IP AMaths Notes (Upper Sec, Year 3-4): 00) Overview

Study guide08 Nov 2025, 00:00 ZUpdated 17 Jul 2026

Eclat's Upper Secondary IP Additional Mathematics map, with quick links to every topic recap and clear national-comparator boundaries.

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For Integrated Programme students: Your current school materials, teacher instructions, and assessment scope take precedence because IP topic sequence and depth vary by school. This is an Eclat IP guide, not the O-Level / SEC G3 exam-track guide.

How this chapter applies

Eclat core: the 20 numbered chapters form Eclat's current upper-secondary IP A-Math route, with official topics split into smaller teaching units where that improves practice.
School-sensitive extension: Modulus Functions and Standard Deviation are retained as explicit school-sensitive or pathway extensions rather than being presented as K341 core.
2027 national comparison: K341 has 10 official top-level topics. Eclat separates these into more chapters, including Linear Law as the owner for K341 G2.5 and Kinematics as the owner for K341 C1.18.
Check your school: use the current scheme of work to decide chapter order, extension coverage, calculator conventions, and assessment depth.
Exam-track route: use the separate O-Level and SEC G3 Additional Mathematics notes for K341 topic ownership.

Q: What does IP AMaths Notes (Upper Sec, Year 3-4): 00) Overview cover?
A: Syllabus map for Upper Secondary Additional Mathematics with quick links to every topic recap.

Preparing for IP Additional Mathematics means stitching algebra, calculus, trigonometry, and applied modelling into one coherent toolkit. Use this index to decide which note you need today.

The 20-chapter structure is a teaching sequence, not a claim that K341 has 20 official topics. The 2027 national syllabus has 10 top-level topics. Eclat splits those topics into smaller chapters where students benefit from focused practice. Linear Law belongs to K341 Topic G2.5, Partial Fractions belongs to Topic A4, and Kinematics belongs to Topic C1.18. Modulus Functions and Standard Deviation remain clearly labelled IP extensions rather than K341 core.

Keep the full topic roadmap handy via our IP Maths tuition hub so you can jump into related drills, quizzes, or diagnostics as you move through these notes.

New to the Integrated Programme? Start with What is IP? | Browse all free IP notes.

The core idea is simple: IP AMaths is a toolkit: algebra, graphs, trigonometry, calculus, and modelling.

Use it as a working check: Use this page as the routing map. Pick the weak topic, open that note, do the worked example, then attempt the Try This prompt.

Reviewed by

Marcus Pang·Managing Director (Maths)

Sequence	Focus area	Quick reminder
01	Indices and Surds	Laws of indices, rationalising denominators.
02	Logarithms and Exponentials	Change of base, solving exponential models.
03	Linear Law	Straight-line fitting, gradients from data.
04	Simultaneous Equations	Graphical and algebraic solutions.
05	Quadratic Functions	Completing the square, discriminant analysis.
06	Coordinate Geometry (Lines)	Distance, midpoint, gradient, normal form.
07	Parabolas and Circles	Standard forms and locus interpretation.
08	Plane Geometry	Angle chasing with algebraic lengths.
09	Polynomials	Factor and remainder theorems, root bounds.
10	Binomial Theorem	General term, approximation via first terms.
11	Modulus Functions	Piecewise forms, modulus inequalities.
12	Trigonometry I	Radian measure, core identities.
13	Trigonometry II	Trig equations, auxiliary angle.
14	Differentiation Fundamentals	First principles, power rule.
15	Differentiation Techniques	Product, quotient, chain, implicit.
16	Applications of Differentiation	Tangents, normals, rates of change.
17	Integration Essentials	Reverse power rule, substitution.
18	Partial Fractions	Decomposition, repeated factors.
19	Kinematics	Displacement, velocity, acceleration from calculus.
20	Standard Deviation	Comparing spread across data sets where your school includes it.

If the prompt shows...	First move	Likely next note	Common trap
Logarithms or exponentials with unknowns	State the domain, then convert to an algebraic equation.	02 Logarithms and Exponentials, then 05 Quadratic Functions	Solving the quadratic first and forgetting to reject invalid roots.
A curve plus a tangent or normal	Differentiate before substituting the point.	14 Differentiation Fundamentals, then 16 Applications of Differentiation	Using a secant gradient as if it were the tangent gradient.
Trig expressions with angles in different forms	Convert all angles to the same unit and choose one identity family.	12 Trigonometry I, then 13 Trigonometry II	Mixing degrees and radians in the same line of working.
Motion described by $s$ , $v$ , or $a$	Decide whether to differentiate or integrate from the quantity given.	19 Kinematics, then 14 or 17 as needed	Treating velocity and displacement as interchangeable.

IP AMaths Notes (Upper Sec, Year 3-4): 00) Overview

How this chapter applies

Sources

1 How to use these notes

2 Topic map

Mixed-topic first-move checkpoint

3 Worked example - Mixed-topic practice circuit

4 Practice Quiz

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