How to Solve A level Maths Problems

How to Solve A level Maths Problems Solving A Level Maths Problems: A Guide ChaptersCalculusDifferentiationMechanicsBy studying Maths, you can first of all expect to develop a range of key skills that are sought after by employers and that will also help you throughout your day to day life. For example, Maths encourages logical thinking, decision-making and problem-solving, all of which are vital to survive in modern society.To add to that, Maths is a key area of study for those seeking a career in the Finance, Engineering and Information Technology industries. Just some jobs that are directly related to a Maths qualification are Chartered Accountant, Investment Analyst, Systems Developer and Secondary School Teacher of Maths, all of which include making use of Maths concepts like those we will be looking at below.Solving A Level Maths Problems: The Overarching Themes Of A Level MathsThe AQA A Level Mathematics (7357), which was taught from September 2017, with the first exams being sat in 2018 onwards, covers a broad range of Maths themes.Some of this conte nt includes Trigonometry, Sequences and series, Exponentials and logarithms, Differentiation, Integration, Vectors, Statistical hypothesis testing, Kinematics as well as Algebra and functions.Trigonometry is just one of the core themes you will come across in Maths. Photo by Internet Archive Book Images on Visual huntWhile all of the content covered is in the syllabus for a reason, there are some overarching themes that we will focus on below which are almost like gateways to other areas of studies within Mathematics, as well as tools that can be implemented in your professional career.While many will not use all, if any, of the specific skills outlined in this article, they are nonetheless studies that are relatable and can be referred to in many aspects of mathematical, technological and scientific roles, and may even prove useful in other industries too.Maths Help For Students With Regards to Solving Maths ProblemsRemember that solving Maths problems is reliant on completing a nu mber of steps correctly to reach a solution. As such, it is important that you not only learn how to do the correct working out processes, but that you also practice putting them on show.During exams, pupils will be given marks not only for getting a correct answer but also for backing this up with a trail of written sums, equations or the like. Consequently, even if you make a mistake down the line, you could still get awarded some points for the method you used.This means that even if you get a wrong answer, you could still make up some points in comparison to someone who did get the right answer but didn’t note down their working out.So, don’t let two years of studying tools and methods go to waste, make sure you brush up on the ways of solving problems and display this knowledge in your exams!One of the best tips for Maths students is to write down all of their working out as they could still get points even if the answer is wrong or incomplete.A Closer Look At The Maths The mes Featured On An A Level CourseIf y = a function of x (an expression containing x's and numbers), then the derivative of y with respect to x is written dy/dx.In addition to the above simple rule, you will almost certainly learn about Differentiating x to the power of something, bringing the power down to in front of the x and then reducing the power by one, along with studying Notation, the ways of writing the derivative.Along with this power rule, other underlying themes within the Explicit Differential umbrella are the constant rule, the constant multiple rule, the sum rule and the difference rule.Differentiation is, as stated above, concerned with curves and gradients, therefore, using all of the above knowledge, you will ultimately be able to Differentiate the equation of a curve, finding a formula for its gradient.If all of this sounds a bit perplexing, rest assured that your Maths teacher will be able to explain the processes and functions so that they come to you easily.Mec hanicsFinally, this now-compulsory module will make its appearance during your A Level Maths course, shedding light on Acceleration, Newton's Laws, Vectors, Impulse and Momentum, Projectiles, Centre of Mass and much, much more.Acceleration is on the list when it comes to your Mechanics module. Photo by www.twin-loc.fr on Visual huntThe module is absolutely vital for anyone with an interest in pursuing a career in the engineering industry, as it will teach you the fundamentals of Mechanics principles.Fascinating content for fast car enthusiasts too, the equations and functions can be extremely useful to many, with a range of transferable skills on offer. For example, the study of acceleration caused by gravity is also linked to Physics courses and is relevant to scientists looking at gravitational acceleration at different points on Earth too.The aim of this module is to ‘up-skill’ students within the mechanical field, enabling them to solve real-world problems. At the end of the module, you should have the confidence to apply how the maths and physics principles allow engineers to innovate and design.Look for the right  maths tutor  on Superprof!Sound Challenging? Don't Worry, You're Doing Great!While it is impossible to educate you on advanced Maths functions in a few short paragraphs, we hope that you now have a better overview of some of the themes covered, and can appreciate the level of detail you will be exposed to during your A Level Maths course.Take comfort from the fact that many people find Maths challenging as a subject, and that it is perfectly normal for you to need a little time or extra tuition to help you along the way.Remember also that the content you will be learning at A Level is no longer part of your compulsory education, so all the things you are learning are already adding noteworthy skills to your resume. Just think, even as a teenager you will have a higher level of knowledge and skill in this area than most adults who are much o lder and wiser than you!As a matter of fact, adults who once passed their Maths qualifications back in the day would probably struggle to complete the content you are studying now, which shows that you can very feel proud of your achievements to date.While this might be down to them not using the acquired skills enough and thus losing or forgetting them, it could also be because the Maths syllabus has grown more advanced over the years, producing  more talented and skilled mathematicians than ever before.

