P1-S6 roadmap
Learning Path
A P1-S6 roadmap from primary number sense to senior secondary exam readiness.
Transit legend
Hong Kong transit-style math roadmap
Colored Subway routes represent core math concepts. Each Subway station branches into its own bus route of related subconcepts students can study next.
Subway core concept
Bus detailed concept
6 Grade · 25 Topic
S1
Grade terminal
S1 · Secondary 1
Age 12–13 · Number sense, algebra foundations, angles, ratios
CompletedIn progressNot started
Subway S1-1
Integers
CompletedFoundation
mastery86%
Number line
BUS S11-A
Zero origin
Left/right direction
Compare positions
Directed numbers
BUS S11-B
Positive and negative
Absolute value
Ordering rules
Operations
BUS S11-C
Add/subtract signs
Multiply/divide signs
Brackets
Word problems
BUS S11-D
Temperature
Money and elevation
Reasonableness
Subway S1-2
Algebra Basics
In progressFoundation
mastery62%
Patterns
BUS S12-A
Term rules
Sequences
Input-output tables
Expressions
BUS S12-B
Variables
Like terms
Formulas
Substitution
BUS S12-C
Replace values
Order of operations
Check units
Simple equations
BUS S12-D
Balance model
Inverse operations
Self-checks
Subway S1-3
Angles
Not startedCore
mastery0%
Angle facts
BUS S13-A
Straight line
At a point
Vertically opposite
Parallel lines
BUS S13-B
Corresponding
Alternate
Interior
Polygons
BUS S13-C
Triangle sum
Exterior angles
Regular polygons
Diagrams
BUS S13-D
Label unknowns
Reason chains
Proof notes
Subway S1-4
Ratios
CompletedFoundation
mastery78%
Ratio language
BUS S14-A
Part-to-part
Part-to-whole
Simplify
Equivalent ratios
BUS S14-B
Scaling up
Scaling down
Ratio tables
Rates
BUS S14-C
Unit rate
Speed
Price per item
Scale
BUS S14-D
Map scale
Drawing scale
HK contexts
Subway S1-5
Statistics
Not startedCore
mastery0%
Data types
BUS S15-A
Categorical
Discrete
Continuous
Charts
BUS S15-B
Bar charts
Pie charts
Line graphs
Averages
BUS S15-C
Mean
Median
Mode
Variation
BUS S15-D
Range
Outliers
Compare groups
S2
Grade terminal
S2 · Secondary 2
Age 13–14 · Linear equations, coordinates, transformations
CompletedIn progressNot started
Subway S2-1
Linear Equations
CompletedCore
mastery82%
Balance model
BUS S21-A
Equal sign meaning
Do both sides
Visual checks
One-step
BUS S21-B
Add/subtract
Multiply/divide
Fractions
Two-step
BUS S21-C
Collect constants
Unknown first
Brackets
Applications
BUS S21-D
Word equations
Unknown choice
Check roots
Subway S2-2
Coordinates
In progressCore
mastery54%
Axes
BUS S22-A
Origin
Quadrants
Scale
Plot points
BUS S22-B
Ordered pairs
Grid accuracy
Read coordinates
Straight lines
BUS S22-C
Gradient idea
Intercepts
Line patterns
Transform grids
BUS S22-D
Image points
Vectors
Coordinate rules
Subway S2-3
Transformations
Not startedCore
mastery0%
Reflection
BUS S23-A
Mirror line
Equal distance
Image labels
Rotation
BUS S23-B
Centre
Angle
Direction
Translation
BUS S23-C
Vector
Move every point
Invariant shape
Enlargement
BUS S23-D
Scale factor
Centre
Similar figures
Subway S2-4
Probability
Not startedCore
mastery0%
Outcomes
BUS S24-A
Event language
Favourable cases
Impossible/certain
Sample space
BUS S24-B
Lists
Tables
Tree diagrams
Theoretical
BUS S24-C
Fractions
Equally likely
Complements
Simulation
BUS S24-D
Dice trials
Relative frequency
Compare results
S3
Grade terminal
S3 · Secondary 3
Age 14–15 · Polynomials, quadratics, trigonometry, circles
CompletedIn progressNot started
Subway S3-1
Polynomials
CompletedCore
mastery74%
Terms
BUS S31-A
Coefficients
Degree
Like terms
Expand
BUS S31-B
Single brackets
Double brackets
Identities
Factorize
BUS S31-C
Common factor
Grouping
Quadratic factors
Structure
BUS S31-D
Patterns
Check by expand
Equivalent forms
Subway S3-2
Quadratic Patterns
In progressChallenge
mastery49%
Tables
BUS S32-A
First differences
Second differences
Prediction
Graphs
BUS S32-B
Plotting
Scale
Intercepts
Parabolas
BUS S32-C
Vertex
Axis
Opening
Equations
BUS S32-D
Roots
Model choice
Interpret coefficients
Subway S3-3
Trigonometry Basics
Not startedChallenge
mastery0%
Right triangles
BUS S33-A
Hypotenuse
Opposite
Adjacent
Sine
BUS S33-B
SOH
Find side
Find angle
Cosine
BUS S33-C
CAH
Calculator mode
Applications
Tangent
