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To conjugate a verb in the pluperfect tense in French, you need three parts: the subject pronoun (ie. Je, tu il, nous, vous, ils); the imperfect of avoir or être; and the past participle of the verb. It’s important to have a good understanding of the perfect tense before attempting the pluperfect tense.
Let’s break it down.
For all the verbs that use avoir in the normal past perfect tense (that’s most verbs), avoir is also used in the pluperfect.
To form avoir in the imperfect, simply add the imperfect endings to av:
J’ av ais avais
Tu av ais avais
Il/elle/on av ait avait
Nous av + ions = avions
Vous av iez aviez
Ils/elles av aient avaient
All the other verbs use être, just like in the perfect tense. This includes all reflexive verbs (eg se lever/s’habiller) and the ‘MRS VAN DE TRAMP’ verbs:
Sortir Remember verbs formed from these verbs also use être, for
Venir example ‘devenir’ from ‘venir’ or ‘rentrer’ from ‘entrer’
To form être in the imperfect, add the imperfect endings to ét:
J’ ét ais étais
Tu ét ais étais
Il/elle/on ét ait était
Nous ét + ions = étions
Vous ét iez étiez
Ils/elles ét aient étaient
Once you have the correct form of the imperfect, you just add the past participle of the verb – the same one that is used for the perfect tense.
Examples: aider – aidé
faire – fait
boire – bu
So, let’s put it together. Imagine you want to say I had eaten. ‘Manger’ means ‘to eat’ so you are working with that verb and because it’s ‘I’ you use the subject pronoun ‘je’. In the perfect tense, ‘manger’ uses ‘avoir’ so that’s the verb you use here, put into the imperfect tense, conjugated in the first person ‘I’ form. Putting it together we have:
Subject pronoun Avoir in imperfect Past participle of manger
J’ avais mangé
Another example: She had gone. ‘Aller’ means ‘to go’ and you are using ‘elle’ for ‘she’. Aller is a MRS VAN DE TRAMP verb so you use être instead of avoir.
Subject pronoun Etre in imperfect Past participle of aller
Elle était allée
Careful here – remember how in the perfect tense you need to add an ‘e’ to the past participle for females and an ‘s’ if there’s more than one person? The same goes for the pluperfect tense – that’s why there’s an extra ‘e’ on the past participle of aller.
One more example – a tricky one! They (male) had gone to bed. The verb ‘se coucher’ is used to say ‘to go to bed’ – it’s a reflexive! So this time, just like in the perfect tense, we need to include the reflexive part of the verb (me, te, se, nous, vous, se), and it goes in front of the ‘être’ that’s been put in the imperfect tense. So, you are using ‘ils’ for they and être, as with all reflexives.
Subject pronoun Reflexive bit Etre in imperfect Past participle of coucher
Ils s’ étaient couchés
And don’t forget that extra ‘s’ on couché to show more than one person.
So, just remember those three parts – subject pronoun, imperfect of avoir or être, past participle – and, as long as you conjugate them correctly, you can’t go wrong!see more
To substitute a number into an algebraic expression, all you need to do is re-write the expression in exactly the same way, except replacing the variable (letter) with the number. It always makes it clearer to put the number in brackets too. Then you can simplify your new expression and you have your answer!
Let's have a look at an example.
3x+7 where x = 5
So here, x is the variable and you are substituting in the number 5. All you do is write back the expression but with 5 instead of x. And don’t forget those brackets!
3(5) + 7
Now to simplify, just multiply out the brackets and add the 7:
3 x 5 + 7
= 15 + 7
And that’s your answer!
How about a harder example:
2y2 – 3y + 4 where y = 2
You do this one in exactly the same way, but this time the variable is y and the number is 2. So, write back the expression with 2 (in brackets!) instead of y:
2(2)2 – 3(2) + 4
And simplify… remember, always do the brackets first:
2 x 22 – 3 x 2 + 4
= 2 x 4 – 3 x 2 + 4
Multiplication always comes before addition and subtraction:
= 8 – 6 + 4
One more example, this time with two variables.
4x2 – y2 + 2xy where x = - 3 and y = 4
You have to be a bit more careful with this one – make sure you include the negative sign in the brackets when you replace x with (-3) and instead of y, write 4.
4(-3)2 – (4)2 + 2(-3)(4)
= 4 x (-3)2 – (4)2 + 2 x -3 x 4
Remember when you square a negative number you get a positive solution:
= 4 x 9 – 16 + 2 x -3 x 4
= 36 – 16 + (-24)
= - 4see more