MH1101: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's calculus ii course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH1101.
Sia generates MH1101 practice questions, walks through antiderivatives and substitution rule step by step, and quizzes you on the material the exam weights most heavily.
Worked example
You need to decide whether the series with terms n! divided by n to the power n converges. Which test is the right first choice, and why?
Read the shape of the term before reaching for a test. A factorial and an nth power both grow faster than any polynomial, and both behave much better under division than under integration or comparison. That observation alone should point at the ratio test.
Evaluate the limit and read off the conclusion. The ratio test states that a limit strictly below 1 gives absolute convergence, strictly above 1 gives divergence, and exactly 1 gives no information — which is why the test is a first choice here and not a universal one.
Check why the alternatives fail. The integral test requires you to integrate a function of a continuous variable, and a factorial is not defined on one without extending it. The comparison test needs a series whose behaviour you already know and a valid inequality; the harmonic series shares nothing structural with this one.
The trap: Option C is the trap because it pattern-matches on surface appearance rather than on growth rate. The presence of n somewhere in a denominator says nothing about convergence. NTU teaches the comparison test in week 8 and the ratio and root tests in week 9, and the sequencing is the point: by week 9 you are expected to choose a test from the structure of the term, not from what the term superficially resembles. classic slip!
One exam decides 60% of your grade. Summative assessment. This whole page is built around that.
Overview
What MH1101 is, and where it sits
MH1101 is the second half of NTU's core calculus sequence. The published aim is to develop definite integrals and their applications to areas and volumes, the Fundamental Theorem of Calculus, integration techniques, tests for the convergence and divergence of sequences and series, the interval and radius of convergence of power series, differentiation and integration of power series, and Taylor series.
The course splits cleanly at about week 6, and the two halves ask for different things. The first half is technique: substitution, integration by parts, trigonometric substitution, partial fractions, numerical integration. You get better at it by doing volume. The second half is judgement: given a series, decide whether it converges and prove it with the appropriate test.
That second half is where grades separate, and the assessment structure confirms it. The mid-semester quiz in week 8 is mapped to ILOs 1 to 5 — the integration half. The 60% examination is mapped to ILO 2 and ILOs 5 through 11, which is almost entirely sequences, series, power series and Taylor series. In other words, the material you meet last carries the most marks.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH1101 hard, and how much time does it take?
MH1101 is manageable if you keep a weekly rhythm and treat the back half as the main event. The pattern is consistent: it starts gently and steepens, and the heaviest assessment is the part that separates grades.
The difficulty curve and the assessment weighting point the same way: the back half is harder and worth more. Front-loading effort there is the highest-return decision in the course.
Is this course for you
Who tends to do well, and who tends to struggle
You will likely do well if
- You start the convergence tests as a decision problem, not a memorisation problem — for each test, when it applies and when it is inconclusive.
- You front-load integration technique in the first six weeks so the second half has room; the assessment weighting rewards exactly that allocation.
- You attend lectures for the polling activities. Twelve are run and eight are needed, so absence has slack but not much.
- You treat absolute versus conditional convergence in week 9 as load-bearing; power series in week 10 depend on it directly.
You may struggle if
- You leave power series and Taylor series to revision week. They arrive in weeks 10 to 12 and carry ILOs 9 to 11 into a 60% final.
- You memorise convergence tests without their inconclusive cases — a ratio limit of exactly 1 is the case that catches people.
- You treat the online homework as low stakes because it is 5% and 10%; combined they are the same weight as the participation and homework buffer that separates grades.
- You assume the mid-semester quiz predicts the final. It covers ILOs 1 to 5; the final covers ILO 2 and ILOs 5 to 11.
- Build a one-page convergence decision chart: divergence test, integral, comparison, limit comparison, alternating, ratio, root — each with its trigger and its inconclusive case.
- Derive the Maclaurin series for the standard functions once from the definition, then get fast at producing new ones by substituting, differentiating and integrating known ones. Week 11 is explicitly about the second skill.
- Practise the Error Bound in week 12 as a numerical estimate, not an abstract statement; it is what turns a Taylor polynomial into a usable approximation.
