Paper 1
120 minutes
No calculator
Compulsory short- and extended-response questions with an emphasis on analytical methods, clear working and mathematical reasoning.
IB MATH AA HL · YEAR 5 & YEAR 6
IB Math tuition
in Singapore.
Tim Gan Math offers IB Mathematics: Analysis and Approaches Higher Level (AA HL) tuition for Year 5 and Year 6 students in Singapore. Learn with Mr Gan at Bukit Timah or join online, with structured notes, IB practice and TGM Study Hub access.
From S$110per two-hour lesson · Paid by term · Bukit Timah & online
Two hours to work it through
Learning continues after classA clearer path
through AA HL.
Year 5 & 6IB Diploma AA HL support
Mr Ganyour tutor for both year groups
In class + at homeone connected learning programme
Find your weekly class A WEEK AT TIM GAN MATH
The lesson is just
the beginning.
AA HL asks you to connect ideas and explain your reasoning. Our programme links your weekly lesson to the practice, explanations and support you need between classes.
01 / YOUR WEEKLY LESSON
Make sense of
the next step.
The move from Year 4 or IGCSE into AA HL can feel steep. Mr Gan starts with the underlying concepts, works through examples and helps you put the method into practice.
- Two-hour weekly lessons for Year 5 and Year 6
- Build foundations before tackling harder questions
- Attend at Bukit Timah or join online
2 hoursto ask.
to understand.
to understand.
A space to think. A tutor to ask. A fresh start every week.INSIDE TIM GAN MATH ↗
YOUR AA HL TOPIC MAP
Five connected areas.
One stronger foundation.
- 01Number & Algebra
- 02Functions
- 03Geometry & Trigonometry
- 04Statistics & Probability
- 05Calculus
Concept → worked example → independent practice
02 / FROM CLASS TO YOUR DESK
Build on what
you understand.
Structured notes connect each new concept to worked examples and practice. Revisit the reasoning after class, then use the AA HL syllabus outline to see how the topics fit together.
- Lesson notes and worked examples to revisit
- Coverage across all five AA HL topic areas
- A foundation for the step up from Year 4 to Year 5
03 / PRACTISE. REVIEW. UNDERSTAND.
Get unstuck.
Then try again.
Use the IB Mathematics question bank to practise a topic, check your approach and work through the steps that need another look. Video explanations and handwritten solutions help make revision more deliberate.
- Curated IB Mathematics practice questions
- Video and handwritten explanations
- Bring unresolved questions back to Mr Gan
04 / SUPPORT BETWEEN LESSONS
The support
comes home.
TGM Study Hub brings recorded lessons, handwritten solutions and worksheets together. Review at your own pace, then ask through WhatsApp or the online community when you need more guidance.
- Revisit recorded lessons and learning materials
- Use worksheets and solutions for targeted revision
- Stay connected through WhatsApp consultation
Study Hub resources are available while enrolled in the programme.
Meet your tutorYOUR IB MATH TUTOR
Your IB Math tutor: Mr Gan.
Mr Gan teaches both Year 5 and Year 6 AA HL classes. His approach begins with clear explanations and strong conceptual foundations, followed by practice that builds in difficulty.
- Ex-MOE educator · 18 years of teaching experience
- Postgraduate Diploma in Education (Mathematics), NIE
- Master of Science (Mathematics for Educators), NTU (NIE)
Mr GanIB Mathematics AA HL · Year 5 & Year 6THE BIG PICTURE
Your IB Math AA HL syllabus.
Five topic areas, from Number & Algebra to Calculus. Explore the full outline and assessment structure for 2026 examination sessions.
View syllabus
THE BIG PICTURE
Your IB Math AA HL syllabus.
Five topic areas, from Number & Algebra to Calculus. Explore the full outline and assessment structure for 2026 examination sessions.
How AA HL is assessed
Paper 2
120 minutes
Graphic display calculator required
Compulsory short- and extended-response questions. A GDC is required, although not every part needs technology.
Paper 3
60 minutes
Graphic display calculator required
Two compulsory extended-response problem-solving questions that assess sustained reasoning across the syllabus.
Internal Assessment
Individual exploration
Technology used where appropriate
A mathematical exploration in which students investigate a chosen topic and communicate their mathematics clearly.
