If I had studied, I would have passed the exam.
Conditional sentences type 3:

If I had studied, I would have passed the exam. (long form)
If I'd studied, I'd have passed the exam. (short form)

I had - I'd
I would - I'd

Why is the short version of would and had exactly the same?
I

Question

If I had studied, I would have passed the exam.
Conditional sentences type 3:

If I had studied, I would have passed the exam.   (long form)
If I'd     studied, I'd         have passed the exam.   (short form)

I had -> I'd  
I would -> I'd

Why is the short version of would and had exactly the same?
I

Answer

H and W are relatively weak sounds which are often dropped in auxiliary and modal verbs.

Your examples are correct.  Here are more examples.

We will > We'll
We have > We've
We had > We'd 
We would > We'd
We would have > We'd have > We'd've
We would have > We would've > We'd've