A Comforting Thing... - Introvert Whisperer

Introvert Whisperer / A Comforting Thing... - Introvert Whisperer A Comforting Thing My blog followers â€" today’s post is a bit out of the norm for me as it’s not my usual actionable career advice.   Nevertheless, there are a couple of good gold nuggets I thought you might want to consider regarding finding comfort. The company Tommy John (men’s underwear) featured my input on things that bring me comfort in a savvy info-graphic they created. Who can’t use a few more comforting things to make life great!? Here are a few other comfort tips I have to share: Let’s face it, I find great comfort in a good cookie. It’s good for days that are tough and days that are great you can never go wrong with a good cookie. When I’m stressed, I search YouTube or Facebook for cute kittens or animals videos. Any stress melts away as you focus on the immense love you can feel for an animal. On Sunday afternoons’, I like to search for cheesy sci-fi movies to kick back and do nothing but take in mindless content. It’s comforting as it hails back to what I did as a kid. Enjoy! Dorothy

Online Probability Tutoring

Online Probability Tutoring Probability Tutors are Online Now. Get Probability Homework Help 24/7. Probability theory has found its way into almost every aspect of life, but that hasnt made it any easier to understand. The complex concepts that make up Probability can leave you scratching your head. Tutor Pace has the expert online tutors you need to solve your Probability dilemmas. Our online probability tutor are available 24/7 to guide you step-by-step through your challenges Personalized Online Probability Tutoring Unlike other online tutors, we dont lump you in with a bunch of other students during sessions. Each tutoring experience is a one-on-one interaction between you and a online Probability tutor, so you get all the attention you need to grasp important concepts. Probability Homework Help Everyone has had the experience of getting stumped on homework. Our online tutors are always ready to walk you through each problem and help you grasp the theories you need to solve even the most difficult problems. In addition to homework help, you can: Study for an upcoming test Go over a concept from earlier in the year Get help for a project or assignment Verify a homework answer you are unsure of Learn advanced Probability concepts Tutor Pace is committed to your success, and we guarantee our tutors will give you greater confidence toward your studies. Sign up now and earn the grades you deserve.

How to Better Your Relationship With Your Boss - Introvert Whisperer

Introvert Whisperer / How to Better Your Relationship With Your Boss - Introvert Whisperer How to Better Your Relationship With Your Boss How to Better Your Relationship With Your Boss â€" Get along with your boss like a boss.   Many people are puzzled when it comes to this topic. How to have a good relationship with your boss? You want your boss to know you’re a good worker and to keep things professional, but you don’t want your relationship to be too official. How to make your boss notice you for all the right reasons, and appreciate  you because of them? People really care about the relationship that they have with their boss that sometimes they get too stressed about it and ruin it by overthinking. There are a few general rules that everyone should follow when it comes to their bosses if you want to better the relationship and get the appreciation and respect that they deserve. And who wouldn’t want that, right? 1. Don’t rely on emailing

