BMAT 2009-S1

The graph below is a cumulative plot of the length of reigns of British kings or queens from 1066 to the present. The vertical axis shows the number of monarchs who had reigned for  less than the number of years plotted on the horizontal axis.

I recently asked four members of my class to draw bar charts of some data that we collected. Every student managed to produce a bar chart, but they all drew exactly two bars at the wrong height on their graph. I drew the correct bar chart from the data. Unfortunately, I didnít label any of the charts so I now donít know which one is the correct one.

Last winter, heavy snowfalls prompted criticism of the Government for failing to ensure that the country is prepared for severe weather. Billions of pounds were lost to businesses through workers being unable to make their journey to work during a week of heavy snowfall. Others felt that these costs should be accepted philosophically. Given that the likelihood of a prolonged period of heavy snow in the UK is very low, it could be said that the high cost of investing in preventative measures would be unreasonable. Governments have to make an assessment of the probability of the event occurring, the cost of preventative measures and the cost of the event happening. In some cases the cost of preventative measures is too high when the risk is low. The recent severe weather is one such case. One might also consider the threats of pandemics such as bird flu, or asteroids hitting the earth, both of which might be considered ‘low risk but high cost.’

On a recent train journey I was drawn into a conversation by an elderly couple who were keen to tell me all about their grandchildren.

Although proud of them all, their one complaint was the constant expense of buying birthday presents. There is at least one birthday amongst the grandchildren every calendar month, and April is particularly expensive for them because it sees the birthdays of three of the five pairs of twins.

I remember them saying that they have exactly twice as many granddaughters as grandsons, but after they had left the train I realised that they hadn’t told me how many grandchildren they have in total.

There has been far too much fuss about the dangers of young people using the drug ecstasy. We need to get things in proportion. The use of ecstasy causes only 30 deaths per year in Britain, whereas horse riding causes 100 deaths per year. Thus campaigns over recent years to discourage young people from using ecstasy are not necessary. As the comparison with horse riding clearly shows, taking ecstasy is nowhere near as dangerous as many people believe.

1. More young people may use ecstasy if there were no campaigns about its dangers.

2. The argument assumes that horse riding should not be considered too dangerous.

3. There may be fewer young people using ecstasy than engaging in horse riding.

I have three choices for my membership of the local sports club. The details of the memberships are as follows:

I currently have a Bronze membership and I know the number of times that I will need to hire equipment in the coming year. I am considering changing to either Gold or Silver membership. If I did, the total cost for either would be the same.

UNREPORTED CRIME
A survey by Lynne Featherstone

On the basis of both anecdotal and documented evidence that many crimes are not reported to the police, I undertook a survey to provide a snapshot of the level of the non-reporting of crime. In doing so I was particularly interested in why people did not report crimes to the police and what these reasons show about the level of public confidence in the police service.

Survey
The questions on the reporting of crime were included in a wider survey on crime and disorder that was sent out to residents in a single north London borough during the second half of last year.

Respondents were asked whether they had been a victim of or witness to a crime in the last year, and if they answered ‘yes’, whether they reported it to the police. Those who answered ‘no’ were asked why they did not report the crime to the police. Those who answered ‘yes’ were asked whether they were satisfied or not with the speed of the police response and the follow-up work by the police afterwards.

2093 replies were received, according to which the following findings were recorded:

• Of those who responded, 1119 experienced or witnessed a crime in the last year (54%).

• Of these, 421 did not report the crime to the police (38%).

• Of those who did not report the crime, 215 did not do so because they lacked confidence in the police for one reason or another.

• Of those who did not report the crime, 133 did not do so because they thought the crime concerned was not important enough.

• Of those who did report it, 224 were not satisfied with the speed of the police response while 324 were not satisfied with the work of the police to follow up the report.

Base your answers on the assumption that the respondents in the survey are and remain representative of the resident population of the borough, and that they respond to questions truthfully.