- Work past papers under a two-hour clock. Sixty percent of the grade is decided in a single two-hour sitting.
Syllabus
The 13 topics, topic by topic
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Antiderivatives, definite integrals, the Fundamental Theorem of Calculus
Week 1; ILO1Riemann sums, area, and the theorem that links differentiation to integration.
T2 · Substitution rule, improper integrals, area between curves
Week 2; ILO2-3The first technique, the first classification problem, and the first application.
T3 · Volumes and integration by parts
Week 3; ILO3-4Solids of revolution, and the technique that reverses the product rule.
T4 · Trigonometric integrals, trigonometric substitution, partial fractions
Week 4; ILO4The three techniques that turn awkward integrands into standard ones.
T5 · Numerical integration and limits of sequences
Week 5; ILO5-6Approximation when no closed form exists, and the pivot into sequences.
T6 · Finding limits of sequences
Week 6; ILO7Formal evaluation of sequence limits, and the vocabulary of convergence.
T7 · Monotonic sequences and series
Week 7; ILO7-8Monotone convergence, and the move from sequences to their partial sums.
T8 · Integral test and comparison test
Week 8; ILO8The first two convergence tests, in the week the mid-semester quiz falls.
T9 · Absolute and conditional convergence, ratio test, root test
Week 9; ILO8The distinction that matters most for power series, plus the two workhorse tests.
T10 · Power series, radius and interval of convergence
Week 10; ILO9Representing a function as a series, and determining where that representation is valid.
T11 · Manipulating geometric series, term-by-term differentiation and integration, Taylor and Maclaurin series
Week 11; ILO10Building new series from known ones rather than from the definition.
T12 · Convergence via the Error Bound, binomial series, limits using power series
Week 12; ILO11Verifying that a Taylor series actually represents its function.
T13 · Summary
Week 13A consolidation week with no new content published.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Examination (2 hours) | 60% | Two-hour examination assessed against ILO 2 and ILOs 5 to 11, point-based marking on short answer questions. Examination period. Summative assessment. |
| Mid-semester Quiz | 20% | Short answer quiz covering ILOs 1 to 5, point-based marking. Week 8. Continuous assessment. |
| Homework 2 | 10% | Online assignment delivered through a commercial homework platform, covering ILOs 6 to 8. Second half of semester. Continuous assessment. |
| Homework 1 | 5% | Online assignment delivered through a commercial homework platform, covering ILOs 1 to 3. First half of semester. Continuous assessment. |
| In-lecture participation activities | 5% | In-lecture polling activities. Complete 8 of 12 for full marks; the best 8 scores are used. Across the semester. Continuous assessment. |
- The five components sum to 100. NTU publishes no separate hurdle on the examination. Where a make-up assessment cannot be arranged after a documented absence, the outline states the total course marks are rescaled to a base of 100%.
- The two-hour examination carries 60% and is mapped to ILO 2 and ILOs 5 to 11 — sequences, series, power series and Taylor series, plus improper integrals. The 20% mid-semester quiz in week 8 covers ILOs 1 to 5, the integration half. This split is the single most useful planning fact about the course: the integration techniques are tested early and cheaply, the series material is tested late and expensively.
This is an exam-cram course. With the exams at 80% of the grade and the examination (2 hours) alone at 60%, your result is overwhelmingly decided by how well you perform under time pressure. Summative assessment.
Final exam timing: Two-hour examination during the examination period. Confirm the exact date and venue on your exam timetable.
How to actually pass it
A weekly rhythm, two checklists, and the traps to avoid
The course rewards consistency over cramming, and practice over re-reading. Here is the loop that works, then what to have nailed before each exam.
The weekly loop
Before the mid-semester checklist
- Describe definite integrals through Riemann sums and area, and state the Fundamental Theorem of Calculus.
- Classify and evaluate improper integrals.
- Apply integration to areas between curves and volumes of solids of revolution.
- Evaluate integrals by substitution, parts, trigonometric substitution and partial fractions, and estimate them numerically.
Before the final heaviest topics
- Evaluate sequence limits using the formal definition and determine convergence of series with appropriate tests.
