UniGeniusQCE Maths Methods

QCE Maths Methods

What is in QCE Maths Methods Units 3 and 4

Ten topics in two units. Unit 3 is further calculus and an introduction to statistics; Unit 4 is further calculus, trigonometry and statistics. Both papers of the external examination can test all of Units 3 and 4.

Weeks before the external examination
Hours a week for Maths Methods
Calculus
Trigonometry
Statistics

26 weeks, 104 hours in all

Start with Calculus

48 of your hours. It is 5 of the 10 units in the course, 50%.

Hours per area
AreaYour hoursShare of the course
Calculus4850%
Statistics38.440%
Trigonometry9.610%

Week by week

  1. Week 1Calculus
  2. Week 2Calculus
  3. Week 3Calculus
  4. Week 4Calculus
  5. Week 5Calculus
  6. Week 6Calculus
  7. Week 7Calculus
  8. Week 8Calculus
  9. Week 9Calculus
  10. Week 10Calculus
  11. Week 11Calculus
  12. Week 12Calculus
  13. Week 13Statistics
  14. Week 14Statistics
  15. Week 15Statistics
  16. Week 16Statistics
  17. Week 17Statistics
  18. Week 18Statistics
  19. Week 19Statistics
  20. Week 20Statistics
  21. Week 21Statistics
  22. Week 22Statistics, Trigonometry
  23. Week 23Trigonometry
  24. Week 24Trigonometry
  25. Week 25Timed paper 1 (Paper 1 style, technology-free), then review every lost mark
  26. Week 26Timed paper 2 (Paper 2 style, technology-active), then review every lost mark

Check your units with the free test

External assessmentOne examination worth 50%, set and marked by the QCAA
Paper 1Technology-free, 25%: short response and multiple choice
Paper 2Technology-active, 25%: short response and multiple choice
Time5 minutes perusal and 90 minutes working time for each paper; the formula book is provided
Internal assessmentSet by your school: a modelling task 20%, two short response examinations 15% each

Unit 3: Further calculus and introduction to statistics

  • Differentiation of exponential and logarithmic functions: e, ln(x), their inverse relationship and their derivatives.
  • Differentiation of trigonometric functions and the chain, product and quotient rules.
  • Further applications of differentiation: the second derivative, concavity, points of inflection and optimisation.
  • Introduction to integration, and discrete random variables, Bernoulli and binomial distributions.

Unit 4: Further calculus, trigonometry and statistics

  • Further integration: the fundamental theorem, areas under and between curves, the trapezoidal rule and total change.
  • Trigonometry: the sine rule with the ambiguous case, the cosine rule, the area formula and problems in two and three dimensions.
  • Continuous random variables and the normal distribution, including z-scores and quantiles.
  • Sampling and sample proportions, and approximate confidence intervals for a population proportion.

How this course maps the syllabus

The course gives each of the ten topics its own unit, plus a unit on the external examination. Each has a lesson, multiple choice questions and short response questions in the style of both papers. Internal assessment is set by your school, so the course describes it but does not practise it. Set the planner above with the weeks you have and how sure you are of each area, and it splits your hours.

Try 3 questions

  1. Paper 1 · Multiple choice · 1 mark · Calculus of exponential and logarithmic functions

    If y=ex2−3xy = e^{x^{2} - 3 x}, then dydx\dfrac{dy}{dx} is
    Answer it, every step marked

  2. Paper 1 · Short response · 4 marks · Calculus of exponential and logarithmic functions

    Answer each part without technology.
    Answer it, every step marked

  3. Paper 2 · Multiple choice · 1 mark · Calculus of exponential and logarithmic functions

    The table shows values of ah−1h\dfrac{a^{h} - 1}{h} for h=0.0001h = 0.0001, correct to four decimal places. a2.52.72.83.0ah−1h0.91630.99331.02971.0987\begin{array}{c|cccc} a & 2.5 & 2.7 & 2.8 & 3.0 \\ \hline \dfrac{a^{h} - 1}{h} & 0.9163 & 0.9933 & 1.0297 & 1.0987 \end{array} Based on the table, which interval contains the value of aa for which lim⁡h→0ah−1h=1\displaystyle\lim_{h \to 0} \dfrac{a^{h} - 1}{h} = 1?
    Answer it, every step marked

Next step

Take the free testTake the course tour

Questions people ask

What is the external examination worth?

50%. It has two papers, Paper 1 (technology-free) and Paper 2 (technology-active), each worth 25%. Internal assessment set by your school makes up the other 50%.

Which syllabus does the course follow?

The QCAA Mathematical Methods 2025 syllabus (version 1.3), Units 3 and 4.

Does this course cover Specialist Mathematics?

No. It is built for Mathematical Methods only.