---
title: "Unit 1 – Limits and Continuity - AP Calculus AB/BC"
description: "Review Unit 1 – Limits and Continuity for AP Calculus AB/BC with Fiveable study guides and practice resources."
canonical: "https://fiveable.me/ap-calc/unit-1"
type: "unit"
subject: "AP Calculus AB/BC"
unit: "Unit 1 – Limits and Continuity"
---

# Unit 1 – Limits and Continuity - AP Calculus AB/BC

## Overview

Review Unit 1 – Limits and Continuity for AP Calculus AB/BC with Fiveable study guides and practice resources.

## Study Guides

- [1.12 Confirming Continuity over an Interval](/ap-calc/unit-1/confirming-continuity-over-an-interval/study-guide/HVxTuBB73RiPPODABBib)
- [1.5 Determining Limits Using Algebraic Properties of Limits](/ap-calc/unit-1/determining-limits-using-algebraic-properties-limits/study-guide/HjStgVKViPGZj1CxYwEB)
- [1.13 Removing Discontinuities](/ap-calc/unit-1/removing-discontinuities/study-guide/InY5nKkX7B44HNb3T0fD)
- [1.11 Defining Continuity at a Point](/ap-calc/unit-1/defining-continuity-at-point/study-guide/JbsR9iQfAzCznNOCG6JK)
- [1.2 Defining Limits and Using Limit Notation](/ap-calc/unit-1/defining-limits-using-limit-notation/study-guide/NWqOTUfp5qyR2oC2s4GD)
- [1.4 Estimating Limit Values from Tables](/ap-calc/unit-1/estimating-limit-values-tables/study-guide/OJmciOeNSSLqtWYs9iZT)
- [1.15 Connecting Limits at Infinity and Horizontal Asymptotes](/ap-calc/unit-1/connecting-limits-at-infinity-horizontal-asymptotes/study-guide/W2SxFtLQMyeLuJkKjbcs)
- [1.14 Connecting Infinite Limits and Vertical Asymptotes](/ap-calc/unit-1/connecting-infinite-limits-vertical-asymptotes/study-guide/Xe93DTYjtipyxVutx2Pq)
- [1.16 Working with the Intermediate Value Theorem (IVT Calc)](/ap-calc/unit-1/working-with-intermediate-value-theorem-ivt-calc/study-guide/bq6hVlKKjsKVjp0ehmtc)
- [1.7 Selecting Procedures for Determining Limits](/ap-calc/unit-1/selecting-procedures-for-determining-limits/study-guide/jEibswwoSkYlDoRpkkYY)
- [1.3 Estimating Limit Values from Graphs](/ap-calc/unit-1/estimating-limit-values-graphs/study-guide/kafw8fkkBnVt8CdXdtH9)
- [1.1 Introducing Calculus: Can Change Occur at An Instant?](/ap-calc/unit-1/can-change-occur-at-an-instant/study-guide/oVDHiQiKsML50xOGjyjZ)
- [1.6 Determining Limits Using Algebraic Manipulation](/ap-calc/unit-1/determining-limits-using-algebraic-manipulation/study-guide/rf9HZ2V3D6dDLvWD595E)
- [1.8 Determining Limits Using the Squeeze Theorem](/ap-calc/unit-1/determining-limits-using-squeeze-theorem/study-guide/0Ax6y3Qku88ex24KGwiG)
- [1.10 Exploring Types of Discontinuities](/ap-calc/unit-1/exploring-types-discontinuities/study-guide/w0TgEsiaFrXpMnMus4he)
- [1.9 Connecting Multiple Representations of Limits](/ap-calc/unit-1/connecting-multiple-representations-limits/study-guide/yqwkWFeEpKWR6f8NQvRv)

