DPST1012 Fundamentals of Mathematics B
The Complete Exam Bible · T3 2026DPST1012 Overview
- Term 3, 2026
- 6 units of credit
- Level 1 (Diploma)
- Delivered by UNSW College
- Weekly workshop and tutorial
A pre-calculus course on the way to Mathematics 1A
DPST1012 Fundamentals of Mathematics B is a Level 1 (Diploma) course worth 6 units of credit, taught in the UNSW College Diplomas of Science, Engineering and Computer Science and delivered by UNSW College on behalf of UNSW Sydney.
- Assessed by Online engagement, weekly entry quizzes, workshop and tutorial participation, two short tests and a final exam.
- Hardest step Choosing the method from the form of the question before calculating, then checking the answer against the domain.
- How to prepare Do the online lesson, the worksheet and one chapter of this guide before each workshop, and keep a running rule sheet.
How DPST1012 is assessed
| Component | Weight | Format |
|---|---|---|
| Online Engagement | 15% | Online activities (5%) and Maths Portfolio (10%); ongoing to Week 12; AI tools allowed in an assistive role |
| Workshop Entry Quiz · hurdle | 10% | Weekly Moodle quiz under exam conditions: 5 multiple-choice items, one attempt, 10 minutes |
| On-Campus Participation · hurdle | 25% | Workshops (20%) and tutorials (5%); best 7 of 10 of each count |
| Exams: Week 4 Test | 5% | 40 minutes, in person, paper-based; Assumed Knowledge and the first two topics |
| Exams: Week 8 Test | 5% | 40 minutes, in person, paper-based; Assumed Knowledge and the first five topics |
| Exams: Final Exam · hurdle | 40% | 2 hours, in person, paper-based, in the exam period; all topics; at least 40% required |
Weights are from the Term 3, 2026 course outline and total 100%; the three exam rows make up its 50% Exams task. To pass you need an overall mark of at least 50% and every hurdle: participation in at least 7 of the 10 assessable tutorials and 7 of the 10 assessable workshops with at least 7 of the 10 entry quizzes passed, and at least 40% in the final exam. The course outline's hurdle column also lists 70% for the quiz and participation rows, and the online engagement description asks for evidence of active participation throughout the term. The UNSW Handbook entry for DPST1012 shows a different breakdown (Assignment 15%, Midterm 25%, Board Tutorials 10%, Final Exam 50%); this guide follows the course outline for this offering, so check Moodle for any update.
Current DPST1012 dates
| Date | Item | Control |
|---|---|---|
| Week of 21 September 2026 | Week 4 Test | Assumed Knowledge and Topics 1 and 2; 40 minutes; 5%. |
| Week of 12 October 2026 | Flexibility Week | No classes. |
| Week of 19 October 2026 | Week 8 Test | Assumed Knowledge and Topics 1 to 5; 40 minutes; 5%. |
| Weeks of 23 November to 7 December 2026 | Study period and final exam | 2 hours, 40%, Topics 1 to 10 and Assumed Knowledge. |
Dates are as published in the Term 3, 2026 course program. Confirm exact deadlines and submission settings in the live LMS.
What DPST1012 covers
Twelve chapters follow the Term 3, 2026 program: the Assumed Knowledge week, functions and their models, polynomials, exponentials and logarithms, trigonometry, differentiation, integration, probability, distributions and statistics.
Sets, Intervals and Algebra Skills
Set notation, union and intersection, the addition and complement rules, interval notation and the algebra toolkitWhy the course starts with sets
The first week of Fundamentals of Mathematics B is labelled Assumed Knowledge, and the syllabus gives it four jobs: set notation, union and intersection, the addition and complement rules, and interval notation.
- Sets, elements and set-builder notation
- Subsets, the universal set and complements
- Union, intersection and disjoint sets
- Addition rule and complement rule
- Three-set survey counting
- Interval notation and rays
Functions, Domain, Range and Graphs
Functions as mappings, notation, domain and range, graphs of ordered pairs, interpolation and one-to-one functionsThe definition that decides everything
Week 2 opens the first topic, Functions, with a single definition: a function maps every element of an input set to exactly one element of an output set.
- A function as a mapping between two sets
- Numerical and non numerical inputs
- Function notation and y = f(x)
- Domain and range from tables and formulas
- Graphs as sets of ordered pairs
- Interpolation and extrapolation
Transformations and Combinations of Functions
Vertical and horizontal translations, sums, scalar multiples, compositions and reciprocals of functionsMoving a graph without redrawing it
The second half of the functions topic shows how new functions are built from old ones. A vertical translation adds a constant to the output, y = f(x) + c, and moves the graph up or down.
