DPST1013 Mathematics 1A
The Complete Exam Bible · T3 2026DPST1013 Overview
- Term 3 2026
- Level 1 Diploma
- UNSW Sydney
- Written final exam
- Homework hurdle
DPST1013 Mathematics 1A is a Level 1 Diploma course taught in Term 3, 2026 at UNSW Sydney. It develops two strands at the same time.
- Assessed by Weekly tutorial work, Maple activities, a typeset assignment, a written midterm and a written final examination.
- Hardest step Turning a familiar formula into a justified solution when the problem changes representation or combines two topics.
- How to prepare Rebuild each method without notes, verify the result independently and write the mathematical conclusion in a complete sentence.
What you get in the full DPST1013 Exam Bible
- 11 chapters, 36 pages — every examinable topic, week by week
- 33 original practice questions in the Final Exam format
- 11 worked examples, solved the way DPST1013 marks
- 29 computed figures, redrawn from the course’s own numbers
- Exam-morning plan for the Final Exam (50%) — what to revise last, where marks are lost
Free on this page: assessment table, chapter map, one worked example, key terms, FAQ. The rest is in the full exam bible.
DPST1013 Course Changes in Term 3 2026
Compared with Term 2 2026
What's new
- ✅Online computing tutorials10%
- ✅Assignment5%
- ✅Mid Term25%
What's changed
- 🔄In Class Homeworkhurdle → 5%
- 🔄Maple Lab Test10% → 5%
- 🔄Final Exam60% → 50%
What's removed
- ❌In Class Tests (3 tests)30%
How DPST1013 is assessed in T3 2026
| Component | Weight | Format |
|---|---|---|
| In Class Homework · hurdle | 5% | Tutorials in Weeks 2 to 11; best fifteen results count; at least 15 out of 30 is required to attend the final exam |
| Maple Lab Test | 5% | Individual forty-minute computer laboratory test in Week 12; sixteen marks |
| Online computing tutorials | 10% | Individual Mobius tutorial sets across Weeks 3 to 12; best eight of eleven sets count |
| Assignment | 5% | Individual typeset mathematical document due in Week 7; approximately five A4 pages; AI cannot be used |
| Mid Term | 25% | Written paper-based examination in person during Week 8; ninety minutes and forty marks |
| Final Exam | 50% | Written paper-based examination in person during the examination period; 150 minutes and eighty marks |
From the course outline for Term 3, 2026 (as of 2026-10-29); dates and venues are subject to confirmation. Always check your own subject guide and LMS for the authoritative timetable. See how DPST1013 has been assessed over time
How DPST1013 has been assessed over time
2 teaching periods tracked. Open an earlier period to see its full assessment.
- Term 3 2026 CurrentSee table above ↑
Term 2 2026ShowHide
Component Weight Format Final examination 60% 2026 Handbook: Examination; solution method and correct workings. Maple Online Tests and Maple Lab Test 10% 2026 Handbook: correct answers and immediate electronic feedback. In Class Tests (3 tests) 30% 2026 Handbook: solution method and correct workings; tutorial feedback. In-Class Homework pass requirement · hurdle T2 outline hurdle: at least 15/30 to attend the final exam; explicit rule conflicts with schedule n/a. The outline assigns a separate 5% within its own alternative schedule. Final exam: 60%. Source: course outline, as of 2026-09-28.
What other students are asking about DPST1013
- Where can I find lecture notes or study guides for DPST1013 at UNSW?
- The DPST1013 study guide in AskSia Library covers Mathematics 1A in 11 chapters, with the assessment table, a chapter-by-chapter topic map, key terms and a worked example, free to read on this page.
- Is there a final exam in DPST1013, and how much is it worth?
- Yes. In the offering this AskSia Library guide is built from, Final Exam carries 50% of the DPST1013 mark; the full split is In Class Homework 5%, Maple Lab Test 5%, Online computing tutorials 10%, Assignment 5%, Mid Term 25%, Final Exam 50%.
- What does DPST1013 cover on vector geometry and projections?
- In AskSia Library's DPST1013 guide, the Vector Geometry and Projections chapter explains dot and cross products, orthogonality, projections, distances, areas and volumes.
- What does DPST1013 cover on complex numbers and polynomial roots?
- In AskSia Library's DPST1013 guide, the Complex Numbers and Polynomial Roots chapter explains cartesian and polar form, De Moivre, roots, conjugates and real factorisation.
- What does DPST1013 cover on linear systems and gaussian elimination?
- In AskSia Library's DPST1013 guide, the Linear Systems and Gaussian Elimination chapter explains row operations, echelon form, consistency, pivots, free variables and parameters.
