MAST10006 · Calculus 2
The Complete Exam Bible · S1 2026Calculus 2
Calculus 2 is the University of Melbourne's broad, procedure-heavy first-year analysis subject — limits & continuity, sequences & series, Taylor series, hyperbolic functions and the complex exponential, six techniques of integration, first- and second-order differential equations, and multivariable calculus. The final exam is 60% of your grade, closed-book, in person, with no calculator, covering the whole subject, so the marks come not just from the right answer but from choosing the right technique, justifying it (name the theorem, check its conditions) and using correct notation. This guide teaches each method to exam standard: the trigger that tells you which tool to reach for, the worked procedure, and the trap examiners watch for.
What MAST10006 covers
Eight teaching blocks → one exam-ready map. Each links to its free chapter guide.
How MAST10006 is assessed
| Component | Weight | Format |
|---|---|---|
| Final written exam | 60% | End of semester · 3 hours, closed-book, in person, no calculator · covers all content |
| Mid-semester test | 20% | In semester · 45 minutes |
| Assignments (best 6 of 7) | 20% | Across the semester — one free miss; confirm the exact dates in your subject guide |
L'Hopital's rule — the signature limit, mark by mark
- +1Substitute first and name the form. At x = 0 the top is e0 − 1 − 0 = 0 and the bottom is 0, so the limit is the indeterminate form 0/0 — L'Hopital's rule is legal.
- +1Differentiate top and bottom separately: the limit becomes limx→0 (ex − 1) / (2x).
- +1Check the form again: at x = 0 this is still 0/0, so apply the rule a second time: limx→0 ex / 2.
- +1Evaluate: e0 / 2 = 1/2. State the answer.
Key terms
- Limit
- Where a function f(x) is heading as x closes in on a point a — whether or not f is even defined there. The two-sided limit exists if and only if the left and right one-sided limits agree.
- L'Hopital's rule
- For an indeterminate quotient 0/0 or ∞/∞, the limit of f/g equals the limit of f′/g′ — provided that right-hand limit exists. You must verify the indeterminate form before differentiating, and may iterate while it stays indeterminate.
- Convergence test
- A named rule (divergence, comparison, limit comparison, ratio, root, integral, alternating) for deciding whether an infinite series adds up to a finite total. The exam skill is reading the shape of the terms and choosing the test that resolves the series.
- Integrating factor
- The multiplier μ = e∫P dx that turns a linear first-order ODE y′ + P(x)y = Q(x) into an exact derivative d/dx(μy) = μQ, which then integrates directly.
- Hessian test
- For a function of two variables, the determinant D = fxxfyy − (fxy)2 at a stationary point classifies it: D > 0 with fxx > 0 is a local minimum, D > 0 with fxx < 0 a local maximum, D < 0 a saddle, and D = 0 inconclusive.
MAST10006 FAQ
Is MAST10006 hard?
It is broad and procedure-heavy rather than conceptually deep: limits, sequences/series, Taylor, hyperbolic functions, the complex exponential, six integration techniques, first- and second-order ODEs and two-variable calculus are all examined in one 3-hour closed-book paper. The difficulty is doing the right method by hand, accurately, under time — so the safest preparation is drilling the worked procedures until they are automatic.
How is MAST10006 assessed?
The final exam is 60% of your grade: 3 hours, closed-book, in person, with no calculator, covering the whole subject. The remaining 40% is a mid-semester test (about 20%) and weekly assignments (about 20%, best 6 of 7 counting). Confirm this year's exact dates and weights in your subject guide.
Can I bring notes or a formula sheet into the MAST10006 exam?
The exam is closed-book and allows no calculator, but you may bring one double-sided A4 sheet of your own notes, and you are given the official Calculus 2 formula sheet. The smart play is to put on your A4 only what the provided sheet does not already give you — the decision rules for which test or substitution to use, your re-usable templates, and the trap reminders.
What is on the MAST10006 final exam?
Short- and long-answer questions across the whole subject: evaluating limits (often with L'Hopital), deciding series convergence with the right test, Taylor series and remainder bounds, hyperbolic and complex-exponential integrals, the six integration techniques, solving first- and second-order ODEs, and multivariable stationary-point classification with the Hessian. If a question specifies a method, you must use it.
Is using AskSia for MAST10006 cheating?
No. AskSia is a study reference written in our own words — we host none of your lecturer's files, and Sia teaches you the method to earn the marks; it does not complete or sit your assessments.
How to study for the exam
Treat MAST10006 as a set of technique chains you drill until they run on autopilot, because under exam pressure you only do reliably what you have done many times. The recurring chains are: indeterminate form → name it, then L'Hopital; series? → read the shape, choose the test, check its conditions; √(x² ± a²) → trig or hyperbolic substitution; linear ODE → integrating factor; second-order ODE → discriminant decides the case; two-variable stationary point → Hessian determinant. Because the exam is closed-book with no calculator, the examiner can only test whether you can execute the method by hand and justify it — so show every line, name every theorem, and use the past and sample exams (timed, by hand) as your highest-leverage practice while you build your one double-sided A4.