UNREPORTED CRIME
A survey by Lynne Featherstone

On the basis of both anecdotal and documented evidence that many crimes are not reported to the police, I undertook a survey to provide a snapshot of the level of the non-reporting of crime. In doing so I was particularly interested in why people did not report crimes to the police and what these reasons show about the level of public confidence in the police service.

Survey
The questions on the reporting of crime were included in a wider survey on crime and disorder that was sent out to residents in a single north London borough during the second half of last year.

Respondents were asked whether they had been a victim of or witness to a crime in the last year, and if they answered ‘yes’, whether they reported it to the police. Those who answered ‘no’ were asked why they did not report the crime to the police. Those who answered ‘yes’ were asked whether they were satisfied or not with the speed of the police response and the follow-up work by the police afterwards.

2093 replies were received, according to which the following findings were recorded:

• Of those who responded, 1119 experienced or witnessed a crime in the last year (54%).

• Of these, 421 did not report the crime to the police (38%).

• Of those who did not report the crime, 215 did not do so because they lacked confidence in the police for one reason or another.

• Of those who did not report the crime, 133 did not do so because they thought the crime concerned was not important enough.

• Of those who did report it, 224 were not satisfied with the speed of the police response while 324 were not satisfied with the work of the police to follow up the report.

Base your answers on the assumption that the respondents in the survey are and remain representative of the resident population of the borough, and that they respond to questions truthfully.

1 If a resident who reported a crime in the past year witnesses or experiences a crime in the coming year, there is at least a 50% chance that they will not report it to the police.

2 The majority of residents in the borough are dissatisfied with the police response to reported crime, and/or lack confidence in the police.

3 Of those who reported a crime in the past year, over 120 gave more than one reason for saying they were dissatisfied with the police response.

UNREPORTED CRIME
A survey by Lynne Featherstone

On the basis of both anecdotal and documented evidence that many crimes are not reported to the police, I undertook a survey to provide a snapshot of the level of the non-reporting of crime. In doing so I was particularly interested in why people did not report crimes to the police and what these reasons show about the level of public confidence in the police service.

Survey
The questions on the reporting of crime were included in a wider survey on crime and disorder that was sent out to residents in a single north London borough during the second half of last year.

Respondents were asked whether they had been a victim of or witness to a crime in the last year, and if they answered ‘yes’, whether they reported it to the police. Those who answered ‘no’ were asked why they did not report the crime to the police. Those who answered ‘yes’ were asked whether they were satisfied or not with the speed of the police response and the follow-up work by the police afterwards.

2093 replies were received, according to which the following findings were recorded:

• Of those who responded, 1119 experienced or witnessed a crime in the last year (54%).

• Of these, 421 did not report the crime to the police (38%).

• Of those who did not report the crime, 215 did not do so because they lacked confidence in the police for one reason or another.

• Of those who did not report the crime, 133 did not do so because they thought the crime concerned was not important enough.

• Of those who did report it, 224 were not satisfied with the speed of the police response while 324 were not satisfied with the work of the police to follow up the report.

Base your answers on the assumption that the respondents in the survey are and remain representative of the resident population of the borough, and that they respond to questions truthfully.

The Penguin Theatre Group is designing a brochure to publicise their new production. The brochure will be made from a single sheet of paper which will be folded exactly in half twice, the final shape being a right angled triangle as shown below:

A magic pill that makes you slim with no side effects would be the 21st century’s ‘goose that laid the golden egg’. With 13 million people forecast to be obese by 2010, the market for a miracle cure is huge. Consumer groups are concerned, however, that “slimming pills” are at best expensive and useless, as they will not have any effect unless people also reduce their intake of food. At worst they can cause side effects and be addictive. People who are worried about their weight often fail to be cautious about what looks like a miracle cure. So why are manufacturers allowed to sell these pills and make grand claims for their effectiveness? Because most slimming pills are not licensed as medicines and so are not subject to strict controls: they are controlled by food regulations. The government should act now to protect people from their own ignorance, and make slimming pills subject to the same strict controls as medicines.

