Lesson Notes
Basic addition and subtraction
Understanding the basic concepts of addition and subtraction
View NotesAddition and subtraction (I)
Performing addition of two numbers (at most two digits, possibly with carry)
View NotesInquiry and investigation
Discovering and constructing mathematical knowledge through inquiry
View NotesPictograms
Creating and interpreting simple pictorial graphs
3-digit numbers
Recognise 3-digit numbers (count, read, write, odd/even)
Addition and subtraction (II)
Perform addition of not more than three numbers (each up to 3 digits, with carry)
Basic multiplication
Recognise the basic concept of multiplication
4-digit numbers
Recognise 4-digit numbers (count, read, write, odd/even)
Addition and subtraction (III)
Perform subtraction of two numbers (up to 3 digits, with borrowing)
Length and distance (III)
Recognise metre (m)
Time (II)
Tell time to the nearest minute (analog/digital)
Money (II)
Recognise the notes in circulation in Hong Kong
3-D shapes (II)
Recognise the concept of faces of a 3-D shape
Angles
Recognise the concept of angles
Directions and positions (II)
Recognise the four main directions: east (E), south (S), west (W), north (N)
Inquiry and investigation
Through various activities, discover and construct knowledge; improve ability to inquire, communicate, reason, and conceptualise math concepts
Time-recording and timing devices
Recognise time-recording and timing devices in modern and ancient times
Block charts
Recognise block charts
Basic computation
Divisibility tests, prime factorization, GCD/LCM, and mixed operations with integers, fractions, and decimals
View NotesDirected numbers
Understanding positive and negative numbers, comparing magnitudes, and performing operations with directed numbers
View NotesApproximate values and numerical estimation
Rounding to significant figures, place values, decimal places, and estimation strategies
View NotesRational and irrational numbers
Understanding nth roots, rational/irrational numbers, and operations with quadratic surds
View NotesUsing percentages
Solving problems involving percentage changes, discount, profit/loss, and compound interest
View NotesRates, ratios and proportions
Understanding and applying rates, ratios, and direct/inverse proportions in real-life contexts
View NotesAlgebraic expressions
Representing phrases algebraically, working with sequences, and introducing function concepts
View NotesLinear equations in one unknown
Formulating and solving linear equations to solve word problems
View NotesLinear equations in two unknowns
Graphing linear equations and solving simultaneous equations using various methods
View NotesLaws of integral indices
Understanding and applying laws of indices in algebraic expressions and equations
View NotesPolynomials
Operations with polynomials including addition, subtraction, multiplication, and division
View NotesIdentities
Working with algebraic identities and factorization techniques
View NotesFormulae
Manipulating and using formulae to solve mathematical and real-life problems
View NotesLinear inequalities in one unknown
Solving and representing linear inequalities on number lines
View NotesErrors in measurement
Understanding absolute and relative errors in measurements and calculations
View NotesArc lengths and areas of sectors
Calculating arc lengths and areas of sectors using appropriate formulae
View Notes3-D figures
Understanding properties of three-dimensional shapes and their representations
View NotesMensuration
Calculating areas, volumes, and surface areas of various geometric shapes
View NotesAngles and parallel lines
Properties of angles formed by parallel lines and transversals
View NotesPolygons
Properties of polygons including angle sums and regular polygons
View NotesCongruent triangles
Understanding and applying conditions for triangle congruence
View NotesSimilar triangles
Understanding similarity in triangles and applying proportional relationships
View NotesQuadrilaterals
Properties of various quadrilaterals including parallelograms, rhombuses, and trapezoids
View NotesCentres of triangles
Properties of centers of triangles including centroid, orthocenter, and circumcenter
View NotesPythagoras' theorem
Applications of the Pythagorean theorem in right triangles and coordinate geometry
View NotesRectangular coordinate system
Plotting points, calculating distances, and finding midpoints on coordinate planes
View NotesTrigonometry
Introduction to trigonometric ratios and their applications in right triangles
View NotesOrganisation of data
Methods of data collection and organizing data for statistical analysis
View NotesPresentation of data
Creating and interpreting various statistical diagrams and charts
View NotesMeasures of central tendency
Calculating and interpreting mean, median, and mode from data sets
View NotesProbability
Concepts of probability, likelihood, and calculating probabilities of events
View NotesInquiry and investigation
Applying mathematical concepts to solve open-ended problems through investigation
View NotesQuadratic equations in one unknown
Solving quadratic equations using various methods
View NotesFunctions and graphs
Understanding and graphing various functions
View NotesExponential and logarithmic functions
Working with exponential and logarithmic functions and their applications
View NotesMore about polynomials
