I am an Engineering Math student at the University of Bristol. I have a range of interests, which cover maths, history and law, and would love to help others in these areas as well as encourage the same enthusiasm I have in others! I am patient and willing to go through questions and exam technique step-by-step.
I am friendly and have worked with young people before through the Air Cadets, where I gained experience teaching all I knew about the Air Training Corps to brand new cadets, as well as taking part in work within my community and collecting for charities.
I'm happy to help with any questions you may have within my subject areas, don't hesitate to ask! I will tailor the session exactly to your needs, and can help any day of the week. Please feel free to contact me at anytime, and I look forward to meeting you!
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The European Convention on Human Rights is a convention set up by the 47 members of the European Council, following the atrocities of World War 2. This council includes countries such as Russia and Switzerland, as well as all members of the European Union, and it therefore upholds the rights of around 800 million people. The European Court of Human Rights (ECtHR) enforces these rights in Strasbourg, France, with UK citizens being given the right to application to the court in 1966. The Human Rights Act 1998 was a landmark Act passed by the 'New Labour', who promised to make strides towards the protection of human rights. This is in line with the Rule of Law, a set of ideals that underpin the UK's unwritten constitution.
To understand how far the HRA protects us, we might first look at its sections and how far they go to ensure there is no infrigment on our rights. Firstly, it made the ECHR enforcable in UK courts under S7, meaning UK citizens no longer have to go through the long, expensive process of taking their case to Strasbourg. S6 also introduced the rule that public authorities cannot act in a way that is incompatible with the convention. This includes the Government and the courts, and as such, the ECHR can be enforced even in civil cases, such as Thompson and Venables v NGN and Douglas and Others v Hello Ltd, as courts denying a ruling against an infringement on the ECHR would go against their obligation under s6.
The HRA 1998 also offers protections through the new powers afforded to judges, relating to legislation. S3 states that domestic legislation must be interpreted 'so far as it is possible to do so in a way that is compatible with the convention'. This means a purposive approach to interpretation is demanded, which is starkly different to the government's historic preference for a literal approach. This may be criticised for its apparent erosion on Parliamentary Soveireignty and the making of law by unelected judges, but all actions are in the name of Human Rights and the interests of the British people. Lord Steyn states that it is very important for judges to apply law in this way to protect people, and that interpretation may often seem linguistically strained. He argues that one should avoid the use of a declaration of incompatibility, though, under S4 of the HRA. These DIs can be issued by the High Court and above, and send a clear message to Parliament that the law needs to change. Although not likely, with S10 setting out the fast track system for amending incompatible legislation, Parliament could in theory ignore a DI, because of the idea of Parliamentary Sovereignty which is, according the Professor Blackstone, the idea that 'What parliament doth, no authority on earth can undo', and this includes parliaments binding future parliaments.
It is clear, then, that the HRA has its weaknesses, which are in support of the statement. More can be found in the sections and through the basic functions of the British constitution. S2 requires courts to simply 'take into account' rulings in Strasbourg, meaning courts are not bound and could go against such a ruling. An example is the case of Jamie Reynolds, where the judge argued the ruling in Vinter v UK that whole life orders are a breach of A3, freedom from inhumane and degrading treatment, arguing that he is instead bound by British courts. UK courts have also been know to ignore rulings along side the UK government. This was seen after Hirst v UK, a case that saw the denying of prisoners the right to vote is a violation of A3 ECHR. The UK government ignored the ruling, rejected legislation to amend the rules, and subsequently, the supreme court upheld these decsions in R(Chester) v Secretary of State for Justice.
Another major weakness of the HRA 1998 is that fact that it is not entrenched, as a bill of rights would be, such as the United States Bill of Rights. This is due to the idea of Parliamentary Sovereignty again, so Parliement could scrap the Act and return to civil liberties at any time. This would be problematic for UK citizens, whose rights would be limited to 'residual freedoms'. Hohfeld argues that rights are different to civil liberties in that they put a duty on the state to uphold and protect rights, while liberties are just anything that is not covered by law. More weaknesses can be found through the ECHR itself, which often allows for wide margains of appreciation, such as in Leander v Sweden, where the ECtHR held that it would give members stated wide powers to erode Human Rights in favour of national security, and this was similarly seen in Klass v Germany in terms of covert surveillance and erosion of A8, right to privacy.
The HRA 1998 has its strengths and weaknesses, then, with ideas such as Parliamentary soveirgnty and the UK government's abilitiy to circumvent convention rights limiting its power greatly. A better alternative might be a British Bill of Rights, which was proposed by David Cameron in the Conservatives' 2015 election manifesto. Such a bill would unite the UK citizens around a common set of values, and allow judges to strike out laws deemed 'unconstitutional', as they do no in the USA. Parliamentary sovereignty and weak political will, however, make this an unlikely replacement, and it might also be argued that the current conservative government has no intention of protecting rights further. An example of such an agenda could be seen through the proposed Investagatory Powers Bill 2016, written by former Home Secretary Theresa May, which will likely erode A8 for all citizens, with UK police being given access to internet history for the last 12 months with no authorisation, and the Commission that checks surveillance being limited to one commissioner.