I have two bags of marbles. I know that at least one of the bags contains marbles of only one colour.

I take one marble from the left hand bag, and put it into the right hand bag. I then take a marble from the right hand bag and put it into the left.

I then tip the marbles out of the right hand bag and see that half the marbles are green and half of them red.

1 The left hand bag started off with more than two marbles in.

2 The right hand bag started off with more than two marbles in.

3 The left hand bag started off with marbles of only one colour in.

4 The right hand bag started off with marbles of only one colour in.

A Welsh police station has incorporated ‘colour psychology’ into the design of its cells with the intention of improving the success of interrogation. As well as glass doors thought to reduce claustrophobia, a particular shade of yellow has been used which is said by psychologists to have a positive, calming, mood enhancing effect. Similarly royal blue has been used, as evidence suggests that it enhances communication.

Today is our village’s fund-raising Fun Day. This is the current state of the “Treasure Hunt”, in which entrants put their initials in their chosen square(s).

I have just paid for two squares. I will choose two squares that do not touch each other or any of the squares already taken, either horizontally, vertically or diagonally.

In the Beijing Olympics, in 2008, China claimed to have come out top of the medal rankings on the basis that it won the most gold medals.

Fig 1: Top five nations: gold medals only

The USA contested this on the grounds that it won the most medals, gold, silver and bronze counting one each.

Figure 2: Top five nations: all medals equally weighted

But arguably neither of the above methods of counting gives an accurate picture of relative achievement. The fairest system would be weighting the medals, as follows, and/or comparing the medals won against population or national wealth.

Fig 3: Medals weighted: gold 3, silver 2, bronze 1

Fig 4: Medals weighted (gold 3, silver 2, bronze 1) per million population

In the Beijing Olympics, in 2008, China claimed to have come out top of the medal rankings on the basis that it won the most gold medals.

Fig 1: Top five nations: gold medals only

The USA contested this on the grounds that it won the most medals, gold, silver and bronze counting one each.

Figure 2: Top five nations: all medals equally weighted

But arguably neither of the above methods of counting gives an accurate picture of relative achievement. The fairest system would be weighting the medals, as follows, and/or comparing the medals won against population or national wealth.

Fig 3: Medals weighted: gold 3, silver 2, bronze 1

Fig 4: Medals weighted (gold 3, silver 2, bronze 1) per million population

In the Beijing Olympics, in 2008, China claimed to have come out top of the medal rankings on the basis that it won the most gold medals.

Fig 1: Top five nations: gold medals only

The USA contested this on the grounds that it won the most medals, gold, silver and bronze counting one each.

Figure 2: Top five nations: all medals equally weighted

But arguably neither of the above methods of counting gives an accurate picture of relative achievement. The fairest system would be weighting the medals, as follows, and/or comparing the medals won against population or national wealth.

Fig 3: Medals weighted: gold 3, silver 2, bronze 1

Fig 4: Medals weighted (gold 3, silver 2, bronze 1) per million population

In the Beijing Olympics, in 2008, China claimed to have come out top of the medal rankings on the basis that it won the most gold medals.

Fig 1: Top five nations: gold medals only

The USA contested this on the grounds that it won the most medals, gold, silver and bronze counting one each.

Figure 2: Top five nations: all medals equally weighted

But arguably neither of the above methods of counting gives an accurate picture of relative achievement. The fairest system would be weighting the medals, as follows, and/or comparing the medals won against population or national wealth.

Fig 3: Medals weighted: gold 3, silver 2, bronze 1

Fig 4: Medals weighted (gold 3, silver 2, bronze 1) per million population

In the 2008 Olympics:

1 Norway won 3 gold and 5 silver medals.

2 Iceland won 3 medals.

3 Slovenia won 6 medals, including one gold.

In the Beijing Olympics, in 2008, China claimed to have come out top of the medal rankings on the basis that it won the most gold medals.

