ECON1003 Quantitative Methods in Economics
The Complete Exam Bible · S1 2026ECON1003 Overview
- University of Sydney
- S1 2026
- 7 chapters
- Economics
Quantitative Methods in Economics is the maths engine room of an economics degree — and despite the name it is mathematics, not statistics (no mean, no probability, no regression).
- Assessed by Final examination 50% · Mid-semester exam 40% · Online quizzes 10%
- Key terms Slope-intercept form, Elasticity (point form), Present value (NPV), Lagrangian
- How to prepare Every ECON1003 exam question is procedural: take a function or a system, apply the right technique, interpret the economics, round as asked.
- Most asked What's the best way to study for the ECON1003 exams?
How ECON1003 is assessed
| Component | Weight | Format |
|---|---|---|
| Final examination | 50% | End-of-semester exam · cumulative across all seven topics · formula sheet provided |
| Mid-semester exam | 40% | 60 minutes · covers the early topics (lines, non-linear functions, financial maths and the start of differentiation) · formula sheet provided |
| Online quizzes | 10% | Four quizzes on Canvas across the semester, one week each — confirm the exact split and dates in your unit guide |
What ECON1003 covers
Seven taught topics → one exam-ready map. Each links to its free chapter guide.
Linear Functions
y = mx + c · demand & supply · cost/revenue · linear elasticityThe straight line is the workhorse of ECON1003: every linear model — demand, supply, cost, revenue, a budget — is one equation, y = mx + c, pinned down by its slope m and its intercept c.
- 1.1 Equation, slope and intercept — y = mx + c
- Rearranging a scrambled line before reading m and c
- 1.2 Demand, supply and inverse functions
- 1.3 Cost, revenue, profit and break-even
- 1.4 Linear elasticity — and why it is not the slope
- The budget line and its slope as a price ratio
Non-Linear Functions
Quadratics & the discriminant · exponentials & e · logs · growthWhen the line bends, three function families do the work in ECON1003 — and one big idea links them.
- 2.1 Quadratics: the formula and the discriminant
- Locating the turning point of a parabola
- 2.2 Transformations of functions
- 2.3 Exponential functions and the number e
- 2.4 Logarithms and the log/index rules
- 2.5 Exponential growth and decay
Financial Mathematics
Series · simple/compound/continuous interest · NPV · annuitiesFinancial mathematics is the most procedural topic in ECON1003: every question is 'plug the right numbers into the right formula and grind', and nearly every formula is on the provided sheet.
- 3.1 Sequences and series — arithmetic vs geometric
- 3.2 Simple, compound and continuous interest
- 3.3 Present value and net present value (NPV)
- 3.4 Annuities — future value and present value
- Reducing-balance depreciation
- Debt repayment
Differentiation
The rules · optimisation · turning points · MR = MC profit maxDifferentiation is the spine of ECON1003 — it spans both exams and carries the headline application of the whole unit. A derivative is a rate of change, the slope of the tangent, and economics calls that rate marginal.
- 4.1 The derivative and the differentiation rules
- Product, quotient and chain rules
- 4.2 Higher derivatives, concavity and the second-derivative test
- 4.3 Turning points and points of inflection
- 4.4 Economic applications: marginal functions
- Profit maximisation where MR = MC
Multivariable Calculus
Partials · total differential · MRS/MRTS · the LagrangianReal economic functions depend on several things at once — output on labour and capital, utility on two goods, demand on its own price, income and other prices.
- 5.1 Partial derivatives and cross-partials
- 5.2 The total differential and percentage-change approximation
- 5.3 Production: MPL, MPK, isoquants and MRTS
- 5.4 Utility: indifference curves and MRS
- 5.5 Unconstrained optimisation
- 5.6 The Lagrangian, complementary slackness and the shadow price
Integration
Anti-derivatives · area & surplus · recovering TC from MC · ODEsIntegration undoes differentiation — to integrate a power, raise the index by one and divide by the new index, with the single exception of x⁻¹, which integrates to ln|x|.