- Vertical translations y = f(x) + c
- Horizontal translations y = f(x − h)
- Combining a shift and a stretch
- Sum of functions and scalar multiples
- Composition f ∘ g and g ∘ f
- Reciprocal of a function
Function Models, Equations and Inequalities
Linear, wave and exponential models, residuals and limitations, and the equations f(x) = c and f(x) > cThree families of models
A worksheet in the functions topic introduces the three model families the course returns to all term. Linear functions f(x) = ax + b describe change at a constant rate, such as average height against age through childhood.
- Linear, trigonometric and exponential model forms
- Evaluating a fitted model and its error
- Limitations of a model outside its data
- Solving f(x) = c from a table
- Solving f(x) > c and double inequalities
- Solving from a continuous graph
Linear and Quadratic Polynomials
Polynomial features and degree, linear models, factorising, completing the square, the discriminant and parabola sketchesWhat counts as a polynomial
Week 3 begins the second topic, Polynomial Functions. A polynomial adds together whole-number powers of x, each with a real coefficient, so square roots of x and negative powers are excluded.
- Definition and features of a polynomial
- Degree of a product
- Domain and range by degree
- Linear models: rate of change and constant term
- Factorising quadratics
- Completing the square
Polynomial Division, Factor Theorem and Sketching
Long division, the division algorithm, remainder and factor theorems, end behaviour and root multiplicityDividing polynomials
Higher-degree polynomials appear when a parabola is not flexible enough; the course extends its Sydney temperature model from April to September into a cubic covering January to September.
- Long division of polynomials
- The division algorithm and remainder degree
- The remainder theorem
- The factor theorem and unknown coefficients
- Solving cubics with the four-step toolbox
- End behaviour from the leading term
Exponentials, Logarithms and Inverse Functions
Inverse functions, exponential and log graphs, log laws, exponential and log equations and inequalitiesWhere this topic sits
Topic 3 runs in Week 4, the same week as the first 40-minute test, and it is examined in the Week 8 test and the final exam.
- Exponential functions and their graphs
- Logarithms as inverse exponentials
- Finding an inverse function
- Laws of logarithms and change of base
- Solving exponential equations
- Solving logarithmic equations
Trigonometric Functions and the Unit Circle
Radians, the unit circle, exact values, identities, amplitude and period, and equations over a full revolutionFrom triangles to functions
Topic 4, in Week 5, turns trigonometry from triangle ratios into functions of any angle.
- Radian measure
- The unit circle definition of sine and cosine
- Right-angled triangle ratios
- Angles of any magnitude and reference angles
- Reciprocal functions and the Pythagorean identity
- Amplitude, period and wave transformations
Limits, Derivatives and Their Applications
Limits and continuity, first principles, differentiation rules, stationary points, concavity and optimisationLimits and the meaning of the derivative
Calculus begins in Week 6 with Topic 5, the introduction to differentiation, and continues in Week 8 with its applications; the Week 8 test covers the first five topics.
- Limits and continuity
- Limits at infinity and asymptotes
- First principles and the tangent gradient
- Product, quotient and chain rules
- Derivatives of trigonometric, exponential and log functions
- Stationary points and their classification
Integration and the Fundamental Theorem
Area estimates, antiderivatives, definite integrals, signed area, area between curves and accumulated changeArea as a limit
Topic 7, integral calculus, runs in Week 9 and is examined in the final exam.
- Rectangle estimates of area
- The definite integral
- Antiderivatives and the constant of integration
- The fundamental theorem of calculus
- Standard integrals
- Signed area and area below the axis
Probability, Counting and the Binomial Theorem
Probability rules, tree diagrams, conditional probability, independence, counting and binomial probabilityProbability as set language
Topic 8 runs in Week 10 and reuses the set language of the first week.
- Events as sets and Venn diagrams
- Addition and complement rules
- Tree diagrams and the multiplicative rule
- Conditional probability
- Testing for independence
- Permutations and combinations
Probability Distributions and Statistics
Discrete and binomial distributions, expected value and variance, the Normal distribution, correlation, regression and testingDistributions of random variables
Topic 9 in Week 11 describes random variables by their distributions, and Topic 10 in Week 12 adds statistics before revision.
