MH1810: pass the exams, not just read the notes
Your complete guide to Nanyang Technological University's mathematics 1 course. See where the marks are, work real practice questions, and study with an AI tutor that knows MH1810.
Sia generates MH1810 practice questions, walks through complex numbers and vectors step by step, and quizzes you on the material the exam weights most heavily.
Worked example
Evaluate the integral of x·e^x dx from 0 to 1.
Integrate by parts with u = × and dv = e^x dx, so du = dx and v = e^x.
Evaluate from 0 to 1: (1·e − e) − (0 − 1) = 0 + 1 = 1.
Check the traps: e − 1 forgets the x·e^x term at the upper limit; e ignores the subtraction; e/2 comes from treating x·e^x as if it were x·x.
The trap: Choosing u = e^x and dv = × dx. That makes the remaining integral harder, not easier; the polynomial factor should be the one you differentiate. classic slip!
One exam decides 60% of your grade. Summative assessment. This whole page is built around that.
Overview
What MH1810 is, and where it sits
MH1810 Mathematics 1 is NTU's first-semester mathematics course for engineering students, taught by the Division of Mathematical Sciences. The OBTL document sets its purpose plainly: introduce limits, differentiation and integration with their applications, add complex numbers, vectors and matrices, and prepare first-year engineers for their discipline courses and for year-2 mathematics.
Seventeen intended learning outcomes define the content, from evaluating roots of complex numbers and using dot and cross products in mechanics problems, through derivatives from first principles, Newton's method and curve sketching, to integration by parts, trigonometric substitution, partial fractions, improper integrals, Simpson's rule, and volumes, arc lengths and surface areas by integration.
Assessment is 60% final examination and 40% continuous assessment: online multiple-choice questions 16%, a mid-semester multiple-choice quiz 15% and a take-home test 9%. Three course coordinators are named. The course is 3 AU with 26 lecture hours and 12 tutorials, offered in Semester 1 and Semester 2.
Always treat your own course outline and the exam timetable as authoritative.
Difficulty & time commitment
Is MH1810 hard, and how much time does it take?
MH1810 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 do the online MCQs as they open; 16% of the grade is there for consistent work.
- You can differentiate and integrate mechanically and want to learn why the rules work.
- You keep the algebra tidy — most lost marks in a calculus exam are algebraic.
- You practise past tutorial problems until each integration technique is recognisable on sight.
You may struggle if
- You skip the first four weeks as 'just revision'; complex numbers, vectors and determinants are 15% of the mid-semester quiz on their own.
- You memorise formulae without the Riemann-sum or limit definitions the ILOs ask for.
- You leave the take-home test to the last night; it covers all the post-midterm calculus.
- You cannot yet manipulate trigonometric identities fluently.
- Make a one-page map of every integration technique with the trigger that tells you to use it.
- Practise Simpson's rule and improper integrals by hand — they are ILOs that many students under-prepare.
- Redo each tutorial sheet under exam timing two weeks before the final.
- Work the applications of integration (volumes, arc length, surface area) from the definition, not from memorised formulas.
Syllabus
The 13 topics, week by week
The exam-weight marker on each topic shows where the marks concentrate. The amber topics carry the highest exam weight.
T1 · Complex numbers
Week 1; ILO 1Argand diagram, polar and Euler form, De Moivre's theorem, nth roots, fundamental theorem of algebra.
T2 · Vectors
Week 2; ILO 2Dot and cross products; lines, planes, work and moment problems.
T3 · Matrices
Week 3; ILO 3Matrix operations, inverses and powers.
T4 · Determinants and Cramer's rule
Week 4; ILO 3Cofactors, determinants and solving simultaneous equations.
T5 · Limits and continuity
Week 5; ILO 4One-sided limits, limit theorems, continuity at a point.
T6 · Squeeze theorem and limits at infinity
Week 6; ILO 4Infinite limits and limits of rational functions.
T7 · Continuous functions
Week 7; ILO 4Intermediate and extreme value theorems.
T8 · The derivative
Week 8; ILOs 5-6Definition, differentiability and basic rules.
T9 · Differentiation rules and linearisation
Week 9; ILOs 6-8Product and chain rules, implicit differentiation, linear approximation, Newton's method.
T10 · Extreme values and L'Hopital
Week 10; ILOs 7-8Closed interval method, mean value theorem, indeterminate forms.
T11 · Integrals and Riemann sums
Week 11; ILOs 9, 13Indefinite and definite integrals; the Riemann sum meaning of integration.
T12 · Fundamental theorem and basic techniques
Week 12; ILOs 10-11FTC, basic integration formulae, trapezium and Simpson's rules.
T13 · Advanced techniques and applications
Week 13; ILOs 12-17Substitution, by parts, partial fractions, improper integrals; areas, volumes, arc length, surface area.