Topic-by-topic outline
SL content is the shared foundation; AHL marks the additional Higher Level content. Hours shown are the syllabus teaching hours.
1Number & AlgebraSequences, financial mathematics, proof, logarithms, the binomial theorem, complex numbers and systems of equations.39 teaching hours
1.1 SL
Scientific notation
- Operations with numbers written as a × 10ᵏ
- Use 1 ≤ a < 10 with integer k and communicate an appropriate degree of accuracy
1.2 SL
Arithmetic sequences and series
- nth term: uₙ = u₁ + (n − 1)d
- Sum: Sₙ = n/2[2u₁ + (n − 1)d]
- Sigma notation and applications to modelling
1.3 SL
Geometric sequences and series
- nth term: uₙ = u₁rⁿ⁻¹
- Finite sum: Sₙ = u₁(rⁿ − 1)/(r − 1)
- Sigma notation and real-world applications
1.4 SL
Financial applications
- Compound interest and depreciation
- Use technology to solve problems involving loans, investments and repeated percentage change
1.5 SL
Integer exponents and logarithms
- Laws of exponents for integer powers
- Introduction to logarithms as inverse operations of exponentiation
- Solve simple exponential equations
1.6 SL
Simple deductive proof
- Numerical and algebraic proof
- Correct use of equality (=) and identity (≡)
- Present a logical chain from assumptions to conclusion
1.7 SL
Exponents and logarithms
- Laws of logarithms and rational exponents
- Change of base: logₐx = logᵦx/logᵦa
- Solve exponential equations using logarithms
1.8 SL
Infinite geometric sequences
- Recognise convergence when |r| < 1
- Infinite sum: S∞ = u₁/(1 − r)
1.9 SL
The binomial theorem
- Expand (a + b)ⁿ for positive integer n
- General term and binomial coefficients
- Pascal's triangle and technology
1.10 AHL
Counting principles and binomial extension
- Permutations and combinations
- Extend the binomial theorem to rational exponents
- Determine valid intervals of convergence
1.11 AHL
Partial fractions
- Decompose rational expressions with up to two distinct linear denominator factors
- Use decompositions for simplification and integration
1.12 AHL
Complex numbers
- Cartesian form z = a + bi and i² = −1
- Real and imaginary parts, conjugate, modulus and argument
- Represent complex numbers on an Argand diagram
1.13 AHL
Polar and exponential forms
- z = r(cos θ + i sin θ) = r cis θ
- Euler form z = reⁱᶿ
- Products, quotients and geometric interpretations
1.14 AHL
Complex roots and De Moivre's theorem
- Complex conjugate roots of polynomials with real coefficients
- Use De Moivre's theorem for integer and rational powers
- Find and represent roots of complex numbers
1.15 AHL
Proof methods
- Proof by mathematical induction
- Proof by contradiction
- Use counterexamples to disprove a statement
1.16 AHL
Systems of linear equations
- Solve systems with up to three equations and three unknowns
- Identify unique, infinite or no-solution cases
- Interpret solutions geometrically
Exam focusStudents commonly lose marks through imprecise algebra, missing restrictions and incomplete proof structure.
