DPST1013 Mathematics 1A
The Complete Exam Bible · T2 2026DPST1013 Overview
- UNSW College
- Term 2, 2026
- Level 1 (Diploma)
- 6 units of credit
DPST1013 Mathematics 1A develops the algebra and calculus used to describe geometry, solve equations and justify mathematical conclusions. This guide follows the Term 2, 2026 offering delivered by UNSW College, with the course also identified as MTHS1313 in its teaching materials.
- Algebra route Translate vectors and equations into geometric statements.
- Calculus habit Check the interval and hypotheses before choosing a theorem.
- Computing check Compare exact Maple results with a hand calculation.
- Assessment action Reconcile the Handbook and T2 outline schedules with the course team.
How DPST1013 is assessed
| 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. |
The table follows the 2026 UNSW Handbook. The Term 2, 2026 course outline differs: In Class Homework 5%, Maple Lab Test 5%, Online computing tutorials 10%, Assignment 5%, Mid Term 25%, Final Exam 50%, also totalling 100%. These are conflicting published schedules, not extra components to add together. Confirm which schedule governs your enrolment in Moodle with the course team. The T2 outline explicitly requires at least 50% overall and 15/30 in In-Class Homework, and calls that homework a hurdle for attending the final exam, although its schedule's hurdle column says n/a. That explicit pass condition should not be discarded because of the table label. The outline also expects attendance at least 80% of classes.
Current DPST1013 dates
| Date | Item | Control |
|---|---|---|
| 23 June 2026, 16:00 | Assignment submission | Term 2 submission page deadline; confirm task settings in Moodle. |
| 20 July 2026, 23:59 | Maple Lab Test booking cutoff | Term 2 syllabus booking instruction. |
| 22 July 2026 | Maple Lab Test | Term 2 syllabus: choose an available 40-minute session. |
Dates are as published in the Term 2, 2026 syllabus and assignment submission page. Confirm exact deadlines and submission settings in the live LMS.
What DPST1013 covers
Follow the algebra sequence from vectors to matrices, the calculus sequence from functions to integration, and the computing tools that support both.
Vectors, Lines and Planes
Displacement, vector equations, spanning directions and geometric membership02Vector Geometry and Projections
Dot products, orthogonality, projections, cross products and distances03Complex Numbers and Polynomial Roots
Cartesian and polar arithmetic, powers, roots and polynomial factorisation04Linear Systems and Gaussian Elimination
Elementary row operations, echelon form, consistency and free variables05Matrices, Inverses and Determinants
Matrix arithmetic, transposes, invertibility and determinant properties06Functions, Limits and Continuity
Domains, inequalities, limit laws, continuity and existence theorems07Differentiation and the Mean Value Theorem
Derivative rules, implicit differentiation, rates and theorem conditions08Inverse Functions and Curve Sketching
Restricted inverses, inverse trigonometry, parametric and polar curves09Integration and Improper Integrals
Riemann sums, fundamental theorems, substitution, parts and convergence10Logarithmic and Hyperbolic Functions
Logarithms, exponentials, hyperbolic identities and inverse substitutions11Maple and Mathematical Computing
Expressions, functions, exact computation, plots and linear algebra commandsThe algebra strand starts with vectors as directed quantities and builds towards lines, planes and geometric calculations. Dot products turn angles and orthogonality into arithmetic; projections isolate a component along a direction; cross products produce perpendicular vectors and areas. Complex numbers extend arithmetic beyond the real line, connecting Cartesian coordinates with modulus and argument.
Their polar representation makes powers and roots manageable, while polynomial factorisation explains why conjugate roots matter for real coefficients. Linear systems then introduce row operations, echelon form and the distinction between inconsistent equations and equations with free variables. Matrix arithmetic, inverses and determinants complete that sequence. Calculus asks a different set of questions about functions.
A domain describes which inputs are legal, a limit describes nearby behaviour, and continuity connects nearby behaviour with the actual function value. Differentiation measures local change, while the mean value theorem relates that local rate to change across an interval.
Inverse functions require attention to restricted domains and ranges; curve sketching combines those restrictions with intercepts, asymptotes and derivative signs. Integration brings together accumulated quantities, antiderivatives and carefully stated convergence for improper integrals. Logarithmic, exponential and hyperbolic functions extend the range of problems that can be expressed and solved.
