IP Maths Notes (Lower Sec, Year 1-2): 00) Overview
Download printable cheat-sheet (CC-BY 4.0)15 Nov 2025, 00:00 Z
The lower-secondary phase of the Integrated Programme sets the algebraic, geometric, and statistical habits that feed every Year 3-4 and JC topic. This hub collects structured revision notes, worked drills, and reflection prompts so you can bridge from classroom discussion to exam-ready responses.
How to use these notes
- Read the Learning Targets table and tick off outcomes as you revise.
- Walk through every Worked Example before attempting the Try It Yourself set; the solutions model marking scheme precision.
- Track missteps in a reflection log — note whether they are algebraic slips, concept gaps, or presentation issues.
- Close each study block by sending yourself a WhatsApp summary of the topic; rehearsal in your own words matters for retention.
Topic sequence
| Post number | Focus area | Year | Key skills |
| 01 | Number Systems & Indices | Y1 | Convert between integers, fractions, decimals, and apply index laws without calculator prompts. |
| 02 | Algebraic Expressions & Equations | Y1 | Expand, factor, and rearrange linear equations and inequalities using structured line work. |
| 03 | Ratio, Rate & Percentage Reasoning | Y1 | Solve multi-step rate problems, percentage change chains, and mixture questions cleanly. |
| 04 | Coordinate Geometry & Graphs | Y1-Y2 | Interpret gradients, intercepts, and distance formulas in context. |
| 05 | Quadratic Expressions & Graph Sketching | Y2 | Complete the square, locate turning points, and link contexts to \( y = ax^2 + bx + c \). |
| 06 | Geometry, Congruency & Similarity | Y2 | Apply angle rules, triangle congruency tests, and similarity ratios with annotated diagrams. |
| 07 | Trigonometry in Right Triangles | Y2 | Execute \( \sin \), \( \cos \), and \( \tan \) workflows, including composite height-distance setups. |
| 08 | Mensuration & Circles | Y2 | Calculate arc lengths, sector areas, and surface-area/volume combinations. |
| 09 | Data Handling & Statistics | Y1-Y2 | Build frequency tables, compute averages, and justify graph choices. |
| 10 | Probability Models | Y2 | Build sample spaces, evaluate complementary events, and interpret tree diagrams. |
Bookmark the hub page at https://eclatinstitute.sg/blog/ip-maths-lower-sec-notes and jump into the next topic you need. When you are ready to bridge into Year 3, continue with the IP AMaths Notes.
Study cadence planner
| Week | Focus | Outcome |
| 1 | Posts 01-02 | Number sense and algebraic manipulation accuracy above 90% in workbook drills. |
| 2 | Posts 03-04 | Graph interpretation with annotated axes and clearly labelled gradient/intercept justifications. |
| 3 | Posts 05-06 | Quadratic sketching and geometry proofs without prompting notes. |
| 4 | Posts 07-08 | Confident trig flowcharts and mensuration formula recall. |
| 5 | Posts 09-10 | Statistic write-ups with full sentences and probability diagrams with clean branch labelling. |
Throughout the series we cross-link to anchor posts on tuition strategy, exam technique, and next steps so your revision map stays coherent.