- 6.1 The integral as an anti-derivative and the constant + C
- 6.2 The power rule and the n = −1 (ln) exception
- 6.3 Substitution and integration by parts
- 6.4 The definite integral and area between curves
- 6.5 Consumer and producer surplus as areas
- 6.6 Differential equations: recovering TC from MC, separable growth
Linear Algebra
Matrices · determinants · Cramer's rule · the inverse · solving systemsA matrix is a grid of numbers, sized rows × columns, and linear algebra is how ECON1003 solves systems of equations compactly.
- 7.1 Dimension, transpose and special matrices
- 7.2 Matrix arithmetic and multiplication (AB ≠ BA)
- 7.3 Gaussian and Gauss–Jordan elimination
- 7.4 Determinants: 2×2 and the 3×3 sign pattern
- 7.5 Cramer's rule
- 7.6 The inverse and solving X = A⁻¹B
It teaches seven techniques, all drilled on economic examples: straight lines, non-linear functions, financial mathematics, differentiation, functions of several variables, integration and linear algebra. A formula sheet is provided in both exams, so the examiner cannot test whether you remember a formula — only whether you can apply it.
This guide teaches every method to exam standard: the rule stated plainly, the worked example with real arithmetic, and where the marks hide.
ECON1003 cheatsheet for exam revision
AskSia publishes a free ECON1003 cheatsheet for exam revision, an exam cheat sheet that follows the official permitted-materials rule for this assessment and condenses the topics in this guide.
Worked example · free
Profit maximisation by differentiation — the signature MR = MC question, mark by mark
- +1Write revenue and profit. TR = P×Q = (100 − 2Q)Q = 100Q − 2Q². Profit π = TR − TC = (100Q − 2Q²) − (20Q + 50) = 80Q − 2Q² − 50.
- +1Differentiate and set to zero (the first-order condition). dπ/dQ = 80 − 4Q = 0.
- +1Solve for Q*. 4Q = 80 ⇒ Q* = 20. (Equivalently MR = 100 − 4Q equals MC = 20 at the same Q.)
- +1Find the price from inverse demand: P* = 100 − 2(20) = $60.
- +1Confirm it is a maximum (second-order condition). d²π/dQ² = −4 < 0, so the profit function is concave — Q* = 20 is a maximum, not a minimum.
- +1State the result. Maximum profit π = 80(20) − 2(20)² − 50 = 1600 − 800 − 50 = $750.
Key terms
- Slope-intercept form
- Any straight line written y = mx + c, where m is the slope (how much y changes when x rises by one) and c is the y-intercept (y when x = 0). The workhorse of every linear model in the unit — demand, supply, cost, a budget line.
- Elasticity (point form)
- The responsiveness of quantity to price as a unit-free number, ε = (dQ/dP)(P/Q). The key trap the unit exploits: on a straight-line demand the slope dQ/dP is constant but elasticity changes along the curve, because P/Q changes — so elasticity is not the slope.
- Present value (NPV)
- Today's worth of a future cash flow, found by discounting it back at the interest rate. Net present value sums the discounted inflows minus the cost; a positive NPV means the project adds value. It is the financial-maths topic's payoff calculation.
- Lagrangian
- The technique for constrained optimisation — maximise utility or minimise cost subject to a budget or output constraint. You form L = objective + λ(constraint), set the partial derivatives to zero, and solve; λ is the shadow price, the marginal value of relaxing the constraint. The unit's flagship, highest-mark technique.
- Determinant
- A single number computed from a square matrix that tells you whether the matrix is invertible (det ≠ 0) and underpins Cramer's rule for solving systems. The 2×2 is ad − bc; the 3×3 expands along a row with the + − + sign pattern.
ECON1003 FAQ
Is ECON1003 statistics?
No — and this is the single most common misconception. Despite the name 'Quantitative Methods', ECON1003 is mathematics for economics, not statistics. There is no mean, no probability, no hypothesis testing and no regression.
The seven taught topics are straight lines, non-linear functions, financial maths, differentiation, multivariable calculus, integration and linear algebra — calculus and algebra dressed in demand, cost, utility and production.
How is ECON1003 assessed?
By two written exams and online quizzes: a mid-semester exam (about 40%, 60 minutes, covering the early algebra-and-functions material plus the start of differentiation), a cumulative final exam (about 50%, all seven topics), and four online Canvas quizzes (about 10%, one week each). A formula sheet is provided in both exams. Confirm this year's exact weights and dates in your unit guide.
