Natural Numbers: The natural numbers include whole numbers except 0. Set: A set is a collection of objects, things or symbols which are clearly identified.
The individual objects in the set are called the elements or members of the set. Elements may be specified in two ways: By listing the elements By description E.
In Mathematics, matrices are arrays of numbers arranged in rows and columns. Diagonal Matrix: Also known as square matrix, in which all element zero except the …. Circle Definitions: Geometrical Properties of Circle: If 2 chords in a circle area congruent, then the 2 angles at the centre of the circle are identical.
The bearing of point B from another point A is: An angle measured north to at A. In a clockwise direction. Written as three- figured number i. The bearing of B from A is degree. Congurency: Two geometric figures are congurent, if they are of the same shape and size. Vectors have both magnitude and direction.
Position Vector: Position vectors are also called as end points. O Level Mathematics Revision Notes.Fractions, ratios 6. Percentages 7. Rational and irrational numbers 8. Algebra: simplifying and factorising 9. Equations: linear, quadratic, simultaneous Rearranging formulae Inequalities Parallel lines, bearings, polygons Areas and volumes, similarity Trigonometry Circles Similar triangles, congruent triangles Transformations Loci and ruler and compass constructions Vectors Straight line graphs More graphs Distance, velocity graphs Sequences; trial and improvement Graphical transformations Probability Statistical calculations, diagrams, data collection Functions Calculus In this case, both numbers share a 7, so divide this out: 0.
If the digit following the nth is 5then the nth digit is raised by 1.Maths is a natural science concerned with the study of life and living organisms, including their structure, function, growth, evolution, distribution, and taxonomy.
I hope you find them useful. In addition, your name will be written in the credits section of this post. I need O level Math books. Kindly recommend me some resources so that I may be able to get free pdf books. Im very grateful for your kindness with me………. Contact no. All the subjects are showing error. Pls pls pls pls help………. If we attempt all questions in paper2 in section B of maths olevel including the choice one…will all of our answers be checked or only the first 4???
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The current website has been facing problems with Dropbox. Close Menu O Level. Pakistan Studies. A Level. Computer Science. English Literature. O Level. Files are not opening when i click on it shows an error Please fix it asap. Fixed, sorry. The files are downloading but not opening can u plz check this issue.
I like it. Dearest apologies.We were sad to miss the Aurora as it arrived 3 days after we left. I am a photographer and I took over 2000 photos on this trip. I am still sorting it now and plan to make a photobook of this trip to remind us of the best family vacation ever.
Thank you Hafdis and Nordic Visitor :) It was a fabulous trip. From the moment I made my initial enquiry right through to the end of the trip, everything went smoothly. All the accommodation was lovely, the books and maps were so well done and helpful. There was nothing left unanswered and the staff at Nordic were very helpful and willing to assist in any way they could. Overall one of the best tour group companies I have ever used.
Will definately be recommending Nordic to others and hopefully I will book another trip with you again sometime :) I was a little nervous about using a tour company, but when my wife informed me that it was a self-drive tour, I was okay.
Sigfus did a great job picking out interesting things for us to see and places to stay. I have nothing negative to say about our experience with Nordic Visitor I have already recommended Nordic Visitor to some of my friends and they seem quite impressed with what we were given for our tour.
Congratulations for the entire team of Nordic Visitor. You know how to give a wonderful experience to the customers. All exceptions and extras were handled with extreme care and attention. So, the experience was perfect and I strongly recommend to travel with Nordic Visitor. Although choosing via the internet can be suspect we found your company to be friendly, professional and efficient and we were pleased with the service which we received through your representative.
Helena resolved a few queries we had about travel arrangements very efficiently. The information given was very comprehensive and useful. The hotels were outstanding in all respects, particularly the Hotel Continental in Oslo. All the food was very good. The level of personal service was excellent by all staff.
All of the trips ran very smoothly. We had a problem with a charge our bank made on our payment of the deposit and your finance department were prepared to make alternative arrangements if needed when we were paying the balance. The service from your company was extraordinary.