Article 14 of the European Convention on Human Rights guarantees freedom from discrimination, in relation to access to other convention rights, meaning it is not a stand-alone right. The ECHR was made part of domestic law by the Human Rights Act 1998, and stands along side the Equality Act 2010 to protect people against discrimination in England and Wales.
The Equality Act 2010, was brought in to consolidate previously complex legislation which numbered 116. Before this act, protection against discrimination had been limited, with some of the first legislation passed being only around 40 years ago, through the Race Relations Act 1975 and the Sex Discrimination Act 1985. The piecemeal framework that we had until the act was also complicated and daunting for a common citizen, and so the EA provided a new framework, which defines protected characteristics. These characteristics range from religion to sex, and the protection can be relied upon by those who have the characteristic, as well as those who are percieved to have them, and associated persons. We are further protected from discrimination through EU directives, which have horizontal direct effect on all citizens of the EU.
Indirect discrimination is when a set of rules is applied to everyone, but they happen to have a negative impact on those with a protected characteristic. Some examples of where this type of discrimination by happen are uniform policies in work or a place of education, both places being covered by the Equality Act 2010. In Mandla v Dowell Lee, a Sikh boy was indirectly discriminated against when his school required him to wear a cap, but his religion requires the wearing of a turban. Mandla was denied entry into the school, and it was held by the court that the uniform policy was direct discrimination. G v St Gregory's Catholic School also involved school policy, where G, of African-Caribbean ethnicity, wore his hair in traditional cornrows which he never cut. This was against his schools policy, but as the cornrows were family tradition, the school policy was held to have been indirectly discriminatory on the grounds of race and sex. In contrast, there was the case of R (on the application of Begum) v Denbigh High School, a case in which Begum wished to wear a Jilbab, while her school's unifrom policy required the wearing of a Shalwar Kameeze. In this case, the school was not held to be indirectly discriminatory, as Begum had alternative school options. The judge also noted that the school was the body best placed to decide on a policy involved with such a sensitive issue. A final indirect discrimination case is Eweida v UK, where Eweida was asked to conceal her crucifix necklace while working for British Airways. This was held to be indirect discrimination based on religion.
There are some ways around being caught under indirect discrimination legislation, and they are found under the EA 2010. It is stated that a policy may be discriminatory in the case of job applicants, but such a policy must be crucial to the role required of the person, related to the nature of the job and be a proportionate means of achieving a legitimate aim. It is also a defence, for indirect discrimination specifically, to prove that there was no intention to dicriminate against a protected characteristic upon creating the policy. Professor Helen Fenwick criticises this as being a serious disincentive and flaw in the legislation.
The first thing to consider when converting an expression to impartial fractions is how many fractions you will have in the end. With linear (no powers) brackets, found in the denominator of your initial fraction, the number of partial fractions at the end of your workings coincides with the number of said brackets. For example, a fraction with denominator (x+5)(x-2) would mean a final answer consisting of 2 fractions. However, in cases involving powers, such as this one, there will be an additional fraction in the answer. So, in this case, (x+1)(x-2)^2 will mean an answer consisting of 3 brackets.
Next, we write our fraction out into a kind of placeholder, with A, B and C used in our numerators to represent the answers we hope to calculate. The denominators will be our original brackets on the denominator of the question, each separated into their own fraction, as follows:
(11+x-x^2)/[(x+1)(x-2)^2] = A/(x+1) + B/(x-2) + C/(x-2)^2
Notice that the B and C fractions are almost identical apart from the power of 2 added to only one of the brackets. This power, as well as the linear form in B, ensures we have partial fractions that, if added together once again, would create the original expression in the question.
Next, we multiply through by the original denominator, the brackets. This will create the equation  as follows:
 11+x-x^2 = A(x-2)^2 + B(x+1)(x-2) + C(x+1)
An easy way to work out what your expression should look like in this step is to compare what you have in your brackets through which you are multiplying, and then to look at what is in the denominator of each fraction. Each term (A,B,C etc) will essentially be multiplied by what it does not have in its denominator, as the bracket it does have will cancel. We will use A in the long-hand way as an example:
[A/(x+1)] * [(x+1)(x-2)^2] = [A(x+1)(x-2)^2)]/(x+1) = A(x-2)^2
In this example, the two (x+1) brackets, top and bottom, cancelled, leaving us with the answer. The next step is to look at the brackets paired with our letters, and determine an x value that will equal as many terms as possible to zero. Lets take x=-1 , and substitute this into equation . This will mean our B and C fractions will equal to zero, as follows:
11+(-1)-(-1)^2 = A(-1-2)^2 + B(0) + C(0) = A(9)
We can now rearrange this to find A:
9 = 9A
A = 1
We then repeat this method with new x values to find the value of C:
11+2-4 = A(0) + B(0) + C(3)
3C = 9
C = 3
To find B, we can substitute in our values for A and C, as well as any x value (other than those already used):
11+1-1 = 1(-1)^2 + B(2)(-1) + 3(2)
-2B = 11-1-6
B = 4/-2 = -2
To complete our answer, we rewrite equation , with our values for A, B and C substituted in:
(11+x-x^2)/[(x+1)(x-2)^2] = 1/(x+1) – 2/(x-2) + 3/(x-2)^2
This is our answer, in partial fractions.see more