Maple runs alongside the handwritten work. A computer algebra result is useful only when you know what expression was entered, which variables were assigned and which domain assumptions were intended. The computing chapter therefore distinguishes an expression from a function, an exact result from a decimal approximation, and a plotted suggestion from an algebraic proof.
A clean worksheet records the problem, the commands and a mathematical interpretation of the output. Use the chapter sequence to connect these strands instead of treating each calculation as an isolated trick. A plane equation is also a linear equation; a tangent calculation uses a limit; the integral of a derivative must respect the interval on which the function is defined.
Each worked solution makes those connections explicit and the practice questions use original values so that you must reconstruct the method. Assessment information below separates the published Handbook record from the different T2 course-outline record. Keep those attributions when discussing the weights with your course team.
A stationary value and accumulated area
- 2Differentiate the polynomial: f′(x)=2x-4. Solving f′(x)=0 gives x=2. The candidate lies at the right endpoint of the stated interval; an endpoint is still relevant to an absolute minimum even though the interior derivative test alone is not an endpoint classification.
- 1Complete the square: f(x)=(x-2)²+3. The squared term is nonnegative, and it vanishes at x=2, so the minimum is f(2)=3. This also proves positivity throughout the interval, without relying only on the sketch.
- 2An antiderivative is F(x)=x³/3-2x²+7x. Evaluate F(2)-F(0)=8/3-8+14=26/3. Keep the fraction exact; the integral is approximately 8.667 square units if the axes use consistent length units.
- 1Because f stays above the horizontal axis, the signed integral equals the geometric area under the curve on [0,2]. The minimum height times interval length gives a lower bound of 3×2=6, consistent with the computed 26/3.
Key terms
- Span
- The span of a collection of vectors is the set of all their linear combinations. It describes the positions reachable by scaling and adding the supplied directions. A plane through the origin can be described by two nonparallel spanning vectors; the origin remains included because all coefficients may be zero.
- Projection
- A projection is the component of a vector along a specified nonzero direction. The vector projection of a onto b is ((a dot b)/(b dot b))b. Subtracting that component from a leaves a perpendicular residual, which gives a useful check on distance calculations.
- Complex conjugate
- The complex conjugate of a+bi is a-bi. Conjugation reflects the point in the real axis, and multiplying a complex number by its conjugate gives its squared modulus. This real product is what allows division to be rewritten without an imaginary denominator.
- Pivot
- A pivot is a leading nonzero entry used to organise a row of an echelon system. Pivot columns identify constrained variables, while nonpivot columns may supply free variables. An augmented row with zero coefficients and a nonzero right side signals inconsistency rather than an extra pivot variable.
- Continuity
- Continuity at a point means that the function is defined there and its limit at that point equals the function value. A graph can approach a perfectly good limiting height while still failing continuity because the point is missing or assigned a different value.
- Derivative
- A derivative is the limit of a difference quotient when that limit exists. It measures the slope of the tangent and the instantaneous rate of change. The derivative belongs to a function on a specified domain, so endpoint conventions and points of nondifferentiability require separate attention.
- Antiderivative
- An antiderivative of f is a function whose derivative equals f on the interval being considered. On a connected interval, antiderivatives differ by a constant. Finding one does not by itself establish convergence of an improper integral; the endpoint limit still has to exist.
- Hyperbolic cosine
- Hyperbolic cosine is defined by cosh x=(e^x+e^(-x))/2. Together with hyperbolic sine, it satisfies cosh squared x minus sinh squared x equals one. The sign in that identity distinguishes it from the familiar circular trigonometric identity and affects substitutions and simplification.
- Exact arithmetic
- Exact arithmetic retains symbolic values such as rational numbers and radicals instead of replacing them immediately with decimal approximations. In Maple this distinction helps preserve cancellations and structural identities. Decimal evaluation is useful for interpretation after the exact expression and its assumptions have been checked.
DPST1013 FAQ
Which assessment weights should I use when the Handbook and outline differ?
Treat them as two attributed records. The 2026 Handbook lists a 60% final examination, 10% Maple tests and 30% In Class Tests. Your Term 2 outline instead specifies homework, computing tutorials, a Maple test, an assignment, a midterm and a final exam with weights 5%, 10%, 5%, 5%, 25% and 50%. Neither list can be blended with the other.
Ask the course team through Moodle to identify the schedule applicable to your enrolment before calculating a target final mark.