Fig 1: Top five nations: gold medals only

The USA contested this on the grounds that it won the most medals, gold, silver and bronze counting one each.

Figure 2: Top five nations: all medals equally weighted

But arguably neither of the above methods of counting gives an accurate picture of relative achievement. The fairest system would be weighting the medals, as follows, and/or comparing the medals won against population or national wealth.

Fig 3: Medals weighted: gold 3, silver 2, bronze 1

Fig 4: Medals weighted (gold 3, silver 2, bronze 1) per million population

Great Britain’s population is 62 million, the population of the US is 306 million, and the population of the Russian Federation is 142 million.

1 Great Britain rank below Slovenia but above the USA.

2 The Russian Federation won the equivalent of less than 1 bronze medal for every million of its population.

Maria, a malnourished patient has a regime which requires her to take a drink with her meal at lunchtime which contains 4.0 Joules in 500ml of solution. The drink is made up by adding a powdered energy supplement to water. The supplement contains 2.0 Joules per 100g powder. The change in volume of the water on adding the supplement is negligible.

Nurse Delgado has, left over from made up drinks from other patients, 200ml of drink containing the same supplement which has an energy value of 1.5 Joules and 400ml with an energy value of 2.0 Joules.

Praise is an expression of recognition and a conferment of status. Recognition and status are important factors in our self esteem and well being. No matter how well paid someone is, if their efforts are never acknowledged the cash will not quite compensate. By the same token, someone who feels recognised and appreciated will cheerfully put up with other inconveniences, including a less desirable income. The most valuable kind of praise is that which the recipient knows to be appropriate. Praise should only be given to the extent that it is deserved.

1. People can accurately assess the recognition they deserve.

2. People who give praise can assess the level of praise which is deserved.

3. Promoting others’ self esteem is a duty which we all share.

4. Self esteem produces behaviour which benefits others as well as the individual.

Each blood sample taken at a particular private clinic is given an 8-digit reference number.

Example: 12404360

This was the reference number of the 36th sample taken on 4th September 1993 (124 means the 124th month of operation of the clinic, since opening in June 1983 month 001). The final digit is a security check digit, and has the value that makes the sum of the eight digits a multiple of ten.

A campaign poster on public transport vehicles recently announced that 40% of teenage girls below the age of 16 who become pregnant were found to have been under the influence of alcohol at the time they had sexual intercourse.

1. Young people who are underage drinkers are more likely to be sexually active than those who do not drink.

2. If there were stricter controls on the sale of alcohol to young people there would be fewer teenage pregnancies.

3. At least 40% of girls have consumed alcohol by the age of 16.

The table below summarises GCSE results for five schools in a town.

A graph has been drawn which summarises this data but the graph has not yet been scaled or labelled.

Although it has been known for some time that ants are able to make alarm calls using sound, advances in technology have enabled scientists to discover that ants routinely “talk” to each other in their nests. Using miniaturised microphones and speakers that can be inserted unobtrusively into nests, researchers established that ants have a vocabulary and can talk to each other by rubbing parts of their abdomen together, and the queens can issue instructions to their workers.

But these surprising abilities can be exploited by other parasitic insects, who can mimic the ants to make them their slaves. Rebel’s large blue butterfly ñ an endangered species ñ is a case in point. This species has been found to have learnt to imitate the ants’ sounds so successfully that the butterfly’s caterpillars are carried by ants into the nests where they beg for food and are fed by the worker ants. When a colony is disturbed the ants will rescue the caterpillars before their own broods. They will even slaughter their own young to feed the caterpillars when food is scarce.

Tim works each day from Monday to Friday. At 5pm each day at work Tim receives 7 tokens. At 1pm on any day at work Tim can exchange a certain number of these tokens for a free meal (which always costs the same number of tokens).

On the morning of Monday 1st Tim had 20 tokens. He will take a free lunch on any day that he has enough tokens. The first day that Tim cannot get a free meal is Tuesday 9th.