2FunctionsFunction notation, transformations, quadratics, exponentials, logarithms, polynomials, rational functions and inequalities.32 teaching hours
2.1 SL
Equations of a straight line
- Gradient, intercept and equation y = mx + c
- Parallel and perpendicular lines
- Use different forms of a line equation
2.2 SL
The concept of a function
- Domain, range and function notation
- Functions as mathematical models
- Inverse functions as reflections in y = x
2.3 SL
Graphs of functions
- Sketch y = f(x) from information or context
- Use technology to graph functions, sums and differences
2.4 SL
Key features of graphs
- Intercepts, extrema, asymptotes and symmetry
- Find intersections of curves using technology
- Interpret graph features in context
2.5 SL
Composite and inverse functions
- Composition: (f ∘ g)(x) = f(g(x))
- Identity and inverse functions
- Apply domain restrictions where needed
2.6 SL
Quadratic functions
- Standard, factorised and vertex forms
- Axis of symmetry, intercepts and vertex
- Move fluently between equivalent forms
2.7 SL
Quadratic equations and inequalities
- Factorisation, completing the square and the quadratic formula
- Discriminant Δ = b² − 4ac and nature of roots
- Solve quadratic inequalities
2.8 SL
Reciprocal and rational functions
- Graph f(x) = 1/x and recognise its self-inverse nature
- Analyse f(x) = (ax + b)/(cx + d)
- Vertical and horizontal asymptotes
2.9 SL
Exponential and logarithmic functions
- Graphs of aˣ, eˣ, logₐx and ln x
- Inverse relationships and key graph features
- Applications to growth and decay
2.10 SL
Solving equations
- Solve graphically and analytically
- Use technology appropriately
- Interpret solutions in real-life contexts
2.11 SL
Transformations of graphs
- Translations and reflections
- Vertical and horizontal stretches
- Composite transformations and their order
2.12 AHL
Polynomial functions
- Zeros, roots and factors
- Factor and remainder theorems
- Sum and product of roots
2.13 AHL
Advanced rational functions
- Analyse rational functions with linear or quadratic numerator and denominator
- Vertical, horizontal and oblique asymptotes
- Use division and algebra to expose graph structure
2.14 AHL
Odd, even and self-inverse functions
- Identify odd and even functions algebraically and graphically
- Find inverse functions with domain restrictions
- Recognise and verify self-inverse functions
2.15 AHL
Solutions of inequalities
- Solve g(x) ≥ f(x) graphically and analytically
- Use sign diagrams and critical values
- State complete solution sets
2.16 AHL
Modulus and transformed function graphs
- Graphs of |f(x)| and f(|x|)
- Transformations including 1/f(x), f(ax + b) and [f(x)]²
- Solve modulus equations and inequalities
Exam focusStudents need to connect algebraic, graphical and technological approaches while respecting domains and ranges.
3Geometry & TrigonometryTrigonometry, circular functions, identities, vectors, lines and planes in two and three dimensions.51 teaching hours
3.1 SL
Three-dimensional geometry
- Volume and surface area of common solids and combinations
- Angles between intersecting lines and between a line and a plane
3.2 SL
Non-right-angled trigonometry
- Sine rule and cosine rule
- Area of a triangle: A = ½ab sin C
- Use trigonometric ratios in context
3.3 SL
Applications of trigonometry
- Right- and non-right-angled problems
- Angles of elevation and depression
- Construct clear labelled diagrams from written information
3.4 SL
Radians, arcs and sectors
- Radian measure
- Arc length s = rθ
- Sector area A = ½r²θ
3.5 SL
Unit-circle definitions
- Define sine and cosine using the unit circle
- tan θ = sin θ/cos θ
- The ambiguous case of the sine rule
3.6 SL
Trigonometric identities
- sin²θ + cos²θ = 1
- Double-angle formulae for sine and cosine
- Use identities to simplify and prove results
3.7 SL
Circular functions
- Graphs, amplitude and period of sine, cosine and tangent
- Model with f(x) = a sin(bx + c) + d
- Interpret parameters and transformations
3.8 SL
Solving trigonometric equations
- Graphical and analytical solutions in finite intervals
- Equations reducible to quadratics in sin x, cos x or tan x
- Give all solutions in the stated interval
3.9 SL
Reciprocal and inverse trigonometric functions
- sec, cosec and cot definitions and identities
- arcsin, arccos and arctan
- Domains, ranges and graphs of inverse functions
3.10 AHL
Compound-angle identities
- Formulae for sin(A ± B), cos(A ± B) and tan(A ± B)
- Double-angle identity for tangent
- Derive and apply exact trigonometric results
3.11 AHL
Symmetry and trigonometric graphs
- Symmetry relationships such as sin(π − θ) = sin θ
- Use graph symmetry to transform and solve expressions
3.12 AHL
Vector concepts
- Position and displacement vectors in 2D and 3D
- Vector operations, magnitude and unit vectors
- Prove geometrical properties with vectors
3.13 AHL
Scalar product
- a · b = |a||b| cos θ
- Angles between vectors
- Conditions for perpendicular and parallel vectors
3.14 AHL
Vector equation of a line
- r = a + λb in two and three dimensions
- Parametric and Cartesian forms
- Angles between lines and kinematics applications
3.15 AHL
Lines in space
- Identify coincident, parallel, intersecting and skew lines
- Find and verify points of intersection
3.16 AHL
Vector product
- Compute and use v × w
- Geometric interpretation of |v × w|
- Find areas of parallelograms and triangles
3.17 AHL
Vector equations of a plane
- Parametric, normal and Cartesian forms
- Move between r = a + λb + μc, r · n = a · n and ax + by + cz = d
3.18 AHL
Intersections and angles in space
- Intersections involving lines and planes
- Angles between a line and a plane and between two planes
- Use normals and direction vectors correctly
Exam focusDiagrams, exact values, valid solution intervals and the geometry behind vector equations must be communicated precisely.