We appreciated all of the materials provided. All in all, this was the best booked tour I've taken anywhere in the world. We had a really great time. Norway was beautiful and it was a pleasure to be able to absorb our surroundings comfortable in the knowledge that we were in safe hands.
The small group size made the tour feel quite personal and we got to meet some great people. Special credit to our tour guide, Line.
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She was very professional, an excellent conversationalist, very well traveled and made all the details that would normally frustrate us (timetables, transportation, etc,) seem quite effortless.
During the course of our tour, we also met two other employees of Nordic Visitor (Bjorn and a woman whose name escapes me. We have recently completed the 9 day Natural Wonders of Iceland Tour with Nordic visitor and were very happy with our tour.
We were a little apprehensive initially about booking with an unknown operator. Coming from Australia, there is not a lot on offer from travel agents. Mostly overpriced tours, that did not seem to offer value for money in comparison to this tour and with some the hotel accommodation details were not provided which made us very nervous about booking with them.Warwick Mathematics and Statistics are ranked 3rd in the national research assessment REF 2014.
Warwick Statistics Research Spotlights brochure (big file. Information about parental leave, support for childcare responsibilities and part-time options can be found here. Wallis and Futuna Western Sahara Yemen Zambia Zimbabwe Databases OECD. When analysing data, such as the marks achieved by 100 students for a piece of coursework, it is possible to use both descriptive and inferential statistics in your analysis of their marks.
Typically, in most research conducted on groups of people, you will use both descriptive and inferential statistics to analyse your results and draw conclusions. So what are descriptive and inferential statistics. And what are their differences.
Descriptive statistics is the term given to the analysis of data that helps describe, show or summarize data in a meaningful way such that, for example, patterns might emerge from the data. Descriptive statistics do not, however, allow us to make conclusions beyond the data we have analysed or reach conclusions regarding any hypotheses we might have made.
They are simply a way to describe our data. Descriptive statistics are very important because if we simply presented our raw data it would be hard to visulize what the data was showing, especially if there was a lot of it. Descriptive statistics therefore enables us to present the data in a more meaningful way, which allows simpler interpretation of the data.
For example, if we had the results of 100 pieces of students' coursework, we may be interested in the overall performance of those students. We would also be interested in the distribution or spread of the marks. Descriptive statistics allow us to do this. How to properly describe data through statistics and graphs is an important topic and discussed in other Laerd Statistics guides. Typically, there are two general types of statistic that are used to describe data:When we use descriptive statistics it is useful to summarize our group of data using a combination of tabulated description (i.
We have seen that descriptive statistics provide information about our immediate group of data. For example, we could calculate the mean and standard deviation of the exam marks for the 100 students and this could provide valuable information about this group of 100 students.
Any group of data like this, which includes all the data you are interested in, is called a population. A population can be small or large, as long as it includes all the data you are interested in. For example, if you were only interested in the exam marks of 100 students, the 100 students would represent your population.
Descriptive statistics are applied to populations, and the properties of populations, like the mean or standard deviation, are called parameters as they represent the whole population (i. Often, however, you do not have access to the whole population you are interested in investigating, but only a limited number of data instead.
For example, you might be interested in the exam marks of all students in the UK. It is not feasible to measure all exam marks of all students in the whole of the UK so you have to measure a smaller sample of students (e. Properties of samples, such as the mean or standard deviation, are not called parameters, but statistics. Inferential statistics are techniques that allow us to use these samples to make generalizations about the populations from which the samples were drawn.To use the Live Streaming service you will need to be logged in and have a funded account or to have placed a bet in the last 24 hours.
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Please Gamble Responsibly visit Gamcare. In our Manchester United v Manchester City betting preview we look at the best possible bets between the two sides. The Citizens have broken all sorts of records this season and should they win at Old Trafford for the second successive season they will set a new Premier League record for consecutive wins, with them currently on thirteen.