The Guitarists Guide to Chromatic Scales

The Guitarists Guide to Chromatic Scales How Are Scales Useful for Guitarists? ChaptersWhat Is a Chromatic Scale?What’s the Difference Between a Chromatic Scale and a Diatonic Scale?How Do You Play the Chromatic Scale on the Guitar?Why Use the Chromatic Scale“Life seems to go on without effort when I am filled with music.” - George EliotAlmost everyone in the UK enjoys music in one way or another.  If you want to become a guitarist, it’s important that you stay up-to-date with the news.Learning to play guitar is a long process but it’s definitely worth it once you’ve learnt how to play.  You’ll soon know everything you need to know about pentatonic scales, riffs, the fretboard, strings, etc. You just need to explore every aspect of the guitar and music theory. There’s no way better than playing the chromatic scale.for when you're  working on your technique and doing various exercises.Scales are great for warming up your fingers. (Source: jameslee)It consists of every note, each separated by a semitone.  The notes are all separated by the same in terval and it’s impossible to work out the scale’s key. A chromatic scale is, therefore, atonal because it doesn’t matter which key it is in.A chromatic scale is basically every note until you reach the next octave.  The chromatic scale for C is C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C.Remember that between E and F and B and C there is no semitone. In fact, there is no such thing as E sharp or B sharp. There’s no need to alter any of the notes in this case. There are 12 different notes between each tonic.  In reality. You could alter certain notes. For example, instead of a C#, you could have a Db. However, the two are actually exactly the same note.Find out more about major scales!What’s the Difference Between a Chromatic Scale and a Diatonic Scale?The diatonic scale isn’t very often used on the guitar but it is useful for helping you understand music theory.Natural notes on a piano are usually white. (Source: b1-foto)Diatonic comes from the Greek and means “across the tonics”. The diatonic scale includes the 7 natural notes in music: C D E F G A B C.There is no tonality. You can only play it in one given way. C D E F G A B C. The diatonic scale is also known as C major, which can also be played in other keys.  While it’s useful for understanding harmonics, you may quickly forget its name.The diatonic scale is a part of the chromatic scale.  The latter is made of both chromatic and diatonic semitones all at once.A semitone interval between two notes is a chromatic semitone (between D and D#, for example).A semitone interval between two different notes is a diatonic semitone (between G# and A, for example).Don't forget that guitarists should also learn about minor scales!How Do You Play the Chromatic Scale on the Guitar?The chromatic scale has 12 possible positions. It can be played on an acoustic guitar, electric guitar, or even an electro-acoustic guitar.Play with a metronome and a pick when you practise your scales. (Source: Pexels)The f irst thing you should do is play four consecutive notes on the same string. The goal is to repeat this exercise all over the neck. For example:D string: index finger on the 5th fret, middle finger on the 6th fret, ring finger on the 7th fret, pinky on the 8th fret.G string: index finger on the 5th fret, middle finger on the 6th fret, ring finger on the 7th fret, pinky on the 8th fret.B string: index finger on the 5th fret, middle finger on the 6th fret, ring finger on the 7th fret, pinky on the 8th fret.B string: index finger on the 5th fret, middle finger on the 6th fret, ring finger on the 7th fret, pinky on the 8th fret.You can also do the same exercise on higher frets. Start on the low E string with your index finger on the 4th fret and then work your way up to the high E string. Shift your fingers to a new fret and do it again. Do this until you’re up to the eleventh or twelfth frets. Start off slowly at first and then get faster as you progress.You’ll soon see that by doin g this exercise every day, you’ll make steady progress. Make sure that you don’t start off too far up the fretboard. Practise doing a back and forth motion with the plectrum as well. Each note should last the same amount of time, even when you change strings. You can play with a metronome, too.Furthermore, each note needs to be played cleanly and correctly. Take your time! It’s better to start off slow rather than make a lot of mistakes by trying to go too quickly.This exercise allows you to work on your fingering on your left hand and loosening up your fingers as you do. You’ll work on your dexterity, coordination, flexibility, and precision.The Position of Your Left HandWhile your right-hand positions itself almost naturally by the strings, you need to work on how to position your left hand. You’ll need to bend your wrist and curl your fingers towards the neck.  