Advanced topics in polynomial functions including factor and remainder theorems
View NotesMore about equations
Solving cubic and other higher-degree equations
View NotesVariations
Understanding direct, inverse, and joint variations and their applications
View NotesArithmetic and geometric sequences and their summations
Working with arithmetic and geometric sequences and series
View NotesInequalities and linear programming
Solving systems of inequalities and linear programming problems
View NotesMore about graphs of functions
Transformations of functions and their graphs
View NotesEquations of straight lines
Working with different forms of linear equations and their geometric interpretations
View NotesBasic properties of circles
Understanding fundamental properties of circles and related theorems
View NotesEquations of circles
Working with standard and general forms of circle equations
View NotesMore about trigonometry
Advanced trigonometric concepts, identities, and applications
View NotesPermutations and combinations
Counting techniques using permutations and combinations
View NotesMore about probability
Advanced probability concepts including conditional probability
View NotesMeasures of dispersion
Calculating and interpreting variance, standard deviation, and other dispersion measures
View NotesUses and abuses of statistics
Critically evaluating statistical methods and presentations
View NotesFurther applications
Applying mathematical concepts to real-world problems and scenarios
View NotesInquiry and investigation
Open-ended exploration of mathematical concepts through investigation
View NotesBinomial expansion
Expanding binomial expressions using the binomial theorem
View NotesExponential and logarithmic functions
Advanced applications of exponential and logarithmic functions
View NotesDerivative of a function
Introduction to differentiation and basic differentiation rules
View NotesDifferentiation of a function
Techniques for differentiating various types of functions
View NotesSecond derivative
Understanding and applications of second-order derivatives
View NotesApplications of differentiation
Using derivatives for optimization, related rates, and curve sketching
View NotesIndefinite integration and its applications
Basic integration techniques and their applications
View NotesDefinite integration and its applications
Evaluating and applying definite integrals to area problems
View NotesApproximation of definite integrals using the trapezoidal rule
Numerical methods for approximating definite integrals
View NotesConditional probability and Bayes' theorem
Advanced probability concepts including Bayes' theorem
View NotesDiscrete random variables
Understanding and working with discrete random variables
View NotesProbability distribution, expectation and variance
Analyzing probability distributions and their properties
View NotesThe binomial distribution
Understanding and applying the binomial probability distribution
View NotesThe Poisson distribution
Understanding and applying the Poisson probability distribution
View NotesApplications of the binomial and the Poisson distributions
Practical applications of binomial and Poisson distributions
View NotesBasic definition and properties of normal distribution
Understanding the normal distribution and its key properties
View NotesStandardisation of a normal variable and use of the standard normal table
Working with z-scores and the standard normal distribution
View NotesApplications of the normal distribution
Practical applications of the normal distribution in various contexts
View NotesSampling distribution and point estimates
Introduction to sampling distributions and statistical estimation
View NotesConfidence interval for a population mean
Constructing and interpreting confidence intervals
View NotesInquiry and investigation
Open-ended exploration of M1 concepts through investigation
View NotesOdd and even functions
Understanding and working with odd and even functions
View NotesMathematical induction
Using the principle of mathematical induction for mathematical proofs
View NotesThe binomial theorem
Advanced applications of the binomial theorem
View NotesMore about trigonometric functions
Advanced topics in trigonometry including addition formulas
View NotesIntroduction to e
Understanding the number e and its role in mathematics
View NotesDifferentiation
Advanced differentiation techniques and applications
View NotesApplications of differentiation
Advanced applications of derivatives in optimization and analysis
View NotesIndefinite integration and its applications
Advanced integration techniques and applications
View NotesDefinite integration
Advanced techniques for evaluating definite integrals
View NotesApplications of definite integration
Using definite integrals to solve area, volume, and other applied problems
View NotesDeterminants
Understanding and calculating determinants and their applications
View NotesSystems of linear equations
Solving systems of linear equations using matrix methods
View NotesIntroduction to vectors
Vector operations and representations in two and three dimensions
View NotesScalar product and vector product
Understanding and applying dot and cross products of vectors
View NotesApplications of vectors
Using vectors to solve geometric and physical problems
View NotesInquiry and investigation
Open-ended exploration of M2 concepts through investigation
View Notes