## FAQs

### What topics are covered in AP Calc Unit 1?

AP Calc Unit 1 covers 16 topics built around limits and continuity. You'll work through defining and estimating limits from graphs and tables, using algebraic properties and manipulation to evaluate limits, the Squeeze Theorem, types of discontinuities, continuity at a point and over an interval, removing discontinuities, infinite limits, limits at infinity, vertical and horizontal asymptotes, and the Intermediate Value Theorem (IVT). Here's a quick breakdown of the major clusters:
- **Limits foundations:** Introducing Calculus, Defining Limits and Using Limit Notation, Estimating Limit Values from Graphs and Tables
- **Evaluating limits:** Algebraic Properties of Limits, Algebraic Manipulation, Selecting Procedures, the Squeeze Theorem, Connecting Multiple Representations
- **Continuity:** Types of Discontinuities, Continuity at a Point, Continuity over an Interval, Removing Discontinuities
- **Asymptotes and IVT:** Infinite Limits and Vertical Asymptotes, Limits at Infinity and Horizontal Asymptotes, the Intermediate Value Theorem See the full topic list at [AP Calc Unit 1](/ap-calc/unit-1).

### How much of the AP Calc exam is Unit 1?

Unit 1 makes up 10-12% of the AP Calc exam, so it's a meaningful but not dominant chunk of your score. The unit covers limits and continuity, including evaluating limits algebraically, identifying discontinuities, connecting limits to asymptotes, and applying the Intermediate Value Theorem. Expect several multiple-choice questions drawn directly from these concepts on exam day.

### What's on the AP Calc Unit 1 progress check (MCQ and FRQ)?

The AP Calc Unit 1 progress check in AP Classroom includes both MCQ and FRQ parts that test limits and continuity. The MCQ section pulls from topics like estimating limits from graphs and tables, using algebraic manipulation and the Squeeze Theorem, and identifying types of discontinuities. The FRQ part typically asks you to confirm continuity at a point, remove a discontinuity, or apply the Intermediate Value Theorem with written justification. For the progress check, focus especially on:
- Evaluating limits using algebraic properties and manipulation (Topics 1.5-1.7)
- Identifying and classifying discontinuities (Topics 1.10-1.13)
- Connecting limits at infinity to horizontal asymptotes (Topic 1.15)
- Applying the IVT with a complete written argument (Topic 1.16) Practice with matched questions at [AP Calc Unit 1](/ap-calc/unit-1) before your progress check deadline.

### How do I practice AP Calc Unit 1 FRQs?

AP Calc Unit 1 FRQs most often ask you to justify continuity at a point, remove a discontinuity by defining or redefining a function value, or apply the Intermediate Value Theorem to guarantee a solution exists on an interval. To practice, work through problems that require written justification, not just a numerical answer, since College Board awards points specifically for the reasoning you write down. A solid practice routine for Unit 1 FRQs:
1. Review the definitions for continuity (Topics 1.11-1.12) so you can write them precisely.
2. Practice IVT problems where you state all three conditions explicitly (Topic 1.16).
3. Work through removing discontinuities by identifying the limit and comparing it to the function value (Topic 1.13).
4. After each attempt, check whether your written justification matches what the scoring guideline expects. Find practice problems and worked examples at [AP Calc Unit 1](/ap-calc/unit-1).

### Where can I find AP Calc Unit 1 practice questions?

The best place to find AP Calc Unit 1 practice questions, including multiple-choice and progress-check style problems, is [AP Calc Unit 1](/ap-calc/unit-1). You'll find MCQ practice covering limit estimation from graphs and tables, algebraic limit evaluation, continuity, asymptotes, and the IVT. For a practice-test feel, work through questions from each topic cluster in order so you build the skills progressively before attempting a full mixed set.