How it's assessed
Assessment structure
| Component | Weight | Format & timing |
|---|---|---|
| Continuous assessment: technology-enhanced learning multiple-choice questions | 16% | Online multiple-choice questions through the semester. Across the semester. Continuous assessment. |
| Mid-semester quiz: take-home test (post-midterm topics) | 9% | Take-home test on the post-midterm topics. Second half of semester. Continuous assessment. |
| Mid-semester quiz: multiple-choice questions (ILOs 1-6) | 15% | Multiple-choice questions on ILOs 1-6 (complex numbers, vectors, matrices, limits, derivatives). Mid-semester. Continuous assessment. |
| Final examination (2 hours) | 60% | Two-hour written final examination on all 17 ILOs; point-based marking. Examination period. Summative assessment. |
- The four components sum to 100; the OBTL document publishes no separate hurdle on the examination. Absence from a common test requires an email to the instructor and a Singapore-issued medical certificate submitted to the school office.
- Sixty percent in a two-hour written examination covering all seventeen ILOs. The mid-semester MCQ quiz covers the first six ILOs (complex numbers to differentiation rules) and the take-home test the post-midterm topics, so together they rehearse the whole exam.
This is an exam-cram course. With the exams at 60% of the grade and the final examination (2 hours) alone at 60%, your result is overwhelmingly decided by how well you perform under time pressure. Summative assessment.
Final exam timing: 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
- Find nth roots of a complex number in polar form.
- Compute a cross product and use it for a plane or a moment.
- Evaluate a determinant and solve a system by Cramer's rule.
- Decide continuity of a function using limits.
Before the final heaviest topics
- Differentiate implicitly and apply Newton's method.
- Integrate by parts, by trigonometric substitution and by partial fractions.
- Evaluate an improper integral and test its convergence.
- Compute a volume of revolution by slicing and by shells.
The mistakes that cost marks
Dropping the constant or the bounds. Indefinite integrals need the constant; definite ones need the bounds carried through a substitution.
Wrong root count. A complex number has n distinct nth roots; giving one loses the ILO 1 marks.
Shells versus slices. Setting up the wrong element for a volume of revolution is the most common week-13 error.
Teaching team
Who teaches MH1810
The bios below are factual. We do not rate lecturers; any star ratings are submitted by students who have taken MH1810.
Teaching team as listed in the course materials reviewed. AskSia does not rate lecturers; star ratings are submitted by students who have taken MH1810.
Formula & concept sheet
The vocabulary and formulas you must own
- Polar form
- A complex number written as modulus and argument, r(cos θ + i sin θ).
- Cross product
- The vector perpendicular to two vectors, with magnitude equal to the parallelogram area.
- Determinant
- A scalar from a square matrix that decides invertibility and drives Cramer's rule.
- Limit
- The value a function approaches; the foundation of continuity and the derivative.
- Derivative
- The instantaneous rate of change, defined as a limit of difference quotients.
- Newton's method
- An iterative scheme using tangents to approximate roots of an equation.
- Riemann sum
- A sum of rectangle areas whose limit defines the definite integral.
- Fundamental theorem of calculus
- The link between differentiation and integration.
- Integration by parts
- The product-rule-in-reverse technique for integrals of products.
- Improper integral
- An integral with an infinite limit or an unbounded integrand, evaluated as a limit.
Set texts
The prescribed reading
The syllabus references map straight onto these.
Thomas' Calculus
.
Where it fits
Prerequisites, related courses & why it matters
No prerequisites. Mutually exclusive with MH2813, CE1011, CZ1011, MH1100, MH1101, MH1800 and MH1801. 3 AU; 26 lecture hours and 12 tutorials; offered in Semester 1 and Semester 2.
Your MH1810 study toolkit
Study the course with Sia, not just read about it
Each tool already knows MH1810: 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 MH1810 hard?
It rates moderate on the six-factor rubric, at the harder end. The content is dense — a full calculus sequence plus complex numbers, vectors and matrices in 13 weeks — but 40% is continuous assessment and there is no exam hurdle.
What is the assessment breakdown?
Online multiple-choice questions 16%, mid-semester MCQ quiz 15%, take-home test 9% and a two-hour final examination 60%, per the NTU OBTL document.
Who is it for?
First-year engineering students; it is mutually exclusive with MH1100, MH1101, MH1800, MH1801, MH2813, CE1011 and CZ1011. There are no prerequisites.
Who teaches it?
The OBTL document names three course coordinators: Wang Huaxiong, Wang Li-Lian and Tang Wee Kee.
What is the textbook?
Thomas' Calculus, 13th edition (Pearson, 2016), with Stewart's Calculus as a reference.
What comes next?
MH1811 Mathematics 2, which lists MH1810 as its co-requisite and extends the calculus to several variables, series and differential equations.
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