"mathematic","mathematics","Mathematic" & "Mathematics"

It should be mathematics.
FYI, names of school subjects are not capitalized except for language subjects, specific subjects and special courses.
E.g.:
-science, geography, visual arts, physical education, English language, civics, Malaysia history, etc.

COLOURED PENCILS or COLOUR PENCILS?

They are called as 'coloured pencils', not 'colour pencils'.
A photograph can be described as a 'colour photograph', not a 'coloured photograph' because of its natural colours.

Is it right to say "do correction" (especially for teachers)?

When a student makes a mistake or an error in his/her book, we should put a remark - "PLEASE MAKE A CORRECTION."
Informally, we can say 'Please do a correction'.
If there is more than one error, they need to make corrections.

So, it's wrong to say or write 'please do correction'.

#'Correction' is a countable noun
However, it can also be an uncountable noun if we refer to the general action of 'making something right'.
For example;
'Sentence correction is needed in his essay.'
'There are a few types of geometric correction.'

"Playing with her doll" OR "Playing her doll"??

When we play with something, it's either
-we spend time amusing ourselves with it
OR
- we fiddle/move it about using hands, etc.
"The boy is playing with his pencil." (he's fiddling the pencil in his fingers.)
"She always plays with her doll." (she usually moves her doll with her hands and makes herself amused playing with it)

When we play with someone, that means we play together with him/her.
"I play with my sister."

However, we use play something (without 'with') to show that we 'really take part in that playing activity/game'.
E.g.:
I play the guitar. (NOT 'I play with the guitar.')
I play chess everyday. (NOT 'I play with chess everyday.') 

Think!
Is it 'I play the ball everyday' OR 'I play with the ball everyday' ?

If you play with the ball, that means you take the ball and move it or bounce it without any rules.
However, when you play the ball, it could mean that you play the ball in a game such as football, etc.

GRAMMAR TIPS FOR PMR CANDIDATES!

Here, I've listed 10 grammar items, which as a PMR candidate, you should know about these.
If you do not know any, it's high time for you to figure out and learn!

1)  ARTICLES (a, an, the, zero article)
2)  NOUNS (types of nouns, countable/uncountable, singular/plural forms)
3)  PRONOUNS (personal, possessive, reflexive, relative)
4)  VERBS (including tenses - past, present, future, perfect, subject-verb agreement, modals, etc.)
5)  ADVERBS (different uses of words that describe verbs)
6)  ADJECTIVES (positives, comparatives, superlatives)
7)  CONJUNCTIONS (for example; and, so, although, etc.)
8)  PREPOSITIONS (of position, place, time) *this is the most frequent one
9)  CONNECTORS (logical connectors, sequence connectors)
10)  DETERMINERS (for example; this/those, some/any, etc.)
*you should also have learnt about CONTRACTIONS & PUNCTUATIONS and still remember about them.

This is specially dedicated for my students.  Please make sure your tuition teachers/private tutors stress these rather than the others which are not so important. It's because I don't want your parents to pay them for nothing.

PRONUNCIATION TIPS: Should we really stress the "r" sound in English words?

Look at these words and try to pronounce them.

are, your, more, care, there, for, four, other, or, here, over, hour, before, higher, comfort, hear, never, etc.

Should we sound the 'r' when pronouncing these words?

Actually, there's no need for us to stress the 'r' sound let alone to sound it. It will sound awkward.
However, we sound the 'r' if one of those words is followed by a vowel (a,e,i,o,u).

Here are some tips/examples:
-"Before my eyes" - silent 'r'
 "Before I go...." - with 'r' sound
- "Hear you say" - silent 'r'
  "Here I come" - with 'r' sound
- "Four or five?" - with 'r' sound
  "Four people" - silent 'r'

Now, I've found the reason why people say that Siti Nurhaliza sounds awkward when she sings her English songs.
Anyway, I'm not perfect too as I'm still learning. Peace! :)

*Another thing, be careful when pronouncing "can't" & "can" because they contrast each other.
** "WORD" and "FIRST" - the 'r' is totally silenced.

Can we use apostrophe s ('s) to show Possession of Non-living Things? (Possessive Nouns)

We should use apostrophe s ('s) when writing posssive nouns (for singular nouns not ending in s).
E.g.: The boy's ball. (which means; the ball of the boy)

but is it right to use 'the book's size' or 'the car's front'?

As books and cars are non-living things. It's more appropriate to write;
- The cover of the book.
- The front of the car.

However, we use apostrophes to show possession of periods of time such as "today's date" and "in two weeks' time".
We also use apostrophes to show possession of organizations, the earth, ships and countries, for example, "the university's rules", "the ship's bells", "the city's parks" and "Malaysia's land")

Remember, always use 'of (the)' to show possession of non-living things (especially in formal writing) and use apostrophes for living things.

*How about plants? Should we say "the plant's roots" or "the roots of the plant"?

My answer: We can indicate it as "the roots of the plant" or simply "the plant root". 
*Please take note that when the possessor and the thing possessed are both concrete objects, the possesion can also be indicated without any apostrophe for example, "the car radio", "the hotel room" and "the room door".