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βΎUnit 10

2 min readβ’june 11, 2020

Peter Cao

**Only on the BC Test**- 17-18% of the test
- Roughly
**7 to 8 multiple choice**questions - Always
**one FRQ**on this unit (usually FRQ 6)

Well after going through countless limits, derivatives, and integrals, youβve made it here! Welcome to Unit 10, the last unit of BC Calculus! Before we move on, letβs give yourself a pat on the back!

Anyways, this unit builds from past knowledge of limits, differentiation, and integration, but applies this to a new concept β series. This unit emphasizes the study of **series analysis**. If you havenβt ever heard of analysis in a mathematical before, this is just the study of functions and how they behave over time. Sound familiar? Itβs just a fancy term for calculus used in university, so donβt get bogged down by this term!

There are two main parts to this unit β **Convergence and Divergence** being one and the **Series Approximation to Functions** being the other. The Convergence and Divergence part is concerned with the question, βHow does this series behave over a long period of time as we add more and more termsβ? On the other hand, the Series Approximation to Functions is concerned with the question, βHow can I simply represent a function that will make it easier for me to perform complex operations on them?β

Four of the College Board's mathematical practices for AP Calculus are used in this unit, which will be outlined below.

This means that you should know how to calculate the error bounds to analyze series, with the alternating error bound for alternating series and the Lagrange Error Bound for power series.

This means that you know how to interpret Lagrange and alternating series error bounds as the maximum error of an infinite series given a partial series.

This means that you know how to rewrite any function as an infinite power series.

There are many tests that can be used to determine series convergence and divergence. This means that it is up to you to find the one to use to fit that series.

**Convergence and Divergence Tests**- nth Term Test/Limit Test
- Geometric Series
- Harmonic Series
- p-Series
- Comparison Tests (Limit and Direct)
- Integral Test
- Alternating Series Test
- Ratio Test
**Series Approximation**- Taylor and Maclaurin Series
- Lagrange Error Bounds

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πBig Reviews: Finals & Exam Prep

βοΈFree Response Questions (FRQ)

π§Multiple Choice Questions (MCQ)

βΎUnit 10: Infinite Sequences and Series (BC Only)

πUnit 1: Limits & Continuity

π€Unit 2: Differentiation: Definition & Fundamental Properties

π€π½Unit 3: Differentiation: Composite, Implicit & Inverse Functions

πUnit 4: Contextual Applications of the Differentiation

β¨Unit 5: Analytical Applications of Differentiation

π₯Unit 6: Integration and Accumulation of Change

πUnit 7: Differential Equations

πΆUnit 8: Applications of Integration

π¦Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

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