MH1100: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's calculus i course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH1100.
Sia generates MH1100 practice questions, walks through sets and introduction to the limit step by step, and quizzes you on the material the exam weights most heavily.
Worked example
A function f is continuous at × = 0 but not differentiable there. Which statement correctly describes what has failed?
Separate the two definitions. Continuity at 0 says the limit of f(x) as × approaches 0 exists and equals f(0). Differentiability at 0 says a second, different limit exists: the limit of the difference quotient as the increment goes to zero. These are distinct limits about distinct quantities.
Check the direction of the implication. Differentiability at a point does imply continuity there, which is why the course states it in week 6. The converse does not hold, which is exactly the content of this question and the reason NTU teaches both properties in the same week.
Rule out the distractors. Option B contradicts the premise that f is continuous. Option C contradicts it too, since continuity at 0 requires f(0) to exist. Option D reverses a one-way implication.
The trap: Option D is the mistake worth naming because it is a reasoning error rather than a knowledge gap. The implication runs one way only: differentiable implies continuous. Students who memorise the sentence without its direction reconstruct it backwards under exam pressure. Week 6 pairs the two properties precisely so the asymmetry is visible while both are fresh. classic slip!
One exam decides 60% of your grade. Summative assessment. This whole page is built around that.
Overview
What MH1100 is, and where it sits
MH1100 is NTU's core first calculus course, and the published aim is to introduce the fundamental mathematical concepts of functions, limits, continuity, derivatives and integrals, then extend to computation of derivatives through the sum, product and quotient formulas, the chain rule and implicit differentiation, and to the application of derivatives to optimisation and related rates problems.
Two things about this course surprise students who arrive from an A-level or H2 calculus background. The first is week 3. NTU puts the precise epsilon-delta definition of the limit there, and ILO 3 states that you should be able to prove the limit and continuity of a function at a point or at infinity. That is a proof skill, not a computation skill, and it is examined.
The second is that no prerequisite is published. MH1100 is the entry point, and it is mutually exclusive with a long list of alternative first calculus courses NTU runs for other cohorts, among them MH1800, MH1801, MH1802, MH1805, MH1810, MH1811 and CY1601. If your programme places you in one of those instead, this guide is not the one you want.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH1100 hard, and how much time does it take?
MH1100 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 treat week 3 as the most important week of the semester rather than a formality before the real content.
- You work every quiz as if it counts, because you cannot know in advance which sitting will be one of your two best.
- You can state a theorem's hypotheses before applying it — the mean value theorem in week 9 is assessed as a proof tool under ILO 5.
- You keep a running list of functions that are continuous but not differentiable; that boundary is examined.
You may struggle if
- You reduce the course to differentiation drills and skip the definitions the drills rest on.
- You skip lectures because quiz dates are unannounced — that is precisely the design intent of not announcing them.
- You defer optimisation and curve sketching to revision week; they arrive in week 10 and carry ILOs 6 and 7 into the 60% final.
- You treat Newton's method as a calculator procedure rather than as the tangent-line argument it is built from.
- Write out one full epsilon-delta proof from memory each week from week 3 onward; the structure is what is being marked, not the algebra.
- For each theorem, record the hypotheses, the conclusion and one counterexample showing what breaks when a hypothesis is dropped.
- Practise short answer under time. Every component in this course is short answer, so speed of clean written argument is a graded skill.
- Use both editions of the published text if you can; the exercise sets differ and MH1100 rewards exposure to varied problem statements.
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 · Sets and functions
Week 1; ILO1The vocabulary the rest of the course is written in, set up before any limit appears.
T2 · Introduction to the limit, limit laws, squeeze theorem
Week 2; ILO1-2The intuitive picture of a limit and the algebraic laws that let you evaluate one.
T3 · The precise definition of the limit: epsilon-delta
Week 3; ILO1-3Where the course turns from computation to proof. ILO 3 is assessed on this.
T4 · Advanced limit topics: uniqueness, one-sided limits, limits to infinity
Week 4; ILO1-3Uniqueness of the limit, one-sided limits, and behaviour as the variable grows without bound.
T5 · Continuity, continuous functions and the intermediate value theorem
Week 5; ILO1-3Continuity defined through limits, and the first existence theorem of the course.
T6 · The definition of the derivative; continuity versus differentiability
Week 6; ILO1-2The derivative as a limit, and why differentiable implies continuous but not the reverse.
T7 · Differentiation rules and the calculus of trigonometric functions
Week 7; ILO1-2Sum, product and quotient rules, and the derivatives of the trigonometric functions.
T8 · Chain rule
Week 8; ILO4Composite functions, and the week the mid-semester test falls in.
T9 · Extreme value theory and the mean value theorem
Week 9; ILO5The theory behind optimisation, and the theorem ILO 5 asks you to prove results with.
T10 · Limits at infinity, curve sketching, optimisation problems
Week 10; ILO6-7Assembling the whole toolkit to describe a curve and to optimise.
T11 · Newton's method
Week 11; ILO6A numerical root-finder built directly from the tangent line.
T12 · Antiderivatives
Week 12; ILO1Reversing differentiation, and the bridge into MH1101.