For there to be life elsewhere in the universe, there would have to be planets similar to Earth, i.e. small, rocky planets orbiting at the right distance from their star to ensure that they are not so hot that water boils and not so cold that it remains frozen. Until now techniques have not been sensitive enough to detect such planets. The new Kepler telescope is so sensitive that for the first time astronomers will be able to see if there are Earth-sized planets in the ‘habitable zone’ of their stars – the region where the temperature is right for liquid water to exist at the surface. So if the Kepler telescope finds that such planets exist, we can at last be confident that there is life on planets other than Earth.

A particular company manufactures square floor tiles whose patterns consist of 16 smaller squares of equal size. Two of the smaller square on each tile are black, whilst the rest are white.

When I opened a packet of 12 of these tiles this morning and laid them out as shown below, I thought that they were all different.

On closer inspection, however, I realised that rotation of the relevant tiles would reveal that some are identical to at least one of the others.

It is human nature to try to explain what we observe occurring around us, a process that people engaged in long before physical, biological or social sciences were established as disciplines. The difference between ‘common sense’ explanations and scientific ones lies in the way the two originate. Everyday observations are haphazard, careless and not systematic, whereas those carried out by scientists endeavour to be specific, objective, well focused and systematic, to the extent that they could be replicated by someone else. While there are few true guarantees, the more systematic and organised the studies we conduct, the more likely they will produce valid explanations that can be used to support decisions.

One algorithm for controlling the order in which floors are visited for a lift is called SST or “shortest seek time first”. It keeps a list of all the floors it is currently requested to visit and, after a stop, it will next visit the closest on its list. If two requests are the same distance away, it goes in the direction in which more floors have requested the lift.

A lift using SST has just stopped at floor 7 and its request list contains floors 0, 4, 10, 14 and 16. Just after it starts moving, a new request comes in for floor 7.

The table below shows the value of the Scottish agricultural production in four sectors from 1994 to 1998.

Scottish agricultural output 1994-1998

Commentary on 1998 figures

Largely as a result of the strength of the pound at the time, lower prices were experienced due to farmers having to drop their prices for commodities being exported from the UK. Although prices dropped for some inputs, such as fertiliser and animal feed (again as a consequence of the strength of the pound) this was not enough to prevent farming income experiencing a sharp fall. Scottish farm incomes are still above those experienced in 1980, 1985 and 1986.

The table below shows the value of the Scottish agricultural production in four sectors from 1994 to 1998.

Scottish agricultural output 1994-1998

Commentary on 1998 figures

Largely as a result of the strength of the pound at the time, lower prices were experienced due to farmers having to drop their prices for commodities being exported from the UK. Although prices dropped for some inputs, such as fertiliser and animal feed (again as a consequence of the strength of the pound) this was not enough to prevent farming income experiencing a sharp fall. Scottish farm incomes are still above those experienced in 1980, 1985 and 1986.

The table below shows the value of the Scottish agricultural production in four sectors from 1994 to 1998.

Scottish agricultural output 1994-1998

Commentary on 1998 figures

Largely as a result of the strength of the pound at the time, lower prices were experienced due to farmers having to drop their prices for commodities being exported from the UK. Although prices dropped for some inputs, such as fertiliser and animal feed (again as a consequence of the strength of the pound) this was not enough to prevent farming income experiencing a sharp fall. Scottish farm incomes are still above those experienced in 1980, 1985 and 1986.

The table below shows the value of the Scottish agricultural production in four sectors from 1994 to 1998.

Scottish agricultural output 1994-1998

Commentary on 1998 figures

Largely as a result of the strength of the pound at the time, lower prices were experienced due to farmers having to drop their prices for commodities being exported from the UK. Although prices dropped for some inputs, such as fertiliser and animal feed (again as a consequence of the strength of the pound) this was not enough to prevent farming income experiencing a sharp fall. Scottish farm incomes are still above those experienced in 1980, 1985 and 1986.