Slide 1
Mathematics: analysis and approaches SL/HL
- IB Diploma Programme
- Australian International Academy, Strathfield
- Group
- Group 5 — Mathematics
- Level offered
- Standard Level (SL)
- Teaching hours
- SL: 150 hours
- IB syllabus
- Current DP syllabus, first examined 2021
Course description
Mathematics: analysis and approaches is designed for students who want to develop analytical expertise and a deep understanding of mathematical concepts, with a strong emphasis on constructing, communicating and justifying correct mathematical arguments. Students are encouraged to apply their knowledge to abstract problems as well as those set in meaningful real-world contexts.
The internally assessed mathematical exploration allows students to investigate an area of mathematics of personal interest, developing independence in mathematical learning.
Course structure
- Number and Algebra
- Functions
- Geometry and Trigonometry
- Statistics and Probability
- Calculus
- Mathematical exploration: an individual investigation into an area of mathematics
Students who should consider this course
This course suits students who enjoy mathematics for its own sake and who are considering further study in mathematics, engineering, physical sciences, economics or other fields that draw on calculus-based analytical methods.
Assessment at a glance
| Component | SL % | HL % |
|---|---|---|
| Paper 1 — No technology allowed (external) | 40 | 30 |
| Paper 2 — Technology allowed (external) | 40 | 30 |
| Paper 3 — Extended problem-solving, technology allowed (external, HL only) | — | 20 |
| Mathematical exploration (internal) | 20 | 20 |
External examinations
External assessment is sat in the November session and comprises two written papers at SL, and three at HL, including one extended-response, technology-based problem-solving paper unique to HL.
Subject presentation
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DP Mathematics: analysis and approaches SL/HL — subject presentation (Mathematics Faculty).
Text transcript of the slides (9 slides)
Slide 2
Background
- The DP was established to provide students with a balanced education, facilitate geographic and cultural mobility, and promote international understanding.
- Students explore the nature of knowledge through the mathematical exploration, Theory of Knowledge and the Extended Essay.
Slide 3
Curriculum model overview — teaching hours (SL / HL)
- Number and algebra — 19 / 39
- Functions — 21 / 32
- Geometry and trigonometry — 25 / 51
- Statistics and probability — 27 / 33
- Calculus — 28 / 55
- Internal assessment (exploration) — 30 / 30
- Total — 150 / 240 hours
Slide 4
Syllabus components
- Number and algebra — sequences and series (arithmetic, geometric, infinite series, sigma notation); exponents and logarithms; counting principles, permutations and combinations; the binomial theorem and proof.
- Functions — creating and examining graphs of linear and non-linear relationships.
- Geometry and trigonometry — algebraic and graphical methods for trigonometric equations, identities and factorisation; trigonometry as a model of real-life situations in two and three dimensions.
- Statistics and probability — combined, mutually exclusive, conditional and independent events; discrete random variables and expected value; binomial and normal distributions, z-scores.
- Calculus — related rates, implicit differentiation, optimisation, points of inflection, graphs of f, f′ and f″; integration as anti-differentiation with boundary conditions.
- Internal assessment — students explore, generate hypotheses and ask questions as active learners of mathematics.
Slide 5
Assessment model
- Problem-solving is central to learning mathematics and involves the acquisition of skills and concepts in a wide range of situations, including non-routine, open-ended and real-world problems.
- Inquiry approaches · reasoning · technology · problem-solving · knowledge and understanding · communication and interpretation.
Slide 6
Student assessment throughout the Diploma
- Paper 1 — no technology; Section A short-response and Section B extended-response questions — 90 min SL / 120 min HL — 40% SL / 30% HL.
- Paper 2 — technology allowed; Section A short-response and Section B extended-response questions — 90 min SL / 120 min HL — 40% SL / 30% HL.
- Paper 3 (HL only) — technology allowed; two compulsory extended-response problem-solving questions — 60 min — 20%.
- Internal — the exploration — 30 hours — 20%.
Slide 7
Graphics calculator
- A graphical display calculator is required — TI-84 Plus.
Slide 8
Resources
- Books: Oxford Publications.
- Graphical Display Calculator (TI-84 Plus); Desmos, Wolfram, Excel and GeoGebra.
- Websites: mathforum.org, nrich.maths.org, mrbartonmaths.com, illuminations.nctm.org, mathcentre.ac.uk, Revision Village, InThinking.
- IA assessment criteria; past papers and markschemes.
Slide 9
Questions — thank you
- Speak to the Mathematics Faculty with any questions.