- Discrete distributions as table, function and graph
- Expected value, variance and standard deviation
- Median and mode of a distribution
- The binomial distribution and skewness
- Continuous distributions and the PDF
- The Normal distribution and z-scores
Its course outline gives two aims: to prepare students who will study more mathematics for Mathematics 1A, and to give life-science students who will not a sufficient foundation for their degree.
The assumed knowledge is a pre-calculus course equivalent to NSW HSC Standard Mathematics.
What the term covers
The Term 3, 2026 program has an Assumed Knowledge week on sets and basic skills, then ten topics: functions, polynomial functions, exponential and logarithmic functions, trigonometric functions, an introduction to differentiation, applications of differentiation, integral calculus, probability, probability distributions, and statistics with exam revision.
Week 7 is Flexibility Week. The early topics are built around real data: menus and timetables for the idea of a function, Sydney temperatures for quadratic and cubic models, tides and population for wave and exponential models.
How it is taught
The course uses a flipped classroom.
Each week students work through interactive video lessons, online activities and worksheets before a 3-hour workshop, supported by an AI maths assistant called MA. Entry to the workshop begins with a short quiz, and the workshop is spent solving problems in groups and presenting working to the class.
A 1-hour tutorial consolidates the week, and students keep a Maths Portfolio of three worksheet problems per week, each marked with an emoji or a traffic-light rating plus a short comment on what they tried and what helped.
How this guide follows it
The twelve chapters follow the program in order.
Chapters 1 to 6 cover the Assumed Knowledge, functions and polynomials that the Week 4 test assesses; Chapters 7 to 9 add the topics in the Week 8 test; Chapters 10 to 12 complete the content of the final exam. Each chapter states the rules, works complete examples with every number shown, and ends with practice that has full answers. Integrated practice sets and an exam-morning review close the guide.
Worked example · free
When does the exponential population model reach 20 million?
- 1k = ln(6.946)/120 = 1.9382/120 ≈ 0.01615 per year.
- 1Set 3.7ek(t − 1900) = 20, so ek(t − 1900) = 20/3.7 ≈ 5.405.
- 1Take natural logs: k(t − 1900) = ln 5.405 ≈ 1.6874.
- 1t − 1900 = 1.6874/0.01615 ≈ 104.5, so the model reaches 20 million in about 2004.
Key terms
- Assumed Knowledge
- The Week 1 material on sets, intervals and basic algebra that every later topic relies on.
- Function Notation
- The way of writing a function as f : x ↦ f(x) or y = f(x), naming the output for each input.
- Polynomial
- An expression adding whole-number powers of x, each with a real coefficient, whose leading coefficient is not zero.
- Quadratic Formula
- The rule x = (−b ± √(b² − 4ac))/(2a) that solves any equation ax² + bx + c = 0 with real roots.
- Logarithmic Function
- The inverse of an exponential function, defined only for positive inputs.
- Trigonometric Identity
- An equation between trigonometric expressions that is true for every angle, such as sin²θ + cos²θ = 1.
- Second Derivative
- The derivative of the derivative, which describes concavity and classifies stationary points.
- Binomial Distribution
- The distribution of the number of successes in a fixed number of independent trials with equal success probability.
- Maths Portfolio
- The OneNote collection of three worksheet solutions per week that forms part of the online engagement mark.
- Workshop Entry Quiz
- The 10-minute, five-question Moodle quiz sat under exam conditions at the start of each workshop.
DPST1012 FAQ
How is the final mark made up in Term 3, 2026?
The course outline lists online engagement at 15%, the workshop entry quiz at 10%, on-campus participation at 25% and exams at 50%. The exams part splits into a Week 4 test and a Week 8 test at 5% each and a final exam worth 40%.
What are the hurdle requirements?
There are three in the assessment map: take part in at least 7 of the 10 assessable tutorials, take part in at least 7 of the 10 assessable workshops while passing at least 7 of the 10 entry quizzes, and score at least 40% in the final exam. An overall mark of 50% is also needed to pass.
Which topics do the Week 4 and Week 8 tests cover?
The Week 4 test covers the Assumed Knowledge and the first two topics, functions and polynomials. The Week 8 test covers the Assumed Knowledge and the first five topics, so it adds exponentials and logarithms, trigonometry and the introduction to differentiation.
What happens in the final exam?
It is a 2-hour, paper-based exam held in person during the exam period, worth 72 marks and 40% of the course. The course outline says its questions may involve unfamiliar problems, combined ideas and rigorous arguments, and the papers are not released afterwards.
