1. Do you remember (meet) meeting her at Nam's birthday party last week?

$\longrightarrow$ Do you remember + V-ing?  
2. My mother is busy (cook) cooking dinner in the kitchen. 
$\longrightarrow$ be busy + V-ing 
3. It’s ten years since I last (see) saw her.  
$\longrightarrow$ It’s + thời gian + since + S + last + V (quá khứ đơn)  
4. The price (become) has become more and more expensive recently.  
$\longrightarrow$ S + has/have + V3/ed 
5. I think this institution (widen) has widened twice since 1999. 
$\longrightarrow$ S + has/have + V3/ed + since + mốc thời gian