T13 · Revision
Week 13A consolidation week with no new content published.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Examination (Short Answer Questions) | 60% | Short answer examination assessed against all seven ILOs, point-based marking. Examination period. Summative assessment. |
| Mid-semester Test (Short Answer Questions) | 20% | Short answer mid-semester test covering ILOs 1 to 4, point-based marking. Week 8. Continuous assessment. |
| In-class quizzes, weeks 1-7 | 10% | Three unannounced in-class quizzes at 5% each. You must attempt any two; if all three are attempted the two highest scores count. Weeks 1-7. Continuous assessment. |
| In-class quizzes, weeks 8-13 | 10% | Three unannounced in-class quizzes at 5% each, same best-two-of-three rule as the first half. Weeks 8-13. Continuous assessment. |
- The four components sum to 100. NTU publishes no separate hurdle on the final examination. Where a documented medical absence prevents you from sitting a component, the outline states the total course marks are rescaled to a base of 100%.
- The 60% short-answer final is assessed against all seven ILOs, so nothing in the thirteen weeks is off the table. The 20% mid-semester test in week 8 covers ILOs 1 to 4 — that is everything up to and including the chain rule, with the epsilon-delta material squarely inside it.
This is an exam-cram course. With the exams at 80% of the grade and the examination (short answer questions) alone at 60%, your result is overwhelmingly decided by how well you perform under time pressure. Summative assessment.
Final exam timing: Short-answer 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
- Interpret and use the basic concepts: sets, functions, limits, continuity, derivatives and integrals.
- Evaluate limits, rates of change, derivatives and extreme values.
- Prove the limit and continuity of a function at a point or at infinity using the precise definition.
- Apply the chain rule, curve-sketching techniques and optimisation methods.
Before the final heaviest topics
- Use the mean value theorem to prove a result, not merely to state it.
- Select the right mathematical model for a real problem involving velocity or curve properties.
- Apply calculus techniques to related rate and optimisation problems.
- Compute antiderivatives, the bridge into MH1101.
The mistakes that cost marks
Epsilon-delta treated as decoration. It is week 3 material and ILO 3 is written around it. Courses that teach it and never assess it exist; this is not one of them.
Quizzes treated as optional. Six quizzes at 5% each are 20% of the grade, and the dates are deliberately unannounced.
Continuity and differentiability conflated. Week 6 pairs them so the one-way implication is visible. Reversing it is the most common conceptual error in the course.
Theorem hypotheses skipped. The mean value theorem and the intermediate value theorem are both existence results whose hypotheses do the work. Applying them without checking is where marks go.
Teaching team
Who teaches MH1100
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH1100.
Teaching team as listed in public course information. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH1100.
Formula & concept sheet
The vocabulary and formulas you must own
- Limit
- The value a function approaches as its input approaches a point, whether or not the function is defined there.
- Epsilon-delta definition
- The precise formulation of a limit: for every tolerance on the output there is a tolerance on the input that guarantees it.
- Squeeze theorem
- If a function is trapped between two others that share a limit, it has that limit too.
- One-sided limit
- The value approached from the left or the right alone; the two-sided limit exists only when both agree.
- Continuity at a point
- The limit at the point exists and equals the function's value there.
- Intermediate value theorem
- A continuous function on an interval takes every value between its endpoint values.
- Derivative
- The limit of the difference quotient, giving the instantaneous rate of change.
- Chain rule
- The rule for differentiating a composition of functions.
- Implicit differentiation
- Differentiating a relation that is not solved for one variable in terms of the other.
- Extreme value theorem
- A continuous function on a closed bounded interval attains a maximum and a minimum.
- Mean value theorem
- On a suitable interval, some interior point has instantaneous rate of change equal to the average rate.
- Newton's method
- An iterative root-finder that follows the tangent line to its horizontal intercept.
- Antiderivative
- A function whose derivative is the given function, determined up to an additive constant.
Common acronyms: AU · ILO · IVT · MVT.
Where it fits
Prerequisites, related courses & why it matters
NTU publishes no prerequisite for MH1100. It carries 4 Academic Units and 51 contact hours, delivered as 39 hours of lectures and 12 hours of tutorials, and is offered in Semester 1. It is mutually exclusive with MH110S, MH1800, MH1801, MH1802, MH1805, MH1810, MH1811 and CY1601. The published readings are Stewart's Calculus, 8th edition (Cengage, 2015) and the 9th edition by Stewart, Clegg and Watson (Cengage, 2020).
Your MH1100 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH1100: 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 MH1100 hard?
It rates as moderate, but the difficulty is not where beginners expect. The differentiation mechanics are routine; the epsilon-delta definition in week 3 and the proof-flavoured ILO 3 are what separate grades. The quiz structure softens the risk considerably.
What is the assessment breakdown?
A 60% short-answer final examination, a 20% mid-semester test in week 8, and 20% from six in-class quizzes — three in weeks 1 to 7 and three in weeks 8 to 13, each worth 5%.
Do I have to sit all six quizzes?
No. NTU states you must attempt any two in each half. If you attempt all three, the two highest scores are counted. Dates are not announced in advance.
What does the mid-semester test cover?
It is mapped to ILOs 1 to 4, which spans sets and functions through to the chain rule in week 8 — including the epsilon-delta definition and continuity.
Is there a prerequisite?
None is published. MH1100 is the entry point, though it is mutually exclusive with a long list of alternative first calculus courses including MH1802, MH1810 and CY1601.
What happens if I miss a test for medical reasons?
The published policy is that with an original medical certificate submitted to an administrator, the total course marks are rescaled to a base of 100%.
Study MH1100 with Sia
Work through sets, introduction to the limit, the precise definition of the limit: epsilon-delta and the rest of the course with a tutor that knows it and quizzes you on the topics the assessments weight most heavily.
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