4Statistics & ProbabilityData analysis, probability, random variables, binomial and normal distributions, regression and Bayes' theorem.33 teaching hours
4.1 SL
Concepts of data
- Population, sample and random sample
- Discrete and continuous data
- Sampling bias, reliability and outliers
4.2 SL
Presentation of data
- Frequency distributions and histograms
- Cumulative-frequency graphs
- Median, quartiles, percentiles, IQR and box plots
4.3 SL
Summary statistics
- Mean, median, mode and modal class
- Variance, standard deviation, range and IQR
- Effects of linear changes to data
4.4 SL
Linear correlation and regression
- Scatter diagrams and Pearson's correlation coefficient r
- Least-squares regression line of y on x
- Interpret parameters and make sensible predictions
4.5 SL
Probability concepts
- Trials, outcomes, sample spaces and events
- Complementary events and expected frequency
- P(A) = n(A)/n(U) for equally likely outcomes
4.6 SL
Probability diagrams and rules
- Venn, tree and sample-space diagrams
- Combined and mutually exclusive events
- Conditional probability and independence
4.7 SL
Discrete random variables
- Construct and use probability distributions
- Expected value E(X) and applications
4.8 SL
Binomial distribution
- Model X ~ B(n, p)
- Calculate binomial probabilities
- Mean and variance of a binomial distribution
4.9 SL
Normal distribution
- Model X ~ N(μ, σ²)
- Normal and inverse-normal calculations
- Interpret probabilities using a labelled diagram
4.10 SL
Regression line of x on y
- Select the correct regression line for the required prediction
- Understand the limits of extrapolation
4.11 SL
Formal conditional probability
- P(A|B) = P(A ∩ B)/P(B)
- Tests and consequences of independence
4.12 SL
Standardising normal variables
- z = (x − μ)/σ
- Use z-values to find unknown means or standard deviations
- Inverse-normal calculations
4.13 AHL
Bayes' theorem
- Apply Bayes' theorem for up to three events
- Use conditional probability tables or trees
- Interpret posterior probabilities in context
4.14 AHL
Random variables and probability density functions
- Variance of discrete random variables
- Continuous random variables and probability density functions
- Mean, median, mode, variance and linear transformations
Exam focusStudents must distinguish association from causation, choose valid models and interpret calculator output in context.
5CalculusLimits, differentiation, integration, kinematics, differential equations, volumes of revolution and Maclaurin series.55 teaching hours
5.1 SL
Introduction to calculus
- Informal concept of a limit
- Derivative as gradient function and rate of change
- Connect numerical, graphical and algebraic representations
5.2 SL
Increasing and decreasing functions
- Interpret f′(x) > 0, f′(x) = 0 and f′(x) < 0
- Use derivative information to describe a graph
5.3 SL
Derivatives of polynomials
- Power rule for polynomial terms
- Differentiate sums and scalar multiples
- Find gradients and rates of change
5.4 SL
Tangents and normals
- Equations of tangent and normal lines at a point
- Use perpendicular-gradient relationships
5.5 SL
Introduction to integration
- Anti-differentiate polynomial functions
- Use a boundary condition to determine the constant
- Evaluate definite integrals with technology
5.6 SL
Derivatives of elementary functions
- Differentiate xⁿ, sin x, cos x, eˣ and ln x
- Chain, product and quotient rules
- Differentiate composite functions
5.7 SL
Second derivative
- Relate f, f′ and f″ graphically
- Interpret concavity and changes in gradient
5.8 SL
Maxima, minima and inflection
- Test stationary points
- Optimisation in context
- Points of inflection with zero or non-zero gradient
5.9 SL
Kinematics
- Displacement, velocity and acceleration
- Use differentiation and integration
- Calculate total distance travelled
5.10 SL
Indefinite integrals
- Integrate xⁿ, 1/x and eˣ
- Reverse chain rule and simple substitution
- Composites with linear functions
5.11 SL
Definite integrals and area
- Evaluate definite integrals analytically
- Areas between a curve and an axis