Do I need to memorise all the formulas?
No — a formula sheet is provided in both exams, so the examiner is testing method, not recall. The sheet typically carries the quadratic formula, the interest/annuity/NPV formulas, integration by parts and the aˣ/log derivatives.
What you must wield cold are the procedures: the differentiation rules (power, sum, product, quotient, chain), how to set up TR = P×Q, the Lagrangian conditions, and the matrix methods (elimination, Cramer, inverse).
What's the best way to study for the ECON1003 exams?
Drill the recurring procedural chains until they are automatic, because every exam question is procedural: line → slope/intercept → elasticity; set up TR → differentiate → MR = MC; integrate MC → recover TC; Lagrangian → solve cases → shadow price. Always show every line — method marks and partial credit are real even when the final arithmetic slips.
Is using AskSia for ECON1003 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.
Questions students ask in each ECON1003 chapter
- Why can't I just read the slope off the equation as written?
- Because lines are often handed to you scrambled, such as 2y + 4x − 4 = 0. You must isolate y first: 2y = 4 − 4x ⇒ y = 2 − 2x, so m = −2 and c = 2. Reading the '4' as the slope is the classic blunder — always rearrange to y = mx + c before reading m and c. Chapter 01 · Linear Functions
- Why should I compute the discriminant before solving?
- Because Δ = b² − 4ac tells you how many real roots exist before any arithmetic. If Δ < 0 there is no real root — write 'no real solution' rather than forcing a number. Computing Δ first also catches the common sign slip, where a negative b is mistakenly left negative after squaring (it becomes positive). Chapter 02 · Non-Linear Functions
- How do I avoid the most common financial-maths mistakes?
- Three decisions cause most lost marks. First, compound vs continuous interest — quarterly uses (1 + i/m)^(mt) with m = 4; continuous uses e^(it). Second, getting m (compounding periods per year) right and matching it to t. Third, telling a future-value annuity from a present-value one. Get those three right and the rest is calculator arithmetic. Chapter 03 · Financial Mathematics
- Do I have to use the limit definition of the derivative?
- No. The limit f′(x) = limₖ→₀[f(x+k) − f(x)]/k is shown so you understand what a derivative is, but the lecturer states he will not ask you to differentiate from the limit. In practice you always use the rules — power, constant, sum, product, quotient and chain — not the limit. Chapter 04 · Differentiation
- How do I take a partial derivative?
- Differentiate with respect to the chosen variable while treating every other variable as a constant. For z = x²y + 2y + 4: ∂z/∂x = 2xy (the 2y and 4 are constants in x, so they vanish), and ∂z/∂y = x² + 2 (x² is a constant coefficient). For the functions in this course the cross-partials are equal: fₓₓ = fₕₓ. Chapter 05 · Multivariable Calculus
- Why must I never drop the + C?
- Because the indefinite integral is only defined up to a constant (any constant differentiates to zero). In differential-equation questions — recovering total cost from marginal cost, or solving a growth law — you use a known condition (such as TC(0) = fixed cost) to solve for C. Drop it and you cannot complete the problem. Definite integrals are the only place C disappears. Chapter 06 · Integration
- Why is AB not the same as BA?
- Matrix multiplication is row-of-A dotted into column-of-B, so the order changes which numbers meet. Even for two 2×2 matrices, AB and BA generally give different results — the course shows A = [[1,2],[3,4]], B = [[5,6],[7,8]] where AB = [[19,22],[43,50]] but BA = [[23,34],[31,46]]. Always do the dimension check first: A's columns must equal B's rows. Chapter 07 · Linear Algebra
How to study for the exam
Every ECON1003 exam question is procedural: take a function or a system, apply the right technique, interpret the economics, round as asked. So the win condition is fluent, automatic technique — not memorised formulas (the sheet hands you those).
Drill the recurring chains until they are reflex: line → slope/intercept → elasticity; set up TR = P×Q → differentiate → MR = MC; integrate MC → recover TC; Lagrangian → solve cases → shadow price. Always show every line — method marks and partial credit are real.
Weight your time toward differentiation and the multivariable Lagrangian (they carry the most marks and span both exams), and treat financial maths as free procedural marks once you pick the right formula. Practise on fresh numbers so nothing in the exam can surprise you.
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