- Determine the radius and interval of convergence of a power series.
- Represent functions by manipulating geometric series or by differentiating and integrating known series.
- Find Taylor series and verify convergence using the Error Bound.
The mistakes that cost marks
Choosing a test by appearance. The comparison test is not selected because a term looks like something familiar; it needs a known series and a valid inequality. Growth rate, not resemblance, drives the choice.
Absolute versus conditional convergence blurred. Week 9 makes the distinction because week 10 needs it. A conditionally convergent series can be rearranged to change its sum, and power series arguments assume absolute convergence.
Interval endpoints ignored. Radius of convergence is the easy part. The endpoints have to be tested separately, and they are where marks are quietly lost.
Taylor series treated as a formula to recall. Week 11 is explicitly about manipulating known series. Rederiving everything from the definition under exam time is a self-inflicted constraint.
Teaching team
Who teaches MH1101
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH1101.
Teaching team as listed in public course information. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH1101.
Formula & concept sheet
The vocabulary and formulas you must own
- Fundamental Theorem of Calculus
- The result linking differentiation and integration as inverse operations.
- Improper integral
- An integral with an infinite limit or an unbounded integrand, evaluated as a limit.
- Integration by parts
- The integration rule obtained by reversing the product rule for derivatives.
- Partial fractions
- Decomposing a rational function into simpler fractions that can be integrated term by term.
- Monotonic sequence
- A sequence that is non-increasing or non-decreasing throughout.
- Integral test
- A convergence test comparing a series to the integral of a positive decreasing function.
- Comparison test
- A test establishing convergence or divergence by bounding against a series with known behaviour.
- Absolute convergence
- Convergence of the series formed from the absolute values of the terms.
- Conditional convergence
- Convergence of a series whose absolute-value series diverges.
- Ratio test
- A test using the limit of the ratio of consecutive terms; inconclusive when that limit is exactly 1.
- Root test
- A test using the limit of the nth root of the absolute value of the nth term.
- Radius of convergence
- The distance from the centre within which a power series converges.
- Taylor series
- A power series representation of a function built from its derivatives at a point.
- Error Bound
- An estimate of how far a truncated Taylor series can be from the function it represents.
Common acronyms: AU · FTC · ILO.
Where it fits
Prerequisites, related courses & why it matters
The published prerequisite is MH1100 or CY1601. MH1101 carries 4 Academic Units and 51 contact hours, delivered as 39 hours of lectures and 12 hours of tutorials, and is offered in Semester 2. It is mutually exclusive with MH111S, MH1800, MH1801, MH1802, MH1803, MH1805, MH1810, MH1811 and CY1601. The published readings are Stewart, Clegg and Watson, Calculus: Metric Version, 9th edition (Cengage, 2021) and Hass, Heil, Bogacki and Weir, Thomas' Calculus, 15th edition (Pearson, 2022).
Your MH1101 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH1101: your syllabus, your texts, and where the marks are. Grouped by how you study, from first contact to exam week.
FAQ
Frequently asked questions
Is MH1101 harder than MH1100?
They rate close, but the difficulty sits in a different place. MH1100 asks for proof technique early; MH1101 asks for judgement late. The convergence tests in weeks 8 to 12 are where students who coasted through integration technique lose ground.
What is the assessment breakdown?
A 60% two-hour examination, a 20% mid-semester quiz in week 8, two online homework assignments worth 5% and 10%, and 5% from in-lecture participation activities.
What does the final examination actually cover?
It is mapped to ILO 2 and ILOs 5 through 11 — improper integrals plus the whole sequences, series, power series and Taylor series block. The integration techniques are mostly assessed in the week 8 quiz instead.
How does the participation component work?
In-lecture polling activities. The published rule is that completing 8 out of 12 gives full marks, and the best 8 scores are used to assess each candidate.
What do I need before taking it?
MH1100 or CY1601. Note that MH1101 is mutually exclusive with a long list of alternative calculus courses, including MH1802 and MH1810.
Are the homework assignments on paper?
No. Both are online assignments delivered through a commercial homework platform, so submission is by deadline through that system.
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