What is the homework hurdle in the Term 2 outline?
The narrative requirements say that In-Class Homework is a hurdle: at least 15/30 is needed to attend the final exam. The pass statement also requires that homework result together with an overall mark of at least 50%. Although the assessment schedule labels its hurdle column n/a, that table label does not remove the explicit prose condition.
Check your recorded homework total while there is still time to address a missing result, and ask about the discrepancy rather than assuming the hurdle disappears.
How do algebra and calculus connect in revision?
Choose a relationship rather than memorising two separate lists. Solving simultaneous equations can locate an intersection that you then interpret geometrically. Differentiation gives the direction of a tangent, and integration accumulates a changing quantity over an interval. Both strands demand a domain or an admissible set before calculations begin.
When revising, finish a numerical solution with a statement identifying whether the answer is a point, vector, family of solutions, slope or accumulated quantity. That final identification often exposes a method applied to the wrong object.
How much should I rely on Maple output?
Use Maple to check and explore a result after you have identified the mathematical operation and its assumptions. Retain exact values until approximation is needed, distinguish equality from assignment, and keep expressions separate from functions. A graph may suggest a root or an asymptote, but the plotting window and numerical sampling do not prove the conclusion.
Compare the output with a hand calculation or substitute a proposed solution into the original equation. The computing work is part of the course, so learn the commands as well as the interpretation.
What does a complete theorem-based answer contain?
Name the relevant theorem, verify each hypothesis on the specified interval, and then state the conclusion with the correct quantifier. For an intermediate value argument, continuity and values on opposite sides of the target establish existence, but they do not automatically establish uniqueness. For the mean value theorem, differentiability in the interior accompanies continuity on the closed interval.
A formula written without its hypotheses may look familiar yet fail to justify the actual step. Keep the domain and interval visible while you reason.
Can I use AI or a calculator during assessment?
The T2 outline distinguishes preparation from assessment conduct. The assignment is classified as AI Category 1, so AI tools cannot be used for it. Exam preparation is described as assistive use, but the exam instructions prohibit AI, notes and communication during the paper-based examinations. The specific materials list permits the Casio fx-82AU II 2nd Edition calculator for In-Class Homework and the final exam.
Do not extend that permission to another task or device; follow the current task instructions and ask the course team if the broad and specific wording leaves a doubt.
How can I practise without memorising a worked answer?
Start with a blank page and record only the given quantities and what must be found. Choose a method, work through it, then compare your reasoning with the answer. Change a coefficient or an interval and predict which features of the solution should change before calculating again.
For a projection, the residual should remain perpendicular; for a derivative, a sign chart should agree with the claimed monotonicity; for an integral, differentiating a proposed primitive should recover the integrand. These checks train transferable mathematical judgement rather than recognition of a familiar number.
How to study for the exam
Begin a revision session with one small diagnostic calculation from each strand. A vector membership problem reveals whether coefficients and coordinates are being kept separate; a short limit or derivative reveals whether algebraic simplification and domain restrictions are secure. Work without the answer visible.
When an error appears, classify its cause before repeating the question: a wrong operation, a sign reversal, a missing condition, or an arithmetic slip needs a different repair. Build the algebra sequence around geometric meaning. Draw the vectors or equations before row reduction when a picture is available. After eliminating variables, translate the echelon form back into a statement about intersections or free directions.
In complex arithmetic, keep modulus and argument separate until they are combined in polar form; after taking roots, count distinct arguments over a full turn. For matrices, check dimensions before multiplying and distinguish the existence of an inverse from a method for computing one. Organise calculus around the question being answered.
Existence may call for continuity and an intermediate value argument; uniqueness may need monotonicity. A tangent asks for a derivative at a point, whereas accumulated change asks for an integral across an interval. Before applying a named theorem, underline the domain, endpoints and differentiability assumptions.
For improper integrals, write the limiting expression before evaluating an antiderivative, because a finite-looking substitution can conceal divergence. Reserve a separate computing pass for Maple. Re-enter a short calculation in a clean worksheet, explain the role of each command, and compare exact and numerical results. Keep assignment work within its published AI restrictions.
Use any permitted tutoring to understand a method on independent practice, then return to your own working. As the assessments approach, reconcile the published weighting conflict with your course team rather than basing a target grade on an assumed schedule. Finish mathematical answers by checking the result in the original problem and stating the interval, direction or solution set to which it applies.
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