- Areas between two curves, including sign changes
5.12 AHL
Continuity and differentiability
- Limits, convergence and divergence
- Derivative from first principles
- Higher derivatives and continuity conditions
5.13 AHL
Evaluation of limits
- Indeterminate forms 0/0 and ∞/∞
- Use l'Hôpital's rule or Maclaurin series
- Repeated applications where appropriate
5.14 AHL
Implicit differentiation
- Differentiate relations defined implicitly
- Related rates of change
- Advanced optimisation problems
5.15 AHL
Special functions
- Derivatives of trigonometric, inverse-trigonometric, exponential and logarithmic functions
- Corresponding indefinite integrals
- Use partial fractions to rearrange integrands
5.16 AHL
Integration techniques
- Integration by substitution
- Integration by parts
- Repeated integration by parts
5.17 AHL
Areas and volumes
- Areas bounded by a curve and the y-axis
- Volumes of revolution about the x- or y-axis
- Set up correct limits and radii before integrating
5.18 AHL
Differential equations
- Euler's method for numerical solutions
- Separable, homogeneous and first-order linear equations
- Integrating factors and initial conditions
5.19 AHL
Maclaurin series
- Series for eˣ, sin x, cos x, ln(1 + x) and (1 + x)ᵖ
- Substitution, products, integration and differentiation of series
- Develop series from differential equations
Exam focusMethod marks depend on showing the correct calculus setup, interpreting results and justifying endpoints, extrema and constants.
Schools may teach the same content in different sequences. This outline follows the IB guide for 2026 examinations; the official guide remains the source for assessment requirements. Read the official IB guide (opens in a new tab)
ONE CONNECTED PROGRAMME
IB Math tuition fees.
Weekly teaching, structured materials and support between lessons, with clear fees for each year group.
At Tim Gan Math, we believe in honest, transparent pricing.
Term-based payments only – no hidden fees or surprise add-ons.
What you see is what you pay – regular lessons and materials are included.
Price Protection Guarantee – join in Year 5, keep the same rate through Year 6
Join a trial lesson – find out whether our teaching style suits your learning needs.
IB MATHEMATICS AA HL
Year 5
Build your AA HL foundations.
S$110per two-hour lesson · paid by term
Join in Year 5 and keep the S$110 lesson rate through the end of Year 6.
2026 term dates & fees
| Term & dates | Lessons | Fee (S$) |
|---|---|---|
| Term 126 Jan – 5 Apr | 9 | 990 |
| Term 26 Apr – 27 Jun | 12 | 1,320 |
| Term 328 Jun – 12 Sep | 11 | 1,210 |
| Term 413 Sep – 30 Nov | 11 | 1,210 |
IB MATHEMATICS AA HL
Year 6
Consolidate and prepare for the next exam.
S$120per two-hour lesson · paid by term
For students joining in Year 6. Year 6 classes start in November of Year 5.
2026 term dates & fees
| Term & dates | Lessons | Fee (S$) |
|---|---|---|
| Term 12 Jan – 5 Apr | 12 | 1,440 |
| Term 26 Apr – 27 Jun | 12 | 1,440 |
| Term 328 Jun – 12 Sep | 11 | 1,320 |
| Term 413 Sep – 10 Nov | 11 | 1,320 |
Included with your lessons
- Structured curriculum and teaching
- TGM Study Hub access
- IB Math question bank
- Comprehensive lesson notes
- Online community support
- WhatsApp consultation with instructors
We only accept term payment. Fees are fixed from Year 5 to Year 6 (if you join in Year 5, fees remain at $110/lesson until end of Year 6). Year 6 starts in November.
TRY A LESSON WITH MR GAN
Start with one lesson.
Choose your year group and preferred class. We will contact you to confirm availability and arrange your paid IB Math AA HL trial lesson.
Your IB Math classroom at Bukit Timah
Bukit Timah (King’s Arcade), near Tan Kah Kee MRT. Online attendance is also available.
Bukit Timah
King's Arcade, 559 Bukit Timah Rd, #03-01B, Singapore 269695
5 mins walk from Tan Kah Kee MRT
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One lesson at a time.
Meet Mr Gan, experience an AA HL lesson and see how the programme fits your learning needs.
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