 

10. Just after the 'Big Bang' 13.7 billion years ago, when the first elements were formed, approximately 75% were hydrogen atoms, and nearly all the rest (25%) were helium atoms. If the atomic mass of hydrogen is 1 unit, and of helium is 4 units, what was the average atomic mass of atoms in the universe at that stage?