BUS S33-D
TOA
Gradient link
Word problems
Subway S3-4
Circles
Not startedChallenge
mastery0%
Chords
BUS S34-A
Perpendicular bisector
Equal chords
Distance from centre
Tangents
BUS S34-B
Radius facts
Tangent lengths
Angle with radius
Arcs
BUS S34-C
Minor/major arcs
Sectors
Arc angles
Theorems
BUS S34-D
Cyclic angles
Proof setup
Diagram marks
S4
Grade terminal
S4 · Secondary 4
Age 15–16 · Functions, coordinate geometry, data handling
CompletedIn progressNot started
Subway S4-1
Functions
In progressCore
mastery58%
Input-output
BUS S41-A
Function machine
Mapping
Tables
Notation
BUS S41-B
f(x)
Domain
Range
Graphs
BUS S41-C
Intercepts
Turning points
Rate of change
Models
BUS S41-D
Linear
Quadratic
Real contexts
Subway S4-2
Coordinate Geometry
Not startedChallenge
mastery0%
Gradient
BUS S42-A
Rise/run
Parallel lines
Perpendicular
Distance
BUS S42-B
Pythagoras link
Segment length
Circle radius
Midpoint
BUS S42-C
Average coordinates
Bisectors
Medians
Line equations
BUS S42-D
Slope-intercept
Point-slope
Loci
Subway S4-3
More Algebra
Not startedChallenge
mastery0%
Identities
BUS S43-A
Expansion
Factor forms
Verification
Indices
BUS S43-B
Laws
Negative index
Fractional index
Fractions
BUS S43-C
Rational expressions
Restrictions
Simplify
Rearranging
BUS S43-D
Subject change
Cross multiply
Formula checks
Subway S4-4
Data Handling
CompletedCore
mastery81%
Distributions
BUS S44-A
Shape
Spread
Outliers
Charts
BUS S44-B
Box plots
Scatter
Histograms
Claims
BUS S44-C
Bias
Sample size
Misleading graphs
Interpretation
BUS S44-D
Context
Conclusion writing
Limitations
S5
Grade terminal
S5 · Secondary 5
Age 16–17 · Advanced functions, trigonometry, probability
CompletedIn progressNot started
Subway S5-1
Advanced Functions
In progressExam
mastery46%
Polynomial
BUS S51-A
Degree
End behavior
Roots
Exponential
BUS S51-B
Growth/decay
Parameters
Applications
Logarithmic
BUS S51-C
Inverse idea
Asymptotes
Laws
Compare models
BUS S51-D
Transformations
Fit to context
Limitations
Subway S5-2
Trigonometry
Not startedExam
mastery0%
Identities
BUS S52-A
Pythagorean
Compound angles
Double angles
Graphs
BUS S52-B
Amplitude
Period
Phase shift
Equations
BUS S52-C
Principal values
General solution
Intervals
Applications
BUS S52-D
Bearings
Heights
Modelling cycles
Subway S5-3
Probability
CompletedChallenge
mastery76%
Counting
BUS S53-A
Addition rule
Multiplication rule
Complements
Arrangement
BUS S53-B
Permutations
Combinations
Restrictions
Conditional
BUS S53-C
Given events
Venn diagrams
Bayes idea
Decision trees
BUS S53-D
Branches
Independent/dependent
Expected value
Subway S5-4
Differentiation Intro
Not startedExam
mastery0%
Gradient
BUS S54-A
Secants
Tangents
Rate of change
Limits
BUS S54-B
Approach value
First principles
Continuity idea
Derivative
BUS S54-C
Power rule
Notation
Higher derivatives
Tangent
BUS S54-D
Equation
Normal
Stationary points
S6
Grade terminal
S6 · Secondary 6
Age 17–18 · Calculus, statistics, mixed exam problem solving
CompletedIn progressNot started
Subway S6-1
Calculus
In progressExam
mastery51%
Derivatives
BUS S61-A
Rules
Optimization
Curve sketching
Integrals
BUS S61-B
Antiderivative
Definite area
Constants
Applications
BUS S61-C
Kinematics
Area
Rates
Exam synthesis
BUS S61-D
Mixed questions
Method choice
Mark allocation
Subway S6-2
Statistics
Not startedExam
mastery0%
Sampling
BUS S62-A
Random samples
Bias
Sample size
Normal curve
BUS S62-B
Z-score
Standardization
Percentiles
Estimation
BUS S62-C
Confidence
Margin of error
Hypothesis idea
Interpretation
BUS S62-D
Data summaries
Context
Uncertainty
Subway S6-3
Exam Revision
CompletedExam
mastery72%
Skill audit
BUS S63-A
Weak topics
Formula recall
Priority list
Timed sets
BUS S63-B
Pacing
Question choice
Accuracy check
Error log
BUS S63-C
Concept errors
Careless slips
Review cycle
Paper strategy
BUS S63-D
Mark schemes
Section timing
Final checks
Subway S6-4
Mixed Problem Solving
Not startedExam
mastery0%
Read problem
BUS S64-A
Known/unknown
Diagrams
Constraints
Choose tools
BUS S64-B
Algebra link
Geometry link
Data link
Multi-step plan
BUS S64-C
Subgoals
Assumptions
Sequencing
Reflect
BUS S64-D
Reasonableness
Alternative method
Communicate answer