Can I bring my own calculator?
No. A calculator is supplied for the tests and the exam and no other calculator or device is allowed. The course outline names a CASIO fx-82AU, while the assessment map names the fx-82AU PLUS II, so practise on that model.
Is a formula sheet given in the final exam?
The assessment map says a table of standard integrals and a normal distribution table are provided for the final exam. Other results, such as derivative rules, log laws and exact trigonometric values, have to be remembered.
Can generative AI be used on the assessments?
Only on online engagement, which is in the assistive category. The entry quizzes, the tests and the final exam are in the category where AI tools cannot be used, and using them there is treated as academic misconduct.
Which course comes after this one?
The course outline names Mathematics 1A, DPST1013, as the next step for students continuing in mathematics, and says that this course, together with Mathematics 1A and 1B, gives a foundation for later study in the physical sciences, computer science or engineering.
Questions students ask in each DPST1012 chapter
- Why does the addition rule subtract the intersection?
- Because adding the two group sizes counts every shared member twice, once in each group. Taking away the size of the overlap once leaves each member counted exactly one time, which is what the size of the union means. Chapter 01 · Sets, Intervals and Algebra Skills
- Can two different inputs give the same output?
- Yes, and the rule is still a function. A menu where two dishes cost the same price is a valid function. What is not allowed is a single input with two different outputs. Chapter 02 · Functions, Domain, Range and Graphs
- Why does f(x − 3) move a graph to the right and not the left?
- The new graph has to reach each old value three units later along the x-axis, because x − 3 only equals the old input when x is 3 larger. Arriving later means sitting further right on the axis. Chapter 03 · Transformations and Combinations of Functions
- Why do so many questions ask me to solve f(x) = c?
- Because most real questions take that form once the context is removed: when does the temperature reach 20 degrees, which months have a given rate, how long until a tank is empty. The course treats it as a core idea. Chapter 04 · Function Models, Equations and Inequalities
- Which method should I use to solve a quadratic?
- Try factorising when the leading coefficient is 1 and the numbers are small. Complete the square when you also want the vertex. Use the formula whenever the numbers are awkward, because it always works. Chapter 05 · Linear and Quadratic Polynomials
- When should I use long division instead of the remainder theorem?
- Use the remainder theorem when only the remainder or a yes-or-no factor test is needed. Use long division when you need the quotient, for example to reduce a cubic to a quadratic after finding one root. Chapter 06 · Polynomial Division, Factor Theorem and Sketching
- Why can a logarithm not take a negative input?
- Because a positive base raised to any real power is always positive, so no exponent produces a negative number or zero. The logarithm, which reverses that process, is therefore only defined for positive inputs. Chapter 07 · Exponentials, Logarithms and Inverse Functions
- Why does calculus need angles in radians?
- The simple derivative rules, such as the derivative of sin x being cos x, are only true when x is measured in radians. In degrees an extra conversion factor appears, so the course works in radians from this topic on. Chapter 08 · Trigonometric Functions and the Unit Circle
- Do I need to differentiate from first principles in exams?
- The syllabus lists the first-principles definition, so expect to use it on simple polynomials. Show the expansion, cancel the h, and only then let h approach zero; the rules are used for everything else. Chapter 09 · Limits, Derivatives and Their Applications
- Why does a definite integral not need + C?
- The constant appears in both F(b) and F(a) and cancels when one is subtracted from the other. Any antiderivative gives the same definite integral, so the simplest one, with C equal to zero, is used. Chapter 10 · Integration and the Fundamental Theorem
- What is the difference between mutually exclusive and independent?
- Mutually exclusive events cannot happen together, so their intersection is empty. Independent events can happen together, and one occurring does not change the chance of the other. Events with non-zero probabilities cannot be both. Chapter 11 · Probability, Counting and the Binomial Theorem
- Why is P(X = a) zero for a continuous variable?
- Probability for a continuous variable is area under the density curve, and the area above a single point has no width. So only intervals carry probability, and P(X < a) equals P(X ≤ a). Chapter 12 · Probability Distributions and Statistics
How to study for the exam
Work in the course's own rhythm: lesson and worksheet first, then the matching chapter here, then the practice cards without the answers. Keep one page of rules per topic and rewrite it from memory before each test. From Week 9 onwards, practise with a printed integrals table and normal table, because those are what you will have in the exam room.
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