Make sure you press cleanly onto the strings of the guitar with the tips of your finger and not with the entir e finger. You should make sure that your nails are cut short.Keep your fingers as close to the frets as possible, too. If you’re playing the seventh fret, your finger should be closer to the seventh than the sixth. This is the best place to put your finger without directly pressing on the fret itself. Furthermore, you need to make sure that you don’t move your hand back and forth but rather leave it in the same position. It’s your fingers that should move more than your hand. Your hand should stay in position.It’s a great way to improve your coordination and learn how to play more quickly.  Pay particular attention to your left hand.Finally, keep your fingers pressed down. When you’ve played a note with your index finger, don’t lift off until you’ve played a note with your middle finger. The goal is to improve the strength with which you press down on the frets, especially the pinky, and making the most of the strength in your hand and wrist.Starting to play the guitar takes a lot of time and effort. This is why it’s recommended that you take at least a few guitar lessons London or tutorials before you start teaching yourself. This can help you to avoid picking up bad habits.Why Use the Chromatic ScaleWhen you play the guitar, you have to apply all your knowledge and play a variety of different chords.  Whether you want to play blues, rock, jazz, or improvise solos, the chromatic scale will help you get to grips with your instrument.Take care of your hands and your guitar playing will take care of itself. (Source: MichaelGaida)Warming Up with the Chromatic ScaleYour hand is full of small precise muscles. When you play the guitar, you have to focus on your hands. Like a sportsman, an accomplished guitarist is in complete control of their gestures.  Thus, like with all training, you should warm up before you do anything.Start by stretching your fingers and your wrists:Hold your arm horizontally with your fingers pointing upwards. Gently stretch y our fingers back towards your wrist with the other hand for 5 seconds. Don’t force it and breathe softly while you do. Do this warmup three times for each hand.Do the same exercise as before but with your fingers pointing downwards. Do this three times for 5 seconds on each hand.Link your fingers with both hands held together and do around a dozen circles.Finally, stretch your fingers bu placing your thumb in the palm of your hand, close your fingers over your thumb, and stretch gently downwards. Do this exercises three times for five seconds on each hand.You can now start playing your chromatic scales in groups of three or four notes while paying particular attention to your fingers. The goal isn’t to go as quickly as possible but rather to do it correctly.The Chromatic Scale as a Technical ExerciseAs we saw before, working on chromatic scales is a good technique for learning to play the guitar.  Chromatic scales can help you to loosen up your fingers, strengthen them, improve their agility, dexterity, and timing.If you find the previous exercise too easy, you can always work on your chromatic scales on the 5th, 6th, 7th, and 8th frets.Using a Chromatic Scale for TransitionsSince the chromatic scale is atonal, you can use it for transitioning between two scales.  Two notes that don’t go together can be transitioned to by using the chromatic scale. This technique is particularly useful when improvising.Don't forget to study other scales, too!Adding More Nuance when ImprovisingBeginner guitarists will tend to stick to the scales they know when they’re improvising.  Adding a few chromatic and diatonic semitones could vary your playing. Make sure that you play the notes quickly enough to ensure that your improvising still feels harmonious and interesting.So are you ready to start working on the chromatic scale to enrich your guitar playing?If you want to learn how to play guitar, you should consider getting a private guitar teacher or tutor. On Superprof, a lot of the tutors offer a free guitar lesson for the first hour so you can see how you get along, discuss your goals as a guitar player, and talk about the various techniques that you'd like to learn.If you want to focus on fingerpicking, learning to read tablature, playing licks from your favourite songs, or go through the basics such as tuning your guitar, strumming a basic guitar chord, or working on your rhythm, you just need to tell them. Private tutors are there to tailor your lessons to you!