What DPST1013 covers
Mathematics 1A runs algebra and calculus in parallel. The algebra route moves from vectors and geometry through complex numbers, linear systems and matrices. The calculus route moves from functions and limits through continuity, differentiation, curve analysis, integration, logarithms and hyperbolic functions. Maple supports symbolic calculation, plotting and linear algebra throughout.
Vectors, Lines and Planes
Vector equations, spans, parametric lines, plane forms, membership and intersectionsThis chapter separates points from direction vectors and treats lines and planes as generated sets. It develops parametric vector equations, spans, membership tests, parallelism and intersections.
- Geometric and algebraic vectors
- Parametric line equations
- Spans and plane equations
- Point membership tests
- Parallel, coincident and intersecting objects
- Conversion between vector and normal forms
Vector Geometry and Projections
Dot and cross products, orthogonality, projections, distances, areas and volumesDot products turn angles and orthogonality into scalar calculations, while cross products encode perpendicular directions and area in three dimensions.
- Lengths and angles
- Dot products and orthogonality
- Vector projections
- Distance to a line
- Cross products and areas
- Scalar triple products and volumes
Complex Numbers and Polynomial Roots
Cartesian and polar form, De Moivre, roots, conjugates and real factorisationComplex numbers are treated both as algebraic expressions and as points on the Argand plane. Cartesian form supports addition and conjugation, while polar form turns multiplication into scaling and rotation.
- Cartesian and polar form
- Modulus and argument
- Conjugates and division
- De Moivre's theorem
- Powers and complete root sets
- Conjugate factors of real polynomials
Linear Systems and Gaussian Elimination
Row operations, echelon form, consistency, pivots, free variables and parametersGaussian elimination replaces a linear system with reversible equations that expose its solution structure. Echelon form separates pivot and free variables, while the augmented column reveals contradictions.
- Augmented matrices
- Elementary row operations
- Row-echelon form
- Pivot and free variables
- Consistency and contradiction rows
- Parameterised solution sets
Matrices, Inverses and Determinants
Matrix operations, transformations, invertibility, determinant rules and systemsMatrices represent linear transformations and systems, so dimensions and multiplication order carry meaning. Determinants record signed area or volume scale and detect whether a transformation collapses dimension.
- Matrix dimensions and products
- Transposes
- Determinant geometry
- Row-operation determinant rules
- Matrix inverses
- Solving systems with inverses
Functions, Limits and Continuity
Domains, formal limits, one-sided behaviour, continuity and existence theoremsLimits describe function behaviour near a point without requiring the value at that point. The epsilon-delta definition controls outputs through nearby inputs, while one-sided limits decide existence.
- Function domains and combinations
- Formal finite and infinite limits
- Limit laws and indeterminate forms
- One-sided limits
- Continuity at a point
- Intermediate Value and extrema theorems
Differentiation and the Mean Value Theorem
Derivative rules, implicit rates, theorem hypotheses, extrema and L'HopitalThe derivative is developed from a limit of secant slopes, then calculated efficiently through product, quotient and chain rules. Implicit differentiation and related rates keep dependencies visible.
- Derivative from first principles
- Product, quotient and chain rules
- Implicit differentiation
- Rates and higher derivatives
- Mean Value Theorem
- L'Hopital and optimisation
Inverse Functions and Curve Sketching
Domain restrictions, inverse derivatives, asymptotes, monotonicity and polar curvesInverse functions reverse one-to-one mappings and reflect graphs across the line y equals x. Domain restrictions determine whether an inverse exists and which algebraic branch is valid.
- One-to-one functions
- Domain and range exchange
- Inverse derivatives
- Asymptotes and intercepts
- Monotonicity and concavity
- Parametric and polar curve tracing
Integration and Improper Integrals
Riemann sums, the Fundamental Theorem, techniques, area and convergenceThe definite integral is a limit of signed Riemann sums, and the Fundamental Theorem connects that accumulation to antiderivatives. Substitution and integration by parts reverse familiar derivative structures.
- Riemann sums
- Definite and indefinite integrals
- Fundamental Theorem of Calculus
- Substitution
- Integration by parts
- Improper integrals and comparison
Logarithmic and Hyperbolic Functions
Log laws, exponential inverses, hyperbolic identities, derivatives and integralsThe natural logarithm is introduced through the integral of one over x and inverted by the exponential function. Log laws simplify products and powers only on suitable domains.
- Natural logarithm
- Exponential inverse
- Log laws and domains
- Logarithmic differentiation
- Hyperbolic functions
- Inverse hyperbolic functions and substitutions
Maple and Mathematical Computing
Exact symbolic work, functions, plots, calculus, equations and linear algebraMaple supports exact arithmetic, symbolic functions, calculus, equations, plots and linear algebra. Effective use begins with a mathematical intention, translates it into a precise command and ends by checking and interpreting the result.