### How should I study AP Calc Unit 1?

Start AP Calc Unit 1 by building a solid understanding of what a limit actually means before touching any algebra. Once the concept clicks, work through the evaluation techniques in order: direct substitution, factoring and simplifying, rationalization, and the Squeeze Theorem. Then shift to continuity, where you'll connect limit skills to classifying and removing discontinuities. A practical study plan:
1. **Understand the concept first.** Read through Topic 1.1 and 1.2 to get comfortable with limit notation and the idea of approaching a value.
2. **Practice estimation.** Use graphs (Topic 1.3) and tables (Topic 1.4) to build intuition before jumping to algebra.
3. **Work through algebraic techniques in sequence.** Topics 1.5-1.8 build on each other, so don't skip ahead.
4. **Memorize the continuity definition.** You need to state it precisely for FRQs: the limit exists, the function is defined, and they're equal.
5. **Nail the IVT.** Topic 1.16 shows up on FRQs regularly. Practice writing out all three conditions every time.
6. **Review asymptotes last.** Topics 1.14-1.15 connect limits to behavior you already know from precalc, so they tend to click quickly. All 16 topics with practice are at [AP Calc Unit 1](/ap-calc/unit-1).

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For the progress check, focus especially on:\n- Evaluating limits using algebraic properties and manipulation (Topics 1.5-1.7)\n- Identifying and classifying discontinuities (Topics 1.10-1.13)\n- Connecting limits at infinity to horizontal asymptotes (Topic 1.15)\n- Applying the IVT with a complete written argument (Topic 1.16) Practice with matched questions at <a href=\"/ap-calc/unit-1\">AP Calc Unit 1</a> before your progress check deadline."}},{"@type":"Question","@id":"https://fiveable.me/ap-calc/unit-1#how-do-i-practice-ap-calc-unit-1-frqs","name":"How do I practice AP Calc Unit 1 FRQs?","acceptedAnswer":{"@type":"Answer","text":"AP Calc Unit 1 FRQs most often ask you to justify continuity at a point, remove a discontinuity by defining or redefining a function value, or apply the Intermediate Value Theorem to guarantee a solution exists on an interval. To practice, work through problems that require written justification, not just a numerical answer, since College Board awards points specifically for the reasoning you write down. A solid practice routine for Unit 1 FRQs:\n1. Review the definitions for continuity (Topics 1.11-1.12) so you can write them precisely.\n2. Practice IVT problems where you state all three conditions explicitly (Topic 1.16).\n3. Work through removing discontinuities by identifying the limit and comparing it to the function value (Topic 1.13).\n4. After each attempt, check whether your written justification matches what the scoring guideline expects. 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For a practice-test feel, work through questions from each topic cluster in order so you build the skills progressively before attempting a full mixed set."}},{"@type":"Question","@id":"https://fiveable.me/ap-calc/unit-1#how-should-i-study-ap-calc-unit-1","name":"How should I study AP Calc Unit 1?","acceptedAnswer":{"@type":"Answer","text":"Start AP Calc Unit 1 by building a solid understanding of what a limit actually means before touching any algebra. Once the concept clicks, work through the evaluation techniques in order: direct substitution, factoring and simplifying, rationalization, and the Squeeze Theorem. Then shift to continuity, where you'll connect limit skills to classifying and removing discontinuities. A practical study plan:\n1. **Understand the concept first.** Read through Topic 1.1 and 1.2 to get comfortable with limit notation and the idea of approaching a value.\n2. **Practice estimation.** Use graphs (Topic 1.3) and tables (Topic 1.4) to build intuition before jumping to algebra.\n3. **Work through algebraic techniques in sequence.** Topics 1.5-1.8 build on each other, so don't skip ahead.\n4. **Memorize the continuity definition.** You need to state it precisely for FRQs: the limit exists, the function is defined, and they're equal.\n5. **Nail the IVT.** Topic 1.16 shows up on FRQs regularly. Practice writing out all three conditions every time.\n6. **Review asymptotes last.** Topics 1.14-1.15 connect limits to behavior you already know from precalc, so they tend to click quickly. All 16 topics with practice are at <a href=\"/ap-calc/unit-1\">AP Calc Unit 1</a>."}}]}
```