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Degree: Maths and French (Bachelors) - Exeter University
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The perfect tense is used to describe an action or event that occurred in the past. For example, you would use the perfect tense to express the phrase "I played football yesterday"
The perfect tense is constructed with the subject (I, you, she...) followed by an auxiliary verb and then a past participle.
The majority of French verbs take avoir as the past participle. There is a group of 14 verbs that take être as the auxiliary verb, as well as all reflexive verbs (such as se laver).
Constructing the past participle:
For verbs that end in -er take off the er and add é. For example the past participle of jouer is joué.
For verbs that end in -ir take off the ir and add i. For example the past participle of finir is fini.
For verbs that end in -re take off the re and add u. For example the past participle of vendre is vendu.
The auxiliary verb is used in the present tense so for verbs that take avoir the forms are:
These forms are then followed by the relevant past participle.
For example I played football would be translated as J'ai joué au foot.
Il a fini ses devoirs
Ils ont mangé beaucoup de gâteausee more
The perfect tense is used to for completed actions in the past. For example, le semaine dernier je suis allé en France would translate to last week I went to France. The imperfect is used for incomplete action. For example, j'allais en France would translate to I was going to France.
The imperfect can also be used to describe something that happened regularly in the past, a habitual event. So the imperfect would be used to translate when I was younger I used to pay football - Quand j'étais petit je jouais au foot.
The imperfect can be used to set the scene in the past, so describing the weather on a day in the past would be formed in the imperfect tense: hier il faisait chaud.
Finally, there are situations in which the perfect tense and imperfect tense are used together in the same sentence. For example, I was doing my homework when the telephone rang. 'I was doing my homework' would be translated in the imperfect tense as this is an incomplete action. 'The telephone rang' would be translated in the perfect tense as this is a complete event in the past.
So the sentence as a whole would translate into French to be:
Je faisais mes devoirs quand le téléphone a sonné.see more
Differentation is a type of calculus that allows us to work out the rate of change. For example, if we have a straight line graph such as y=2x, we know that the gradient of the line is 2. If we take a curve such as y=x2+2x+9, the gradient is different at different points on the curve and so we use differentation to work this out.
To carry out differentation you must use the following rule:
Bring the power down to the front and reduce the power by 1.
So how does this rule work in practice?
If we have an equation f(x), after we differentiate it we call it a derivative and use the notation f'(x).
So if f(x)=xa, then f'(x)=axa-1. So we have brought the power a down to the front of x and then reduced a by 1.
Now let's take a numerical example:
f(x)=x2 so then f'(x)=2x
If we have an equation like f(x)=x3+2x2+9x+4 we differentiate each term separately.
The derivative of x3 is 3x2
The derivative of 2x2 is 4x
The derivative of 9x is just 9 as the power reduces to 0
The derivative of 4 is 0. Any number that is not associated with a variable (such as x) will differentiate to 0.
If we wanted to find the gradient of f(x)=x3+2x2+9x+4 at x=2, we differentiate the equation (as done above) and then substitute the appropirate value of x.
We have f'(x)=3x2+4x+9, and then substitute x=2.
So the gradient of the curve at x=2 is 3(22)+4(2)+9=29.see more