QUITE

Quite is a degree adverb. It means less than "very" but more than "a little". It also means "completely, very or totally." 

I was quite good at maths when I was young. (Moderately good but not perfect)

My kids were quite happy to hear that we are going on holiday. (A little excited)

My life is quite different since I met you. (Completely different)

I remembered the man quite clearly now when I shook his hands. (Very clearly)

USE OF QUITE 

► Quite + gradable adjectives and adverbs

When we use quite with a gradable adjective or adverb, it usually means ‘a little, moderately but not very’. It has a similar meaning to ‘rather’ or ‘fairly’:

That car makes you look quite rich. (+ adjective)

She complains about her work quite often. (+ frequency adverb)

The tourists walked quite fast to catch the train. (+ adverb)

► Quite + non-gradable adjectives and adverbs

When we use quite with a non-gradable adjective or adverb, it usually means ‘very’, ‘totally’ or ‘completely’:

The story you told me is quite incredible.

The prime minister said we should ban smoking in public areas. And he is quite right about it.

My sister spends hours every day with her laptop. She is quite obviously fond of computers.

► Quite + nouns

We can use quite + a/an before a noun to give it more importance.

There was quite a noise outside. We couldn't sleep for hours. 

It makes quite a difference when you do your best.

When we use quite + a/an + adjective + noun it means the same as a little or a lot but not completely,

It’s quite an expensive shirt. About 100 Euros.

It’s quite a good movie. (It’s good but not excellent.)

► Quite a bit, quite a few, quite a lot

We often use quite with a bit, a few and a lot to refer to large amounts or quantities.

Whenever I am stuck with technology, I call my brother. He knows quite a bit about computers.

We bought quite a lot of new clothes for the summer.

We also use quite a bit and quite a lot to mean ‘often’:

We visit this place in summer quite a bit. 

I used to watch TV quite a lot before Jason was born. Now I have no time.  

We also use "quite a lot" and "quite a bit" with a comparative adjective or adverb to mean "much":

I used to play rugby when I was quite a bit younger.

My new car is quite a lot more expensive than the old one. 

 
► Quite + verbs

We often use quite with like, enjoy, understand and agree to express our opinions or preferences. It can mean "a bit", "a lot" or "totally" depending on the context. We usually put it in the normal mid position for adverbs 

I quite like having a holiday in Turkey. It is cheap and the hotels aren't bad. (I like a bit)

I quite like staying at home and spending time by myself. (I like it a lot)

RATHER

We use rather to give emphasis to an adjective or adverb. It has a similar meaning to quite when quite is used with gradable words but it is more formal. We often use "rather" it to express something unexpected or surprising.

A: You look a bit tired.
B: Well, I am rather sick.

They were late for the meeting. But they walked rather slowly. 

USE OF RATHER

► Rather with adjective + noun

We can use rather a/an + adjective + noun. We can also use a rather + adjective + noun. With other determiners such as some and those, we can use determiner + rather + adjective + noun.

They had to wait rather a long time before the train arrived. 

They were rather in a dangerous situation when the waves hit the beach. 

Hey, listen to me! I have some rather bad news today.

► Rather a + noun

We often use "rather a" with "a noun" in formal language, especially in writing.

I couldn't study for the final test. So, it was rather a surprise to pass the test. 

► Rather a lot

We generally use "rather" with "a lot" to refer to large amounts and quantities.

The new house cost us rather a lot of money.

He helped me rather a lot when I was in trouble.

We also use rather a lot to mean "often".

We went to the seaside rather a lot when we lived in İzmir.

Students will be working on the project rather a lot in the final weeks of the semester.

► Rather + verb

We often use rather with verbs such as love, hope, enjoy or like and we use it to emphasize verbs. 

I rather liked staying in this nice hotel last summer.

I am rather hoping to finish the semester with good marks. 

► Rather like

We often use rather with like to refer to similarities.

We really enjoyed the party and had a lot of fun, rather like children.

We felt rather like a child at the birthday party with a lot of balloons and a clown. 

► Rather than

We use "rather than" while we are comparing two alternatives and to give more importance to one thing than the other.

Can we have the meeting on Monday rather than Saturday?

I wanted to be a doctor rather than an engineer. But this is life. I am an engineer now. 

We can also use "rather than" at the beginning of a sentence. We can use the verb in base form or with -ing.

Rather than go to the cinema, we stayed at home and watched a DVD. 
Rather than going to the cinema, we stayed at home and watched a DVD.