I think I can see where the confusion arose.
You took three facts which are true ………..
1. We can use much and many in interrogative and negative sentences
Do you have much homework?
I don’t have much homework.
Do you have many exercises?
I don’t have many exercises.
2. We don’t (normally) use much and many in affirmative sentences
I have much homework.
(Grammatically OK but very awkward and outdated — best avoided)
I have many questions.
(OK, but depending on the context, may sound a little unnatural/formal — often avoided)
3. We can use a lot of in affirmative sentences
I have a lot of homework.
I have a lot of exercises.
…….But then, based on the information above, you made the following wrong assumptions:
«We can only use a lot of in affirmative sentences»
«We can’t use a lot of in interrogative and negative sentences»
Neither of these is true. The fact is you can use a lot of in all of those sentence types: not just affirmatives, but also negative and interrogatives:
Do you have a lot of homework?
I don’t have a lot of homework.
Do you have a lot of exercises?
I don’t have a lot of exercises.
Your student’s book is not wrong: it is just misleading.
Just here for the exercises? Click here.
What’s the difference between much, many and a lot?
Much, many, and a lot are quantifiers that all mean ‘a large amount of’. The main difference between these words is that we can use much with uncountable nouns, many with plural countable nouns, and a lot with both types of nouns. However, these words are often mixed up by English learners. Read the examples below to master the difference, then put your knowledge to the test in the free exercises.
Example
Louis and his family are on holiday in Madrid.
In the Plaza Mayor, there were so many people that Louis got lost.
He can’t ask for help because he can’t speak much Spanish.
He doesn’t know many words, and wouldn’t understand the people.
He doesn’t have much money either so he can’t take a taxi to the hotel.
What is he going to do?
Much and Many
In Negative Sentences and Questions
We mostly use much and many in negative sentences and questions.
- We use much with uncountable nouns.
- Examples:
- How much money do you have?
- Louis can’t speak much Spanish.
- We use many with countable plural nouns.
- Examples:
- How many children do they have?
- Louis doesn’t know many Spanish words.
In Positive Sentences
We can use much and many in positive sentences after words like so, too, and as. (A lot is not possible after so, too, and as).
- Examples:
- As usual she has made too many cakes.
- Take as much time as you need.
- We had so much fun at the party.
- They had so a lot of fun in Spain.
Much and many can stand alone in positive sentences, but only in a formal style. Be careful! This is not typical in everyday English, and can sound strange in informal contexts.
- Examples:
- Much has been said about …
- Many politicians believe …
A lot
A lot and lots of are the most flexible quantifiers in English: we can use them in positive sentences with countable and uncountable nouns. They have the same meaning, but a lot of is more common.
- Examples:
- They have met lots of people.
- They have a lot of friends.
- I have a lot of money.
- I have a lot of time.
Although it is possible to use a lot/lots of in negative sentences and questions, it is more common to use much and many.
- Example:
- Do you know many people in your neighbourhood? ↔ Do you know lots of people in your neighbourhood?
Other ways to say ‘a lot’
English has several different words and expressions that have the same meaning as a lot:
- Formal:
- plenty, a great/considerable number, a large/fair amount, numerous, a great deal
- Informal:
- loads, a pile/piles, stacks, tons, mountains, more … than you can poke a stick at
Learn more about much and many, or discover more English quantifiers.
When should “to be” agree with the first noun?
With a sentence covering states, the noun typically agrees with the first noun, such as There is a car. or They are rocks. The verb “to be” describes the noun, and therefore agrees with whether the noun is singular or plural. This can become confusing, however, when “to be” describes a singular noun that groups a plural: nouns such as couple, pair, group, and crowd may all be followed by plurals, but are treated, grammatically, as singular, as they represent one single unit. Consider that “a couple of people” is one object (a couple), because it combines two separate objects (two people) into one unit. Similarly, “a group of doctors”, “a crowd of onlookers”, “a swarm of bees”. The opposite would be true if we defined a group by a plural number or an adverb expressing a plural: “many chairs” and “twelve nurses”, for example, express plurals that are not grouped into one unit.
Usually, the first noun defines the quantity (and tells us “how many”), and with sentences describing states the verb “to be” will agree with the first noun.
- There is a group of librarians waiting for you.
- There are hundreds of clowns coming.
This can be true of “a lot”; if we strictly want to refer to lot as a singular grouping, then the singular “is a lot” is appropriate. It’s been mentioned in the comments below that this is the “correct” usage, but bear in mind data shows roughly half of English speakers are likely to say “are a lot”, and this a pattern that appears in grammar books – so we must question how the language is actually used rather than how the basic rules say it should be used.
Why doesn’t this work for “There are a lot of / There is a lot”?
The ambiguity here comes from “a lot of” appearing to be a noun phrase when it’s actually not used in the same way. When people say “are a lot”, this is used not as a grouping noun but like a quantifying adjective, like “many”. While a singular verb is appropriate with nouns that define the plural into a singular group, “a lot of” refers to a quantity rather than a grouped unit – modifying the noun as “many” would. So the verb agrees with the noun that “a lot of” qualifies, rather than “a lot”. We can therefore have either “are a lot of” or “is a lot of” depending on our interpretation of this sentence. Mostly, we will use “There are a lot of” with countable nouns, when we discuss plurals, and “There is a lot of” with uncountable nouns, but there is of course flexibility here – in many cases it may be down to the individual’s interpretation of the sentence.
- There are a lot of apples.
- There is a lot of meat.
It’s deceptive, but a good example of how exceptions to some of the simple rules of English can work – because words can be used for functions that are not what they immediately appear to be.