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Subject Spotlight: The Hardest Part of Calculus is the Precalculus


For many high school students or first year college students, Calculus will be the apex of their mathematics career or one of the final math classes taken. The only thing more ubiquitous than the presence of Calculus is how difficult it is―AJ’s Calculus department has 72 members and it continues to be the most requested subject for AP Exam tutoring year after year. As a long-time math tutor, I’ve long since come to terms with the reality that Calculus is a difficult subject for students to learn. This continues to be true for most students across different iterations of the class, across different schools, different semesters, and different teachers. 

I have found in recent years that with the disruption to learning caused by the recent pandemic, a lot of Precalculus classes have fallen behind and omitted topics while the AP Calculus curriculum (with the exception of 2020) has remained unchanged. This results in a Precalculus experience that has left behind more content gaps than usual, often without compromising on lower student grades to give any indication that the missing concepts may become problematic later in Calculus

The reality is that any Calculus class is going to primarily cover Calculus concepts―it will not be able to find these loose dependencies and adjust the class curriculum to address them for each student. Doing so certainly wouldn’t be practical, as everyone’s content gaps in the class may be different. 

Ultimately, I have found through working with my students that the key to succeeding in Calculus is to have mastered its prerequisites: to only need to study Calculus, and not have to learn Calculus, Precalculus, and Trigonometry concepts all at the same time. Students should work on finding their own content gaps and addressing them early enough: either

through proactive and meticulous study on their own or with a tutor who is experienced enough to identify productive topics to review and guide them in the right direction. 

Precalculus is not a spectator sport, and neither is Calculus. You can not simply master these subjects by passively attending class and treating class lectures as YouTube videos. Be an active learner and participate in discussions and ask questions in class. 

The secret to success is luck; the non-secret is hard work. Hard work now in Precalculus is an investment that will pay dividends as early as half a year from now in Calculus. 

To work with a member of our exceptional Calculus department, call a director today at (650) 331-3251.

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