Formal pairs suit Writing Task 2. Neutral ones work anywhere. Informal ones belong in Speaking.
1.acquire knowledge
formalgain knowledge through study or experience
Children acquire knowledge more effectively when lessons are linked to real life.
Gain knowledge is a slightly less formal alternative.
2.higher education
formalstudy at university or college after school
Access to higher education should not depend on a family's income.
No article in general statements: access to higher education, not the higher education.
3.compulsory education
formalthe years of school that the law requires
Several countries have extended compulsory education to the age of eighteen.
Compulsory subjects and compulsory military service follow the same pattern.
4.tuition fees
neutralmoney paid to a university or college for teaching
Rising tuition fees discourage many talented students from applying to university.
Always plural in this sense.
5.academic performance
formalhow well a student does in their studies
Regular sleep has a clear effect on academic performance.
Improve, affect and boost all collocate with academic performance.
6.rote learning
formallearning by repetition without real understanding
Exam systems that reward rote learning do little to develop independent thought.
Usually used critically. In Speaking, learn things by heart is more natural.
7.develop critical thinking skills
formallearn to analyse and judge ideas carefully
Debating clubs help teenagers develop critical thinking skills.
Develop and foster both collocate with skills.
8.sit an exam
neutraltake an examination
Students who sit an exam every term become used to working under pressure.
British English. Take an exam is also correct.
Avoid: give an exam → sit an exam
9.attend lectures
neutralgo to talks given by a university teacher
Many students now watch recordings instead of attending lectures in person.
Attend takes a direct object with no preposition.
Avoid: attend to lectures → attend lectures
10.drop out of school
neutralleave school before finishing a course
Teenagers from poorer families are more likely to drop out of school early.
Dropout is the noun: the dropout rate.
11.vocational training
formalteaching practical skills for a particular job
Not every young person benefits from university; vocational training can lead to well-paid careers.
Vocational courses and vocational qualifications follow the same pattern.
12.extracurricular activities
formalactivities such as sport, music or clubs outside normal lessons
Extracurricular activities teach teamwork in a way that classroom lessons rarely can.
Written as one word, no hyphen.
13.a well-rounded education
neutralan education that develops many different skills and interests
Art and music are part of a well-rounded education, not optional extras.
Keep the hyphen in well-rounded before a noun.
14.gain a qualification
neutralsuccessfully complete a course and receive a certificate
Adults who gain a qualification later in life often earn more as a result.
Obtain is more formal; get is more spoken.
15.learn something by heart
informalmemorise something so that you can repeat it exactly
At primary school we had to learn poems by heart, which I actually enjoyed.
Good for Speaking Part 1 and 3. Use memorise in Writing.
16.broaden students' horizons
neutralhelp students learn about and experience new things
Studying abroad broadens students' horizons and makes them more independent.
Horizons is always plural in this phrase.