1. My older sister is majoring in applicable linguistics.(x)
My older sister is majoring in applied linguistics. (√)
applicable是“适用的”，如:These rules are not necessarily applicable to foreigners.(这些规定未必适用于老外。)应用的学科一律用applied，如:applied physics/mathematics / psychology 即“应用物理学/数学/心理学”。
2. My younger brother is now applying to a scholarship. (x)
My younger brother is now applying for a scholarship.(√)
apply to+机关/学校/公司，是指“向某机关/学校/公司申请(某物)或应聘(某职位)”，如:I applied to three universities but was not accepted by any of them.(我向三所大学申请入学但都未被录取。) apply for+事/物，是“应聘(某职位)或申请(某物)”。另外，apply to+人/物，也可表“适用于某人或某物”，如:What applies to me does not apply to you.(适用于我的未必适用于你。)
3. They have applied for a divorce.(x)
They have filed for a divorce. (√)
apply for sth的用法参见之前说明。file for sth 表 “某人正式(向法院)申请离婚或破产等”，为固定用法。
4. Why don't you apply some suntan lotion on your skin?(x)
Why don't you apply some suntan lotion to your skin?(√)
apply sth to sth 表“将某物涂抹在某物上”。
5. I'm supposed to see a dentist at three. Looks like I'm unable to make the
appointment. (x)
I'm supposed to see a dentist at three. Looks like I'm unable to keep the
appointment. (√)
make an / the appoinUnent是指“预约去见某人(尤指医生、律师等)”。而keep an/the appointment是指“履约去见某人"。
6. Mary has made an appointment with Jane, her cousin. (x)
Mary has arranged to meet Jane, her cousin.(√)
make an appointment with只能接医生、律师、商业人士等。约亲友见面须用arrange to meet / see sb。
7. I would appreciate if you could come and pick me up.(x)
I would appreciate it if you could come and pick me up. (√)
appreciate作“感激”或“欣赏”解时，均为及物动词，后须接宾语,如:His boss does not really appreciate him.(他的老板并不真正欣赏他。)appreciate唯一不及物的用法是作“升值”解时，如:The RMB has appreciated for two consecutive weeks.(人民币己经连续升值了两个星期。)
8. The plane was approaching to the airport when we encountered unexpected
turbulence. (x)
The plane was approaching the airport when we encountered unexpected
turbulence.(√)
approach+人/物，表示“朝某人/物接近”，后不需加to。但作名词时，approach可接to，如: we should adopt / take a more flexible approach to the problem.(对于这个问题，我们应该采取更灵活的方式来处理。)
9. Write clearly and logically. Look, these sentences are not appropriate. (x)
Write clearly and logically. Look, these sentences are not relevant. (√)
appropriate意为“适当的”，是指适合某种场合或目的，如:Jeans are not appropriate on formal occasions.(在正式的场合穿牛仔裤并不合适。) relevant是指“与主题有关的”。
10. I don't approve sending our parents to a nursing home. (x)
I don't approve of sending our parents to a nursing home.(√)
approve sth是“正式批准/核准某物”的意思，如:Congress has approved the budget.(国会已批准该预算案。) approve of sth是“赞成/同意某事”的意思。
