# Warwick MA142 Calculus 1: Syllabus, Topics and Practice

> A study guide for Warwick MA142 Calculus 1: real numbers, limits, sequences and series, and continuity, with a topic map and free practice for every topic.

Source: https://practicecalculus.com/courses/university-of-warwick-ma142
Updated: 2026-11-08

## At a glance

- **Module code:** MA142-10
- **Credits:** 10
- **Level:** Undergraduate Level 1 (Year 1)
- **Duration:** 10 weeks
- **Prerequisites:** Not stated in the module catalogue
- **Assessment:** Assignments 15%, on-campus exam 85%
- **Covers:** Real numbers, limits, series, continuity and uniform continuity
- **Next module:** MA143 Calculus 2
- **Practice here:** [Calculus 1](/learn/calculus-1) and the series unit of [Calculus 2](/learn/calculus-2)

## Key takeaways

- MA142 Calculus 1 is a 10-credit, 10-week Year 1 module run by the Warwick Mathematics Institute.
- Its outline syllabus covers real numbers, limits, series, continuity and uniform continuity.
- It treats one-variable analysis with more rigour than school, but with a focus on calculations rather than proofs.
- It is assessed by assignments (15%) and an on-campus exam (85%), and MA143 Calculus 2 follows it.

**MA142 Calculus 1** is a Year 1 module at the University of Warwick, taught by the Warwick Mathematics Institute. It is worth 10 credits and runs for 10 weeks. In the catalogue's own words, calculus "usually stands for Analysis, focused on calculations rather than proving theorems", and MA142 is the first module in that series. This guide maps each MA142 topic to free practice, so you can learn every idea by solving problems with instant feedback.

## What Warwick MA142 covers

The official module catalogue gives a short, indicative outline syllabus: real numbers, limits, series, continuity and uniform continuity. The stated aim is to develop analysis in dimension one "with much greater precision and rigour" than at school, shifting the focus from problem-solving recipes to the concepts behind them.

The learning outcomes say that by the end of the module you should:

- understand the real numbers and the symbol $\infty$ in depth,
- have a working knowledge of sequences and series, including limits and conditional and absolute convergence,
- know the properties of continuous functions.

Compared with a typical first-semester **Calculus 1** course, MA142 spends less time on derivative rules and more on limits, sequences and series. Derivatives and integrals arrive in the follow-on module, MA143 Calculus 2. The catalogue does not list formal prerequisites or the term the module runs in, so check your course handbook for those.

## MA142 topic map

| MA142 topic | Practice | Read |
| --- | --- | --- |
| Real numbers, inequalities and absolute value | [Functions and notation](/learn/calculus-1/functions-warmup/function-notation) | [Absolute value function](/functions/absolute-value-function) |
| Limits of sequences | [Sequences and their limits](/learn/calculus-2/sequences-and-series/sequences) | [Squeeze theorem](/theorems/squeeze-theorem) |
| Limits of functions | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits), [limit laws](/rules/limit-laws) |
| Infinity and limits at infinity | [Limits at infinity](/learn/calculus-1/limits/limits-at-infinity) | [Limits at infinity](/blog/limits-at-infinity) |
| Series and partial sums | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series formula](/rules/geometric-series-formula) |
| Convergence tests | [Comparison tests](/learn/calculus-2/sequences-and-series/comparison-tests) | [Convergence tests](/blog/convergence-tests), [ratio test](/rules/ratio-test) |
| Conditional and absolute convergence | [Alternating series](/learn/calculus-2/sequences-and-series/alternating-series) | [Alternating series test](/rules/alternating-series-test) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| Consequences of continuity | [Intermediate Value Theorem](/learn/calculus-1/limits/intermediate-value-theorem) | [Intermediate Value Theorem](/theorems/intermediate-value-theorem), [Extreme Value Theorem](/theorems/extreme-value-theorem) |

Uniform continuity is a proof-based idea that goes beyond what our lessons cover. Use the continuity lessons to make sure the basic definition is automatic, then work through your lecture notes for the uniform version.

## How MA142 fits with MA143 and MA259

| Module | Year | What it adds |
| --- | --- | --- |
| MA142 Calculus 1 | Year 1 | Real numbers, limits, series, continuity |
| MA143 Calculus 2 | Year 1 | Differentiability, Taylor's theorem, the Riemann integral, integration methods |
| MA259 Multivariable Calculus | Year 2 option | Analysis in several variables and vector calculus |

See the [MA143 guide](/courses/university-of-warwick-ma143) for the next step.

## Example problems at the MA142 level

**1. A limit of a sequence.** Find $\lim_{n \to \infty} \dfrac{3n^2 + 1}{n^2 + 5n}$. Divide top and bottom by $n^2$:

$$\lim_{n \to \infty} \frac{3 + 1/n^2}{1 + 5/n} = \frac{3 + 0}{1 + 0} = 3$$

**2. A geometric series.** Since the ratio is $\tfrac{1}{2}$ and $|\tfrac{1}{2}| < 1$,

$$\sum_{n=0}^{\infty} \left(\frac{1}{2}\right)^n = \frac{1}{1 - \tfrac{1}{2}} = 2$$

**3. Absolute versus conditional convergence.** The alternating harmonic series $\sum_{n=1}^{\infty} \dfrac{(-1)^{n+1}}{n}$ converges by the alternating series test, but $\sum \dfrac{1}{n}$ diverges, so the convergence is conditional, not absolute.

## How to do well in MA142

- **Practise a little every day.** Limits and series reward repetition far more than last-minute revision, and the exam is worth 85% of the module.
- **Learn the standard limits by heart.** Facts such as $\frac{1}{n} \to 0$ and $r^n \to 0$ for $|r| < 1$ appear in almost every series argument.
- **Use the homework.** The catalogue notes that marked work is returned and discussed in small classes, which is the best place to fix gaps early.
- **Watch out for common slips.** Our list of [common calculus mistakes](/blog/common-calculus-mistakes) covers the ones that cost marks most often.

> **Tip:** if a series question feels stuck, ask first whether the terms tend to zero. If they do not, the [nth term test](/rules/nth-term-test) settles it straight away.

## Frequently asked questions

### What is MA142 at Warwick?

MA142 Calculus 1 is a first-year module from the Warwick Mathematics Institute. The catalogue describes it as the first in a series of modules that develop analysis with a focus on calculations. It covers real numbers, limits, series, continuity and uniform continuity.

### Which degrees take MA142?

The 2026/27 module catalogue lists MA142 as core in Year 1 of Data Science, Discrete Mathematics, and Mathematics, Operational Research, Statistics and Economics (MORSE).

### How is MA142 assessed?

Assignments count for 15% and a centrally timetabled on-campus exam counts for 85%. The resit is a single in-person exam worth 100%.

### What comes after MA142?

MA143 Calculus 2, which moves on to differentiability, Taylor's theorem and series, the Riemann integral, methods of integration and improper integrals.

### How should I prepare for MA142?

Make sure your A level algebra and function skills are solid, then get comfortable with limits of sequences and functions. Short daily practice on limits and series builds the fluency the exam expects.