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Berkeley MATH 1B: Calculus II

MATH 1B covers techniques of integration, applications, infinite sequences and series, and first- and second-order differential equations. It's required for engineering, CS, and physical science tracks, and it carries a reputation as one of the toughest lower-division math courses at Berkeley.

Fennie is independent and not affiliated with UC Berkeley. This is an unofficial study guide.

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What makes it hard

1B's reputation comes from the series unit and the differential equations finale — abstract material arriving when students are most fatigued. Exam medians can be strikingly low depending on the instructor, and the course historically has one of the higher non-pass rates among Berkeley math classes.

What you'll cover

  • • Integration techniques
  • • Improper integrals
  • • Sequences and infinite series
  • • Convergence tests and Taylor series
  • • First-order differential equations
  • • Second-order linear differential equations

The MATH 1B study guide

How to study for Berkeley MATH 1B, step by step.

  1. 1

    Make integration technique a daily habit immediately

    MATH 1B assumes technique fluency fast, and you need it automatic before series arrives. A few integrals a day from week one builds the reflexes the back half depends on.

  2. 2

    Treat series as its own course

    The series unit is the most abstract material most students have seen, and it decides most 1B grades. From the day it starts, classify several series daily — fluency with convergence tests is built through volume, not insight.

  3. 3

    Build and drill a convergence-test decision tree

    Write an ordered checklist (divergence test first, then geometric/p-series patterns, then comparison, ratio, root, integral, alternating) and run it until test selection takes seconds. Exams reward fast correct selection.

  4. 4

    Don't fade during the differential equations finale

    Second-order ODEs arrive when energy is lowest, and they're on the final at full weight. Schedule real practice time for the last unit instead of triaging it away.

  5. 5

    Work your instructor's past exams

    1B exam medians swing with the instructor, so past exams from your professor — via the TBP/HKN archives — are the calibration that matters. Work them timed in the week before each midterm.

  6. 6

    Hand the pacing problem to Fennie

    Upload the MATH 1B syllabus and Fennie's Daily Plans spread all three units across the semester with extra series repetitions, plus flashcards for integration patterns and convergence-test conditions built from your actual materials. Free to start.

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How Fennie helps with MATH 1B

Daily Plans spread MATH 1B's three distinct units across the semester with extra repetitions on series, the unit that decides most grades. Use Fennie's chat to build a convergence-test decision tree you can actually apply under pressure, and generate flashcards for integration patterns and series facts the exams expect instantly.

FAQ

Why is MATH 1B considered so hard?

The series unit is the most abstract math many students have seen, and it's followed immediately by differential equations — two hard units back-to-back. Combined with instructor-dependent exams and a real curve, 1B punishes anyone coasting on 1A momentum.

How do I pass MATH 1B at Berkeley?

Treat series as a daily practice habit from the moment the unit starts — fluency with convergence tests is built through volume. Use your instructor's past exams, and don't skip the differential equations material at the end when energy is lowest.

Is MATH 1B harder than MATH 1A?

Most Berkeley students say yes, clearly. 1A is mostly a sharper version of high school calculus; 1B introduces genuinely new and more abstract material. Plan for it to take meaningfully more weekly time.

Pass MATH 1B with a plan, not a cram

Upload your MATH 1B materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.

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