The Red Devils have accumulated 35 points this year which is a huge improvement on this stage twelve months ago when they had just 21. The 54 year-old often gets stick for setting his side up defensively in the big games but due the huge gap in points between the two sides he could be left with no option but to attack, especially with them being at home.
The Citizens have made a blistering start to the season with them dropping points on just one occasion in the Premier League, making them overwhelming favourites to win their third title. Such is the confidence in some that City will do it, Paddy Power have already paid out on them lifting the trophy in May. Their recent trips to Old Trafford have been very productive too, with them losing just two of their last seven trips their which includes four victories.
But City do come into this one on the back of their first defeat of the season after going down 2-1 to Shakhtar Donetsk in Kharkiv on Wednesday night.
All the stats and form point towards a City win and it could potentially be a crucial blow in the title race, but anything is possible here. Missed sitter, unbelievable screamer.Next to your bed.
If the answer is any of the three above, you're one of 96 per cent of motorists that are vulnerable to car thieves using high-tech gadgets to steal vehicles in a matter of minutes. If Elon Musk had peered out of his California office window last week he might have caught a glimpse of the new electric car that's set to challenge his Tesla brand's market dominance.
Recently, a taxi driver told me how he had taken money out of his Isas - and turned to Bitcoin and Premium Bonds instead.
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A foolish strategy - or a genius move. Turkey is the top destination for exports of steel from the European Union, taking 18 per cent of exports last year. The seller sent the phone to me straight away via Royal Mail's 'signed for' service.
Unfortunately, on the day it was apparently delivered, my husband and I were both out. When I got home I saw online that the parcel had been delivered and signed for. I checked with my neighbours and looked for the parcel to no avail.
Royal Mail spoke to the driver who apparently said that he had left it in my mailbox. Savers can now get their hands on four new accounts from National Savings and Investments as it looks to attract more cash into the financial year. There are no guarantees in the world of investment but experience can be drawn on to help shape decision making.
Here a leading expert share his views on what's in store for 2018. History teaches us that bull runs never last forever and eventually markets will plunge into a bear territory, or even worse face a full-on crash.
Most major savings providers waited until this week to make changes to their deals, even though the base rate was hiked by 0.
Just how much you need to cover essential expenses will be personal to you. But it's not hard to calculate it once you've dug out the relevant paperwork and done some basic sums. With the government desperate to get as many drivers to ditch diesel and buy electric cars, it's about time there was a zero-emission model that we can all live with.
Is BMW's i3s that car. We took the new family-friendly hatchback for a test in Lisbon, Portugal, to find out. Should you find yourself putting off renewing your home insurance until tomorrow, or feeling confused by compound interest, you can blame evolution.
We explain why and what you can do. Debra Westowski was told by her bank, Santander, that she couldn't have a credit card even though she had paid off her mortgage and had a good income. Britons thinking about retirement should not rely on their state pension or face up to a huge fall in earnings, a report from the influential OECD shows. The report that put the UK bottom of the pensions league showed retirees face the steepest income drop compared to any other OECD country - behind Mexico, Poland and Japan - if they rely solely on state pension payments.
Paul Thomas travelled to Taibach, in the shadow of the Port Talbot steelworks, to investigate allegations that workers are being badly advised by financial advisers. Steelworkers are being told they can have hundreds of thousands of pounds right now - an alluring prospect - if they give up a steady pension income in the future. Twice as many are closing their doors this year than in 2015 or 2016,So far this year, 962 branches have shut up shop, according to consumer champion Which?.
The closures picked up pace last week, when RBS-NatWest announced it was getting rid of one in four of its branches. Despite petrol and alternative-fuel vehicle registrations rising, a 31 per cent dip in diesel demand saw the total new car market fall by 11. Shops are charging rip-off fees if customers fail to pick up their click-and-collect orders within as little as ten days.
The service allows shoppers to order goods online then pick them up in store.