Travel English A Guide to the English Spoken in South Africa

Travel English A Guide to the English Spoken in South Africa There is no denying that the English spoken in South Africa is challenging to most students of English. Indeed, it is difficult even for native speakers to understand at times. Due to its many periods of colonization it has elements of Afrikaans, (a native language that is like Dutch), Portuguese, Malay as well as many tribal languages.However, don’t worry, there is help at hand. Here is a brief vocabulary guide to the English spoken in South Africa:Keyword: ApartheidApartheid was the system of racial segregation that existed in South Africa from 1948 to 1994. It was introduced and enforced by the ruling National Party during this time.  Non-whites were denied key civil rights like voting and there was a segregation (or division) of all public institutions which separate hospitals, schools, etc for the dominant whites and the oppressed non-whites.Food and DrinkAmasi is used to refer to a drink made from sour milk.Strips of dried and salted meat are called biltong.Bobotie is a meat dish with egg sauce.Mealie is maize.Dumpie is a well-known local beer.Spook and diesel is a spirit mixed with coke.Alcohol is called dop.If you drink too much you could suffer from a babbelas or hangover.If something is tasty you can say it is lekker.ClothesSwimming trunks are called baggies.Running shoes are called takkies.If you have a tendency towards designer clothes you could be called a larney.SocialTo graze means to eat.Dankie is thank you.Rock up means to arrive.A good friend is called a china.A party is called a jawl.If you hear Chips! it means Look out!If you are asked to a social engagement and agree to it, you can say Fixed up!If someone tells you they will be there in now now, it means they will arrive in a little while.If someone tells you they will do something  just now, they might do it in a week, a month or never.If someone wants to bliksem you, you might want to leave quickly as it means they want to hit you.RandomTownships are the  precarious shelters  where the poor people live in the suburbs of the big cities and where the  non-whites lived during the apartheid regime.Crash means to go to sleep.Boere means police.Bergie is the name given to homeless people on the streets.Grassland is called veld.Money is called tom.If something is great or cool it is called bakgat.If something is cool, it is kief.To flog means to sell.A fight is called a barnie.Traffic lights are called robots.Smokes refer to cigarettes.An old person might be referred to as toppie.As we learn vocabulary for a trip to South Africa, lets  watch an uplifting moment in the countrys history the election of Nelson Mandela as the countys first  non-white president in 1994. This event officially marked the end of Apartheid. Here is  Mandelas inaugural  address.Travel English Classes | Inglés para Viajes