- Expressions and functions
- Exact and approximate arithmetic
- Symbolic limits and calculus
- Solving equations
- Parametric, polar and implicit plots
- Vectors, matrices and Gaussian elimination
Algebra begins with geometric and algebraic vectors, then builds lines, planes, dot and cross products, complex numbers, systems of linear equations, Gaussian elimination, matrices, inverses and determinants.
Calculus begins with sets, inequalities and functions, then develops limits, continuity, derivatives, the Mean Value Theorem, inverse functions, curve sketching, integration, logarithmic and exponential functions, and hyperbolic functions. Maple is used as a computer algebra system for symbolic calculation, plots, equations and linear algebra. The assessment structure makes steady practice important.
In Class Homework is worth 5% and is also a hurdle: a student needs at least 15 marks out of 30 to attend the final exam. Online computing tutorials and the Maple Lab Test contribute 15% together, the typeset assignment contributes 5%, the Mid Term contributes 25%, and the Final Exam contributes 50%. The two examinations are written, paper-based and held in person.
The Mid Term lasts 90 minutes and the Final Exam lasts 150 minutes. The official description says exam questions may combine ideas, use unfamiliar settings and require clear, rigorous arguments. This guide therefore does more than collect formulas. Each chapter explains a structural relationship with an original diagram, works a fresh example line by line, identifies a tempting error and ends with short practice.
The final answer is always checked against the original definition, equation, domain or geometric condition.
Worked example · free
Projection with an orthogonality check
- 1Compute v dot u = 12 and u dot u = 9.
- 1Multiply u by 12/9 to obtain the projection (4/3, 8/3, 8/3).
- 1Subtract from v to get the remainder (8/3, -5/3, 1/3).
- 1Dot the remainder with u: 8/3 - 10/3 + 2/3 = 0, confirming orthogonality.
Key terms
- Parametric equation
- A vector description that generates points by varying one or more real parameters.
- Orthogonal projection
- The component of one vector lying in the direction of another non-zero vector.
- Complex argument
- An angle locating a non-zero complex number from the positive real axis, defined modulo a full turn.
- Row-echelon form
- A matrix form whose staggered pivots expose leading variables, free variables and contradiction rows.
- Determinant
- A signed scale factor for area or volume that is non-zero exactly when a square matrix is invertible.
- Continuity
- The condition that a function value exists and equals the limit at the point.
- Derivative
- The limiting instantaneous rate of change or tangent slope of a function.
- Mean Value Theorem
- A theorem guaranteeing an interior tangent slope equal to the endpoint secant slope under stated conditions.
- Inverse function
- A function that reverses a one-to-one mapping by swapping its inputs and outputs.
- Riemann integral
- A signed accumulation defined as the limit of increasingly fine weighted sums.
- Improper integral
- An integral defined through a limit because its interval is infinite or its integrand is unbounded.
- Computer algebra system
- Software that manipulates symbolic mathematical objects while leaving setup and interpretation to the user.
DPST1013 FAQ
How hard is Mathematics 1A?
The published facts show a broad course rather than a difficulty rating: two parallel strands, a 25% midterm, a 50% final and a tutorial hurdle. The main challenge is moving between definitions, calculations and written justification. Weekly retrieval practice is more useful than postponing algebra and calculus until the examination period.
What is the homework hurdle?
In Class Homework is worth 5%, but it also controls access to the final exam. Eighteen tutorial tests are scheduled and the best fifteen results count. A student needs at least 15 marks out of 30. Prepare the released questions before tutorials and use feedback to improve complete written solutions.
What is the final exam format?
The current course outline describes a written, paper-based examination held in person. It lasts 150 minutes, carries 80 marks and is worth 50% of the course. Notes, external tools, AI and communication are not permitted during the exam. The outline does not publish a section or question-count breakdown.
Are past exam papers available?
The course outline says students will be given at least one past exam for preparation, but the captured course folder used for this guide does not include that paper. Check the current Moodle and Microsoft Teams pages for the released file. The practice questions here are original and model topic types, not copied past-paper stems.
How should I prepare for the Maple Lab Test?
Practise from a blank worksheet rather than memorising screenshots. Create exact expressions, functions, vectors and matrices; run the appropriate command; predict the result shape; then verify it independently. The current outline describes a forty-minute in-person laboratory test based on an accessible question bank and worth 5%.
What earns marks in written mathematics?
The published assignment rubric emphasises valid self-contained arguments, concise explanations, clear conclusions, correct grammar and correctly typeset symbols. Examination marking is not published as that same rubric, so do not invent a per-question scheme. Still, those habits make a solution easier to follow and protect method credit.
What is the best revision order?
First secure vector and function language, because later topics reuse those objects. Next drill complex numbers, elimination, derivatives and integration as methods. Then mix chapters: projection with planes, limits with curve analysis, matrices with systems, and substitutions that produce logarithmic or hyperbolic forms. Finish with timed written practice and independent checks.
Questions students ask in each DPST1013 chapter
- How do I test whether a point lies on a line?
- Substitute the point's coordinates into the component equations and solve for the parameter. One common parameter must satisfy every coordinate. If different coordinates require different values, the point is not generated by that line. Chapter 01 · Vectors, Lines and Planes
- What checks prove a projection is correct?
- Add the projection and perpendicular remainder to recover the original vector. Then take the dot product of the remainder with the target direction and confirm it is zero. Passing both checks strongly audits the calculation. Chapter 02 · Vector Geometry and Projections
- How do I choose the correct argument?
- Plot the signs of the real and imaginary parts to identify the quadrant, then use an inverse tangent only for the reference angle. Adjust that angle into the requested principal interval before reporting the polar form. Chapter 03 · Complex Numbers and Polynomial Roots
- What does a zero row mean?
- A completely zero row says one equation was redundant and adds no new restriction. It does not prove inconsistency. A row with zero coefficients and a non-zero augmented entry is the contradiction that proves no solution. Chapter 04 · Linear Systems and Gaussian Elimination
- Why is matrix multiplication order important?
- Matrix multiplication represents composition. Applying B and then A produces AB, while reversing the order applies transformations differently and may not even be dimensionally defined. Products generally cannot be commuted like ordinary numbers. Chapter 05 · Matrices, Inverses and Determinants
- Can a limit exist when the function is undefined?
- Yes. A limit uses nearby values and excludes the point itself. A removable hole can therefore have a finite two-sided limit even though the function value is missing. Continuity fails until the value is defined appropriately. Chapter 06 · Functions, Limits and Continuity
- Why must I state the Mean Value Theorem conditions?
- The conclusion is guaranteed only when the function has no discontinuity between the included endpoints and has a derivative at every interior point. Solving the derivative equation without those facts does not justify the existence claim. Chapter 07 · Differentiation and the Mean Value Theorem
- Why must a domain be restricted before inversion?
- A function such as a full quadratic sends two inputs to the same output, so reversing it would not produce a function. Restricting to one monotone branch creates a one-to-one mapping and fixes the square-root sign. Chapter 08 · Inverse Functions and Curve Sketching
- Why is a definite integral not always an area?
- The definite integral is signed accumulation. Regions below the axis contribute negatively and may cancel positive regions. Geometric area requires finding every crossing, splitting the interval and making each contribution positive. Chapter 09 · Integration and Improper Integrals
- Why do logarithm laws need domain conditions?
- Real logarithms accept only positive arguments. Expanding or combining logs without checking positivity can create expressions on a larger or smaller domain than the original. Absolute values are needed in several antiderivative identities. Chapter 10 · Logarithmic and Hyperbolic Functions
- Why should I enter exact numbers first?
- Exact fractions and symbolic constants preserve factorisation, cancellation and complete solution sets. Decimal input may trigger approximations and hide structure. Request a numerical value after the exact result when the task actually needs one. Chapter 11 · Maple and Mathematical Computing
How to study for the exam
Run algebra and calculus as two weekly tracks instead of finishing one before starting the other. For algebra, draw the object first, then translate it into vectors or a matrix. Verify projections by orthogonality, complex roots by count and spacing, systems by substitution, and inverses by multiplication. For calculus, write the definition or theorem conditions before using a rule.
Check one-sided limits, state continuity and differentiability intervals for the Mean Value Theorem, keep domain restrictions beside inverse functions, differentiate antiderivatives, and write limits for improper integrals. Use Maple after a hand setup to check exact algebra, plots and row reduction; never treat output as a replacement for interpretation.
Build a compact error log with four headings: wrong object, lost domain, sign or arithmetic, and missing conclusion. Rework only the flawed line before repeating the full problem. In the weeks before the final, alternate short retrieval drills with mixed written problems under time.
Allocate time in proportion to the paper's marks, preserve exact values until an approximation is requested, and reserve a closing check for parameters, theorem hypotheses, units and final sentences.
Your AI Mathematics tutor for DPST1013
Stuck on a hard DPST1013 question? Sia is AskSia’s AI Mathematics tutor — ask any DPST1013 Mathematics 1A question and get a clear, step-by-step explanation grounded in how the course is actually taught and assessed. Read this whole study guide free, then take your hardest questions to Sia.