Let LOI Be Your One-Stop Shop For English Idioms

Let LOI Be Your One-Stop Shop For English Idioms For learners of the English  language,  understanding and using English idioms is a never-ending process.  It might feel like your progress moves at a snails pace.  Maybe you have spent  time  learning  dozens of common English idioms and youve been using them successfully.  Thats great!  But what about when you encounter an English idiom for the first time?  This can be tricky because idioms are expressions without a literal meaning.  One of our talented instructors at LOI, Peter, created this interesting and helpful  post that shines a light on a new way to understand  English idioms:https://www.skypeenglishclasses.com/idiomatic-expressions/About English Idioms:Today well be putting some of Peters helpful advice into practice.  If you are reading this post, you obviously have a strong appetite for learning, so, lets get started!Fill in the blanks with  the idiomatic expressions used in this video.  Then, match the expression to a definition listed.  As Peter states in his post, its important to listen for the context, paying attention to facial expression.  Its also helpful to listen for expressions people say commonly, and try to use those more often.  Todays lesson will help you do just that.  We are always  over the moon when we see your responses and get to help by correcting and giving explanations.  So, write your responses in the comments section.  Or, if youd like to spend quality time practicing with a native speaker, schedule a class!Listening Section and Exercise:To see how lithium is pulled from the earth, I went to visit the operations of the ______ ______, SQM.Hes a cheerful engineer who has _____ _____  working in The Great Void.Over millions of years, minerals from the mountains _____ into  the ground.From there, its __ __ ___ ___  to __ ___ _____  and evaporate away the water, _______  the minerals and salt ______.  This is __________ _____.You guys must be excited that Teslas are selling well and that everybodys _______ ____  e lectric cars now.Chile may have the largest lithium deposits in the world, but its starting to ____ ______  countries like Australia and China when it comes to production.In China its a ___-____ ____  with the mining and battery production happening together.This is a ____  Chilean companies have been unwilling to  ____.The feds have put strict quotas on lithium production, and theyve also been trying to act tough and ____ ____  after some politicos were accused of taking bribes from the mines.Environmentalists arent  ____ ____ of the mines either.But there are some  __ ___ ___ _____.Alejandro  ___ _ _____.These odd marvels ____  the modern world  __.Matching and Gap Fill:Next, use the context to match your answers to the following meanings:a.  disappear/go awayb.  batteryc.  starting to liked.  make things in our lives work welle.  people  who really like somethingf.  dominating the respective fieldg.  done something for yearsh. sucki.  has a correct ideaj.  positive aspects of a j obk.  do something risky with hope of successl. prevent embarrassment, shame or judgement of othersm. do its jobn.  place to buy everything at onceo.  become less successfulp.  the suns responsibilityHopefully by this point in the lesson, your relationship with idioms is getting warmer.  Several of these expressions  can also be categorized according to Peters grouping method:Expressions about life: roadExpressions about time:  moneyExpressions about knowledge: foodExpressions about relationships: temperatureExpressions about economics: gardeningExpressions about opinions: buildingExpressions about truth: archaeologyExpressions about intelligence: lightExpressions about opinions: geographyGrouping idioms in this way makes them easier to understand and put into context.  So now the next part of the lesson is to look at each of the following idiomatic expressions and place them into one of the categories above.example: spent years: time/moneygetting into:  _______/________fall behin d: _______/________leave behind: _______/________take a leap (of faith):  _______/________has a point (of view): _______/________make the world run: _______/________Find the English Idioms:Finally, you might have noticed that there are 7  idioms written throughout this post.  Find each idiom and place it in the correct category.  Then, for an extra challenge, write what you think the meaning is according to the category and context of the sentence!  Dont forget to write your responses in the comments section.If you still dont feel like these idioms are crystal clear, were happy to answer your questions in the comments section below, but were even happier to speak with you in a one-on-one lesson, so schedule a class today!

Become a memory guru

Become a memory guru The Journey method of memorising important information is something I came across absolutely accidentally and it struck me how simple and absolutely brilliant it is. Sadly the times of me taking exams have passed but I can still use the technique for shopping lists, phone numbers or addresses. I have always been a big fan of Top Gear and was excited to see that James May has restarted his Man's Lab show which teaches people lost skills. In the first episode of the new series what caught my attention the most is that he was asked to commentate on the Grand National - the most valuable horse race in Europe. In order to be able to cover the race James had to learn 40 horses' names and the colours of their attire. As he only had a few days to prepare for this challenge he asked Dominic O'Brien, the world memory champion, for advice on how to memorise these quickly. Dominic met up with James in a countryside inn where he explained in practice how to use the Journey method to easily remember information. They explored the back garden and attached horses' names and colours to different places around the garden in a way that resembled the names or the patterns in order to make it easier to memorise. By doing that, James was able to successfully commentate on the race with a little help from his sidekick Rory. The Journey method itself originated from Ancient Greece and is based on three main features: imagination, association and location. Imagination helps make regular things more memorable especially if a little bit of fantasy is added so that in your mind, the information you need to remember stands out. When it comes to association, we make connections all the time and don't even stop to notice how it works as it is so natural, but we can also create new artificial association in order to make the forgettable information stand out. And obviously, location is the main ingredient in this method where imagination and association come to help. When using this method you attach a piece of information to a particular place and create a sort of informational journey through your house, town or park - any location will work as long as you know it very well. By creating associations between the information and a place it is very easy to revisit it in your mind when you need to access it. The number of journeys you can create is limitless and you can remember each for a very long time as long as you keep revisiting them regularly. In order to help your brain cope with so much new information you should also focus on healthy wellbeing. Healthy sleeping pattern, no junk food, no binge drinking, exercising and getting all the vitamins will not only boost your mental capacity to remember information but also will make you feel a lot better in general. Training your memory this way and feeding your brain will also benefit you in the long term as it will stave off the symptoms of dementia and will allow you to enjoy a healthy mind for longer. And of course you will never have to worry about where you have left your car or what you needed to buy in the supermarket!